X ^ 3 - 3x ^ 2 - 4x + 15 by x ^ 2 - 5x

`2``3``-3``-2`

Solution : When the given polynomial is divided by a linear polynomial then the remainder is constant.
Let the required number to be added be k.
Let `p(x)=x^(3)-3x^(2)+4x-15+kandg(x)=x-3`.
Then , `g(x)=0rArrx-3=0rArrx=3`.
By factor theorem , p (x) will be divisible by (x-3) if p (3) = 0.
Now , `p(3)=0rArr{3^(3)-3xx3^(2)+4xx3-15+k}=0`
`rArr(27-27+12-15+k)=0rArrk=3`.
Hence , the required number to be added is `3` .

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If Irene is N years old and Tom is twice as old as Irene, the algebraic formula to show how old Tom is would be 2 x N or 2N.

Incorrect answer. Please choose another answer.

7.John has B bats and buys C bats more. He then gives away D bats. Which of the following algebraic statements corretly shows how many bats John has left?

X ^ 3 - 3x ^ 2 - 4x + 15 by x ^ 2 - 5x

X ^ 3 - 3x ^ 2 - 4x + 15 by x ^ 2 - 5x

X ^ 3 - 3x ^ 2 - 4x + 15 by x ^ 2 - 5x

X ^ 3 - 3x ^ 2 - 4x + 15 by x ^ 2 - 5x

If John starts with B bats and buys C more bats, the total number of bats John has would be represented by the formula B + C.

When John gives D bats away, the sum of B + C would subtract D bats to determine how many he has left.

So, the formula is B + C - D.

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8.What is the representation algebraically of the cost of L feet of lumber at Y dollars per foot?

X ^ 3 - 3x ^ 2 - 4x + 15 by x ^ 2 - 5x

X ^ 3 - 3x ^ 2 - 4x + 15 by x ^ 2 - 5x

X ^ 3 - 3x ^ 2 - 4x + 15 by x ^ 2 - 5x

X ^ 3 - 3x ^ 2 - 4x + 15 by x ^ 2 - 5x

There are a variety of ways to show multiplication, L x Y.

LY
L · Y
(L)(Y)

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9.3x + 6x =

X ^ 3 - 3x ^ 2 - 4x + 15 by x ^ 2 - 5x

X ^ 3 - 3x ^ 2 - 4x + 15 by x ^ 2 - 5x

X ^ 3 - 3x ^ 2 - 4x + 15 by x ^ 2 - 5x

X ^ 3 - 3x ^ 2 - 4x + 15 by x ^ 2 - 5x

Incorrect answer. Please choose another answer.

10.5a + 2b - b + 4a =

X ^ 3 - 3x ^ 2 - 4x + 15 by x ^ 2 - 5x

X ^ 3 - 3x ^ 2 - 4x + 15 by x ^ 2 - 5x

X ^ 3 - 3x ^ 2 - 4x + 15 by x ^ 2 - 5x

X ^ 3 - 3x ^ 2 - 4x + 15 by x ^ 2 - 5x

5a + 2b - b + 4a =

5a + 4a + 2b - b =

9a + b

Incorrect answer. Please choose another answer.

11.Find the value of 3abc, where a = 2, b = 3 and c = 4.

X ^ 3 - 3x ^ 2 - 4x + 15 by x ^ 2 - 5x

X ^ 3 - 3x ^ 2 - 4x + 15 by x ^ 2 - 5x

X ^ 3 - 3x ^ 2 - 4x + 15 by x ^ 2 - 5x

X ^ 3 - 3x ^ 2 - 4x + 15 by x ^ 2 - 5x

If a = 2, b = 3 and c = 4,

3abc =

3(2)(3)(4) =

6 x 12 = 72

Incorrect answer. Please choose another answer.

12.The sum of a certain number and 3 times the number is 40. What is the number?

