Free Printable Division of Polynomials (Long Division/Synthetic Division)

1.

What is the quotient when $y^2-16$ divided by $y+4$ ?

a)

$y-4$

b)

$y+4$

c)

$y-8$

d)

$y+8$

2.

What is the remainder when $2x^2+11x+9$ is divided by $x+4$ ?

a)

3

b)

-3

c)

85

d)

-21

3.

Based from the given solution, is the remainder correct?

a)

Yes, because the sign of the terms of the minuend must be changed.

b)

Yes, because the sign of the terms of the subtrahend must be changed.

c)

No, because the remainder of a polynomial divided by another polynomial must always be zero.

d)

No, because the sign of the terms of the subtrahend must be changed and proceed to addition.

4.

In the given example, the term $4x-3$ is considered as the __________.

a)

Divisor

b)

Dividend

c)

Quotient

d)

Remainder

5.

In the given illustrated example, identify the dividend.

a)

$0$

b)

$x+6$

c)

$4x-3$

d)

$4x^2+21x-18$

6.

Consider the illustrated example. If the constant term of the dividend will be changed from -7 to 9, what will be the remainder?

a)

2

b)

16

c)

-2

d)

-16

7.

Solve for the quotient:

\left(5x^3-7x^2-20x+28\right)\div\left(5x-7\right)

.

a)

$x+4$

b)

$x^2-4$

c)

$x+2$

d)

$x^2+4$

8.

Which of the following statements is CORRECT in dividing polynomials?

a)

When a polynomial is divided by another polynomial, the remainder is always a constant.

b)

When a polynomial is divided by another polynomial, the result is always a binomial.

c)

When a polynomial is divided by another polynomial, the dividend should be written in standard form.

d)

When a polynomial is divided by another polynomial, long division is way better than using synthetic division.

9.

Which of the following polynomial will give a remainder of 0 when divided by $x-5$ ?

a)

$x^2+7x+10$

b)

$x^2-3x-10$

c)

$x^2+2x-15$

d)

$x^2+8x+15$

10.

Perform the indicated operation: $\left(3x^3+4x^2-3x-4\right)\div\left(x-1\right)$ .

a)

$3x^2-7x-4$

b)

$3x^2-7x+4$

c)

$3x^2+7x-4$

d)

$3x^2+7x+4$

11.

What polynomial must be divided by $x+3$ to get a quotient of $2x^2+x-5$ ?

a)

$2x^3+7x^2-2x-15$

b)

$2x^3-7x^2+2x-15$

c)

$2x^3+7x^2-2x+15$

d)

$2x^3-7x^2+2x+15$

12.

Eduard was asked by his teacher to divide the polynomial written on the board. Upon checking of his solution, the teacher said that it was incorrect. What could be the possible mistake of Eduard? Refer to his solution.

a)

The sign of the divisor must be positive not negative.

b)

The missing terms between $x^4$ and $16$ must be written as zero.

c)

The sum of $-16$ and $4$ must be $-20.$

d)

The power of the quotient must be $x^4$ not $x^3$ .

13.

Andrei was asked by his teacher to divide the polynomial using synthetic division. If you are Andrei, what must be the first thing you need to do?

a)

Write the polynomial in standard form.

b)

Change the sign of the divisor.

c)

Identify the missing terms of the polynomial.

d)

Divide the polynomial as it is.

14.

Using synthetic division, find the coefficient of $x^2$ when $x^4-5x^3-26x^2+20x-32$ is divided by $x-8$ .

a)

-1

b)

-2

c)

0

d)

4

15.

Using synthetic division, find the remainder when $x^4+4x^3+2x^2+5x+6$ is divided by $x+2$ .

a)

$23$

b)

$9$

c)

$-7$

d)

$-12$

16.

Divide $x^3-7x^2+11x+4$ by $\left(x-3\right)$ .

a)

$x^2-10x+41-\frac{119}{x-3}$

b)

$x^2+4x-1+\frac{7}{x-3}$

c)

$x^2-4x-1+\frac{1}{x-3}$

d)

$x^2-10x+41+\frac{119}{x-3}$

17.

Divide and simplify: $\frac{32x^{-2}y^4z^9}{4x^3y^{-5}z^7}\$

a)

$\frac{8y^9z^2}{x^5}$

b)

$\frac{8yz^2}{x}$

c)

$\frac{8x^5z^2}{y^9}$

d)

$\frac{8xy}{z^2}$

18.

Find the quotient when $x^3-17x+20x^2+15$ is divided by $x+5$ .

a)

$x^2-12x-40$

b)

$x^2-22x+130$

c)

$x^2+25x+108$

d)

$x^2-15x+58$

19.

Using synthetic division, find the quotient when $x^5-32$ is divided by $x-2$ .

a)

$x^4-16$

b)

$x^4+16$

c)

$x^4+2x^3+4x^2+8x+16$

d)

$x^2-2x^3+4x^2-8x+16$

20.

Divide $6x^3+11x^2-4x+15$ by $2x+5$ .

a)

$3x^2-2x-3$

b)

$3x^2-2x+3$

c)

$3x^2+2x+3$

d)

$3x^2-2x-3$

Division of Polynomials (Long Division/Synthetic Division)

Total questions: 20

Worksheet time: 35mins

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