Free Printable Factorize Polynomials

1.

Factorise 3x²+12x

a)

3x(x+4)

b)

3(x²+4)

2.

Factorise: 6m² + 16m

a)

2(3m² + 8m)

b)

2m(3m + 8)

c)

2m(3m - 8m)

d)

not factorable

3.

Factorise 2x+8

a)

2(x+4)

b)

2(x+8)

4.

Factorise 6x+4

a)

2(x+4)

b)

2(3x+2)

5.

Factor x^3 - 2x^2 + x

a)

x(x - 1)(x + 1)

b)

x(x - 1)^2

c)

(x^2 - 1)(x + 1)

d)

(x^2 - 1)(x - 1)

6.

Factor 2x^3 + x^2 - 2x - 1

a)

2x(x - 1)(x + 1)

b)

x(x - 1)^2

c)

(x^2 + 1)(2x + 1)

d)

(2x + 1)(x - 1)(x + 1)

7.

Write the factors of the polynomial from the zeros in the graph.

Remember to look at your roots, multiplicity, and end behavior!!

Use your notes!

a)

(x - 3) (x + 2) (x + 5)

b)

(x - 5) (x - 2) (x + 3)

c)

(x + 3) (x + 2) (x + 5)

d)

(x - 3) (x - 2) (x - 5)

8.

Complete the steps to solve $-x^4+14x^2-45=0$ by factoring.

Choose from the below words

$-\left(x^4-14x^2+45\right)=0$

$-\left(x^4-14x^2-45\right)=0$

$-\left(x^2-9\right)\left(x^2-5\right)=0$

$x=\pm3,\ \pm\sqrt[]{5}$

$x=\pm3,\ \pm\sqrt[]{5}i$

9.

Factor by grouping to find all real solutions to the equation $16x^3-48x^2-x+3$ .

Step 1 - factor out GCF's: (a) (x-3) (b) (x-3)

Step 2 - "commons & leftovers" : (x-3) (c)

Step 3 - factor difference of squares: (x-3) (d)

Step 4 - Solve: (e)

Choose from the below words

$16x^2$

$-1$

$\left(16x^2-1\right)$

$\left(4x+1\right)\left(4x-1\right)$

$x\ =3,\ \pm\frac{1}{4}$

$x=\pm3,\ \pm4$

$\left(8x+1\right)\left(2x-1\right)$

$\left(x+3\right)$

$+1$

10.

Write the factors of the polynomial from the zeros in the graph. Remember to look at your roots, multiplicity, and end behavior!! Use your notes!

a)

(x - 3) (x + 2) (x + 5)

b)

(x - 5) (x - 2) (x + 3)

c)

(x + 3) (x + 2) (x + 5)

d)

(x - 3) (x - 2) (x - 5)

11.

Which of the following option/s are techniques in factoring polynomials? Check all that applies.

a)

Factoring Perfect Square Trinomial

b)

Factoring by Grouping

c)

Common Monomial Factoring

d)

Factoring Differences of Two Squares

12.

What are the factors of the expression x² + 7x + 10?

a)

(x - 2)(x + 5)

b)

(x + 2)(x - 5)

c)

(x - 2)(x - 5)

d)

(x + 2)(x + 5)

13.

The process such as _________ is the decomposition of polynomial into a product of two or more polynomials.

a)

Factoring

b)

Rationalizing

c)

Counting

d)

Multiplying

14.

Factor the expression
$x^2-x-6$

a)

(x+2)(x-3)

b)

(x-2)(x+3)

c)

(x-2)(x-3)

d)

x(x-3)

15.

Comletely factorize the expression

12x - 9.

a)

4(3x + 3)

b)

3(4x + 3)

c)

4(x - 3)

d)

3(4x - 3)

16.

Completely factor the expression

8ax + 12a - 4az.

a)

4(2ax +3a - az)

b)

2a(4x + 6 - 2z)

c)

4a(2x + 3 - z)

d)

x(8a + 12a - 4az)

17.

ax + bx + cx = x(a + b + c) is an example of what factoring technique?

(a)

18.

Factor the perfect square trinomial

x² - 18x + 81

a)

(x - 9)(x + 9)

b)

(x - 3)(x + 9)

c)

(x + 9)(x + 9)

d)

(x - 9)(x - 9)

19.

Completely factorize the perfect square trinomial (9x² + 24x +16).

a)

(3x + 4)²

b)

(3x - 4)(3x + 4)

c)

(3x + 4)(3x - 4)

d)

(3x - 4)²

20.

Completely factor the polynomial expression 4x² - 25y².

a)

(5x - 2y)(5x + 2y)

b)

(2x - 5y)(2x + 5y)

c)

(xy - 5)(xy + 2)

d)

(xy + 5)(xy -2)

Factorize Polynomials

Total questions: 20

Worksheet time: 20mins

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