X ^ 3 - 3x ^ 2 - 4x + 15 by x ^ 2 - 5x

X ^ 3 - 3x ^ 2 - 4x + 15 by x ^ 2 - 5x

X ^ 3 - 3x ^ 2 - 4x + 15 by x ^ 2 - 5x

X ^ 3 - 3x ^ 2 - 4x + 15 by x ^ 2 - 5x

8 + 3(8) = 32

9 + 3(9) = 36

10 + 3(10) = 40

11 + 3(11) = 44

Incorrect answer. Please choose another answer.

13.Joe is lending Frank $500 and Frank has 4 years to pay it back. Joe is charging 6% interest. Frank wants to determine how much interest he'll pay over the 4 years.  He sets up the formula, interest (i) = loan amount (l) x rate (r) x time (t).  Find i.

X ^ 3 - 3x ^ 2 - 4x + 15 by x ^ 2 - 5x

X ^ 3 - 3x ^ 2 - 4x + 15 by x ^ 2 - 5x

X ^ 3 - 3x ^ 2 - 4x + 15 by x ^ 2 - 5x

X ^ 3 - 3x ^ 2 - 4x + 15 by x ^ 2 - 5x

i = l x r x t

l = $500, r = 6% and t = 4 years

l = $500 x .06 x 4

i = $30 x 4

i = $120

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14.In V = 2m - 3, V is which of the following?

X ^ 3 - 3x ^ 2 - 4x + 15 by x ^ 2 - 5x

X ^ 3 - 3x ^ 2 - 4x + 15 by x ^ 2 - 5x

X ^ 3 - 3x ^ 2 - 4x + 15 by x ^ 2 - 5x

X ^ 3 - 3x ^ 2 - 4x + 15 by x ^ 2 - 5x

A dependent variable is a variable that depends on one or more other variables. In this equation, V depends on the value of m.

An independent variable is a variable that can have its value chosen without considering the values of other variables.  In this equation, m is an independent variable.

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15.In B = 3 + 4w, 3 is which of the following?

X ^ 3 - 3x ^ 2 - 4x + 15 by x ^ 2 - 5x

X ^ 3 - 3x ^ 2 - 4x + 15 by x ^ 2 - 5x

X ^ 3 - 3x ^ 2 - 4x + 15 by x ^ 2 - 5x

X ^ 3 - 3x ^ 2 - 4x + 15 by x ^ 2 - 5x

A constant is a value that does not change. In this equation, 3 is a fixed number that will not change.

A coefficient is a number used to multiple a variable.  In this equation, 4 is a coefficient of the independent variable w.

Incorrect answer. Please choose another answer.

16.V = bdt. Solve the formula for d.

X ^ 3 - 3x ^ 2 - 4x + 15 by x ^ 2 - 5x

X ^ 3 - 3x ^ 2 - 4x + 15 by x ^ 2 - 5x

X ^ 3 - 3x ^ 2 - 4x + 15 by x ^ 2 - 5x

X ^ 3 - 3x ^ 2 - 4x + 15 by x ^ 2 - 5x

Incorrect answer. Please choose another answer.

17.B = 1hm.  Solve the formula for h.
         2

X ^ 3 - 3x ^ 2 - 4x + 15 by x ^ 2 - 5x

X ^ 3 - 3x ^ 2 - 4x + 15 by x ^ 2 - 5x

X ^ 3 - 3x ^ 2 - 4x + 15 by x ^ 2 - 5x

X ^ 3 - 3x ^ 2 - 4x + 15 by x ^ 2 - 5x

Incorrect answer. Please choose another answer.

18.The absolute value of -14 is 14.

X ^ 3 - 3x ^ 2 - 4x + 15 by x ^ 2 - 5x

X ^ 3 - 3x ^ 2 - 4x + 15 by x ^ 2 - 5x

The absolute value of a number, even a negative number, is a positive number.

Incorrect answer. Please choose another answer.

