Free Printable Operations on Polynomials

1.

Perform the division.

$\frac{4x^3-28x^2-29x-24}{x-8}$

a)

$4x^2+4x+3$

b)

$4x^2-4x-3$

c)

$4x^2+4x-3$

d)

$4x^2-4x+3$

2.

Use synthetic division to find the quotient and the remainder.

$\frac{x^5+7x^4+7x^3-13x^2+7x-13}{x+5}$

a)

Quotient

$x^4-2x^3+3x^2+2x-3$

Remainder $-2$

b)

Quotient

$x^4+2x^3-3x^2+2x-3$

Remainder $2$

c)

Quotient

$x^4-2x^3+3x^2-2x+3$

Remainder $2$

d)

Quotient

$x^4+2x^3-3x^2+2x-3$

Remainder

$-2$

3.

Use Long Division or Synthetic Division

$\frac{x^4+625}{x-5}$

a)

$x^3+5x^2+25x-125+\frac{1250}{x-5}$

b)

$x^3-5x^2+25x-125+\frac{1250}{x-5}$

c)

$x^3+5x^2-25x+125-\frac{1250}{x-5}$

d)

$x^3+5x^2+25x+125+\frac{1250}{x-5}$

4.

The 3rd term in the expression of $\left(7x+8\right)^3$ is

a)

$1344x$

b)

$-1344x$

c)

$1344x^2$

d)

$1434x$

5.

You divide two polynomials and obtain the result

$x^2-3+\frac{6}{x+1}$

What is the dividend?

a)

$x^3+x^2-3x+3$

b)

$x^3+x^2-3x-3$

c)

$x^3-x^2-3x+3$

d)

$x^3-x^2-3x-3$

6.

A box with an open top is formed by cutting squares out of the corners of a rectangular piece of cardboard and then folding up the sides. If x represents the length of the side of the square cut from each corner, and if the original piece of cardboard is 14 inches by 13 inches, what size square must be cut if the volume of the box is to be 168 cubic inches?

a)

$2in\ by\ 2in\ square$

b)

$3in\ by\ 3in\ square$

c)

$4in\ by\ 4in\ square$

d)

$5in\ by\ 5in\ square$

7.

Use synthetic division to find the function value.

$f\left(x\right)=x^3-2x^2-2x-1,\ find\ f\left(-3\right)$

a)

$-40$

b)

$40$

c)

$30$

d)

$-30$

8.

Use synthetic division to find the quotient and the remainder.

$\frac{6x^5-5x^4+x-4}{x+\frac{1}{2}}$

a)

$6x^4-8x^3+4x^2-2x+2$ $Remainder\ -5$

b)

$6x^4+8x^3-4x^2+2x+2$ $Remainder\ 5$

c)

$6x^4-8x^3+4x^2-2x+2$ $Remainder\ -2$

d)

$6x^4+8x^3-4x^2-2x+2$ $Remainder\ -2$

9.

Expand the expression using the Binomial Theorem. (Pascal's Triangle)

$\left(w-s\right)^6$ . What is the 4th term of the expression?

a)

$20w^3s^3$

b)

$-20w^3s^3$

c)

$-20w^4s^2$

d)

$-20w^2s^4$

10.

A rectangular patio has an area of $3m^3+19m^2+m\ -\ 63$ Find the length if the width is $3m+7$

a)

$m^2+4m-9$

b)

$m^2-4m+9$

c)

$m^2-4m-9$

d)

$m^2+4m+9$

11.

What is the remainder when (x¹³ + 10) is divided by (x + 1)?

a)

9

b)

10

c)

11

12.

The expression $x^3-kx^2+2x+5$ leaves a remainder of 2 when divided by $x-3$ . Find the value of k.

a)

4

b)

-4

c)

8

d)

-8

13.

What is the proper way to write the answer (Quotient) for the following problem?

a)

$2x^3-x^2-25x\ -\ 12$

b)

$2x^4-x^3-25x^2-12x+0$

c)

$2x^4+x^3-25x^2\ -\ 12x+0$

d)

$2x^4-x^3+25x^2-12x+0$

14.

What is the value of k such that $\left(x^3+kx^2-9x-36\right)\div\left(x+4\right)$ has a remainder of zero?

a)

$4$

b)

$-4$

c)

$\frac{1}{4}$

d)

$-\frac{1}{4}$

15.

A population of birds in a small county can be modeled by the polynomial $f\left(x\right)=x^3-57x^2+1162x+1094$ where x = 1 corresponds to July 1, x = 2 to July 2, and so on. For what days does f estimate the population to be 8550?

a)

July 11th

b)

July 12th

c)

July 13th

d)

July 14th

16.

Use long division to find the quotient and the remainder

$\frac{x^4+4x^3-4x^2-17x+30}{x^2+3x-2}$

a)

$\left(x^2+x+5\right)\ R\ 20$

b)

$\left(x^2-x+5\right)\ R\ 20$

c)

$\left(x^2-x-5\right)\ R\ -20$

d)

$\left(x^2+x-5\right)\ R\ 20$

17.

Use long division to find the quotient and the remainder

$\frac{8t^4+10t^3+20t^2+9t+30}{2t^2+4t+5}$

a)

$\left(4t^2-3t+6\right)\ R\ 0$

b)

$\left(4t^2+3t+6\right)\ R\ 12$

c)

$\left(4t^2-3t-6\right)\ R\ 2$

d)

$\left(4t^2-3t+6\right)\ R\ 12$

18.

The volume of a box is $3p^4+12p^3+12p^2$ The height is $p$ and the width is $p+2$ What is the length?

a)

$3p^2+6p$

b)

$3p^2-6p$

c)

$-3p^2+6p$

d)

$-3p^2-6p$

19.

If a submarine goes $2k^3+14k^2+10k-42$ miles in $2k+6$ hours, what is its rate of speed?

a)

$k^2-4k-7\ \frac{miles}{hour}$

b)

$k^2+4k-7\ \frac{miles}{hour}$

c)

$k^2+4k+7\ \frac{miles}{hour}$

d)

$k^2-4k+7\ \frac{miles}{hour}$

20.

What polynomial, when divided by $-4a^3x^5$ , yields $7a^6x^7-12x^4-6a$ as a quotient?

a)

$-28a^9x^{12}+48a^3x^9+24a^4x^5$

b)

$28a^9x^{12}+48a^3x^9+24a^4x^5$

c)

$-28a^9x^{12}-48a^3x^9+24a^4x^5$

d)

$-28a^9x^{12}+48a^3x^9-24a^4x^5$

21.

Determine whether $x-4$ is a factor of $f\left(x\right)=x^5-2x^3+4x+1$

a)

Yes, because the remainder is 0

b)

Yes, because the remainder is not equals to 0

c)

No, because the remainder is 0

d)

No, because the remainder is not equals 0

22.

Factor completely: $x^6-4x^5-45x^4$

a)

$x^4\left(x^2-4x-45\right)_{ }$

b)

$x^4\left(x-5\right)\left(x+9\right)$

c)

$x^4\left(x-5\right)\left(x-9\right)$

d)

$x^4\left(x+5\right)\left(x-9\right)$

23.

Factor completely:

$81p^4-625$

a)

$\left(9p^2-25\right)\left(9p^2+25\right)$

b)

$\left(9p^2+25\right)\left(9p^2+25\right)$

c)

$\left(3p-5\right)\left(3p+5\right)\left(9p^2+25\right)$

d)

$\left(3p-5\right)\left(3p+5\right)\left(3p+5\right)\left(3p+5\right)$

Operations on Polynomials

Total questions: 23

Worksheet time: 2hrs 42mins

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