19.- 3 + (-14) =

X ^ 3 - 3x ^ 2 - 4x + 15 by x ^ 2 - 5x

X ^ 3 - 3x ^ 2 - 4x + 15 by x ^ 2 - 5x

X ^ 3 - 3x ^ 2 - 4x + 15 by x ^ 2 - 5x

X ^ 3 - 3x ^ 2 - 4x + 15 by x ^ 2 - 5x

- 3 + (-14) =

- 3 - 14 = - 17

Incorrect answer. Please choose another answer.

20.20 - (-6) =

X ^ 3 - 3x ^ 2 - 4x + 15 by x ^ 2 - 5x

X ^ 3 - 3x ^ 2 - 4x + 15 by x ^ 2 - 5x

X ^ 3 - 3x ^ 2 - 4x + 15 by x ^ 2 - 5x

X ^ 3 - 3x ^ 2 - 4x + 15 by x ^ 2 - 5x

Incorrect answer. Please choose another answer.

21.Add the following: 3x - 2y + 2y + 3z + 2z - 4x - 5y.

X ^ 3 - 3x ^ 2 - 4x + 15 by x ^ 2 - 5x

X ^ 3 - 3x ^ 2 - 4x + 15 by x ^ 2 - 5x

X ^ 3 - 3x ^ 2 - 4x + 15 by x ^ 2 - 5x

X ^ 3 - 3x ^ 2 - 4x + 15 by x ^ 2 - 5x

3x - 2y + 2y + 3z + 2z - 4x - 5y =

 3x - 4x - 2y - 5y + 2y + 3z + 2z =

-x - 5y + 5z

Incorrect answer. Please choose another answer.

22.6x - 10 = 4(x + 3). Solve for x.

X ^ 3 - 3x ^ 2 - 4x + 15 by x ^ 2 - 5x

X ^ 3 - 3x ^ 2 - 4x + 15 by x ^ 2 - 5x

X ^ 3 - 3x ^ 2 - 4x + 15 by x ^ 2 - 5x

X ^ 3 - 3x ^ 2 - 4x + 15 by x ^ 2 - 5x

6x - 10 = 4(x + 3)

6x - 10 = 4x + 12

6x = 4x + 22

2x = 22

x = 11

Incorrect answer. Please choose another answer.

23.x - 6 = 17. Solve for x.

X ^ 3 - 3x ^ 2 - 4x + 15 by x ^ 2 - 5x

X ^ 3 - 3x ^ 2 - 4x + 15 by x ^ 2 - 5x

X ^ 3 - 3x ^ 2 - 4x + 15 by x ^ 2 - 5x

X ^ 3 - 3x ^ 2 - 4x + 15 by x ^ 2 - 5x

x - 6 = 17

x = 17 + 6

x = 23

Incorrect answer. Please choose another answer.

24.Which of the following is not a grouping symbol?

X ^ 3 - 3x ^ 2 - 4x + 15 by x ^ 2 - 5x

X ^ 3 - 3x ^ 2 - 4x + 15 by x ^ 2 - 5x

X ^ 3 - 3x ^ 2 - 4x + 15 by x ^ 2 - 5x

X ^ 3 - 3x ^ 2 - 4x + 15 by x ^ 2 - 5x

Grouping symbols such as parentheses, brackets and braces in math will contain numbers, variables and operations. The grouping symbol tells you to do the operation first. An arrow, on the other hand, is an implicaiton notation to show that both sides of an notation are equal.

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25.A minus sign that precedes a parenthesis causes the sign of each term within the parentheses to change when the parentheses are removed.

X ^ 3 - 3x ^ 2 - 4x + 15 by x ^ 2 - 5x

X ^ 3 - 3x ^ 2 - 4x + 15 by x ^ 2 - 5x

If a minus sign appears outside of a parentheses, the minus sign changes the terms within the parentheses when the parentheses is removed. For example,

- (2x - 4y)

-2x + 4y

Incorrect answer. Please choose another answer.

26.If X equals 5, what is the value of 6X + 2X - X?

X ^ 3 - 3x ^ 2 - 4x + 15 by x ^ 2 - 5x

X ^ 3 - 3x ^ 2 - 4x + 15 by x ^ 2 - 5x

X ^ 3 - 3x ^ 2 - 4x + 15 by x ^ 2 - 5x

X ^ 3 - 3x ^ 2 - 4x + 15 by x ^ 2 - 5x

If x = 5,

6x + 2x - x =

6(5) + 2(5) - 5 =

30 + 10 - 5 = 35

Incorrect answer. Please choose another answer.

27.If 10 is separated into two parts, one of which is y, represent the second part.

X ^ 3 - 3x ^ 2 - 4x + 15 by x ^ 2 - 5x

X ^ 3 - 3x ^ 2 - 4x + 15 by x ^ 2 - 5x

X ^ 3 - 3x ^ 2 - 4x + 15 by x ^ 2 - 5x

X ^ 3 - 3x ^ 2 - 4x + 15 by x ^ 2 - 5x

If 10 is separated into two parts, one of which is y, the second part will be 10 - y.

Incorrect answer. Please choose another answer.

28.Find 3 consecutive numbers such that 3 times the first is equal to 8 more than the sum of the other two.

X ^ 3 - 3x ^ 2 - 4x + 15 by x ^ 2 - 5x

X ^ 3 - 3x ^ 2 - 4x + 15 by x ^ 2 - 5x

X ^ 3 - 3x ^ 2 - 4x + 15 by x ^ 2 - 5x

X ^ 3 - 3x ^ 2 - 4x + 15 by x ^ 2 - 5x

x = 1st number

x + 1 = 2nd number

x + 2 = 3rd number

3x = x + 1 + x + 2 + 8

3x = 2x + 11

x = 11

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29.The ratio of the height of two buildings is 7 to 5. The first building is 210 feet tall. How tall is the second building?

X ^ 3 - 3x ^ 2 - 4x + 15 by x ^ 2 - 5x

X ^ 3 - 3x ^ 2 - 4x + 15 by x ^ 2 - 5x

X ^ 3 - 3x ^ 2 - 4x + 15 by x ^ 2 - 5x

X ^ 3 - 3x ^ 2 - 4x + 15 by x ^ 2 - 5x

7/5 = 210/x

7x = 1,050

x = 150

Incorrect answer. Please choose another answer.

30.Factor the polynomial 5x - 15. 

X ^ 3 - 3x ^ 2 - 4x + 15 by x ^ 2 - 5x

X ^ 3 - 3x ^ 2 - 4x + 15 by x ^ 2 - 5x

X ^ 3 - 3x ^ 2 - 4x + 15 by x ^ 2 - 5x

X ^ 3 - 3x ^ 2 - 4x + 15 by x ^ 2 - 5x

When factoring, look to see what you can take out of a parentheses to put out front of it.  It is the opposite of distributing in polynomial expressions.

The first term 5x can be factored (5)(x).

The second term 15 can be factored (5)(3).

5 is the only factor common to both terms.  Divide out the 5 from the terms and move the common factor to the front of the parentheses.

What is the quotient 3x 2 4x 15 divided by x 3?

Summary: The quotient of (3x2 + 4x - 15) ÷ (x + 3) is 3x - 5.

What must be added to x 3 3x 2 4x 15 to obtain polynomial which is exactly divisible by x 3?

<br> Hence , the required number to be added is `3` .

What must be added to x3 3x2 4x 13 so that the result is exactly divisible by x 3?

What must be added to x3 – 3x2 + 4x – 13 to obtain a polynomial which is exactly divisible by x – 3? thus, -(-1) = 1 should be added to f(x) to make it exactly divisible by (x-3).

What is the remainder when x³ 3x² 4x 6 x 3?

Loved by our community. Step-by-step explanation: -6 is the remainder when x³+3x²+4x+6 is divided by x+3.