Free Printable EXPLAIN: Factoring Quadratics (Leading Coefficient 1)

1.

Find two numbers that multiply to -40 and add to -6

a)

1, -40

b)

2, -20

c)

4, -10

d)

5, -8

2.

Find two numbers that multiply to -36 and add to 9.

a)

18, -2

b)

12, -3

c)

9, -4

d)

6, -6

3.

Write a + or a - sign in each box so the expressions on each side of the equal sign are equivalent.

a)

+,+

b)

+,-

c)

-, +

d)

-, -

4.

Write a + or a - sign in each box so the expressions on each side of the equal sign are equivalent.

a)

+,+

b)

+,-

c)

-, +

d)

-, -

5.

Write a + or a - sign in each box so the expressions on each side of the equal sign are equivalent.

a)

+,+

b)

+,-

c)

-, +

d)

-, -

6.

Write a + or a - sign in each box so the expressions on each side of the equal sign are equivalent.

a)

+,+

b)

+,-

c)

-, +

d)

-, -

7.

Match each quadratic expression in standard form with its equivalent expression in factored form.

a)

(x+5)(x+7)

b)

(x+5)(x-7)

c)

(x-5)(x+7)

d)

(x-5)(x-7)

8.

Match each quadratic expression in standard form with its equivalent expression in factored form.

a)

(x+5)(x+7)

b)

(x+5)(x-7)

c)

(x-5)(x+7)

d)

(x-5)(x-7)

9.

Match each quadratic expression in standard form with its equivalent expression in factored form.

a)

(x+5)(x+7)

b)

(x+5)(x-7)

c)

(x-5)(x+7)

d)

(x-5)(x-7)

10.

Match each quadratic expression in standard form with its equivalent expression in factored form.

a)

(x+5)(x+7)

b)

(x+5)(x-7)

c)

(x-5)(x+7)

d)

(x-5)(x-7)

11.

Which equation has exactly one solution?

a)

A

b)

B

c)

C

d)

D

12.

Multiply (x+2)(x+2). You can double distribute or use the diagram we learned!

a)

$x^2+4x+4$

b)

$x^2-4x+4$

c)

$x^2+4$

d)

$x^2-4$

13.

Multiply (x+2)(x-2). You can double distribute or use the diagram we learned!

a)

$x^2+4x+4$

b)

$x^2-4x+4$

c)

$x^2+4$

d)

$x^2-4$

14.

Multiply (x-2)(x-2). You can double distribute or use the diagram we learned!

a)

$x^2+4x+4$

b)

$x^2-4x+4$

c)

$x^2+4$

d)

$x^2-4$

15.

The greatest common factor is the largest number that divides evenly into the integers you are comparing. For example, the GCF of 8 and 20 is 4.

Find the GCF of 9 and 15.

a)

1

b)

3

c)

5

d)

9

e)

15

16.

Find the GCF of 12 and 30

a)

2

b)

3

c)

4

d)

5

e)

6

17.

Find the GCF of 2, 4, and 10

a)

1

b)

2

c)

4

d)

10

18.

When working with the GCF of variables with exponents, it's quite simple. it is ALWAYS the smallest of the exponents. You don't have to think about factors at all! For example, the GCF of $x^3\ and\ x^7\ is\ \ x^3$
Find the GCF of $x^{20}\ and\ x^{13}$

a)

$x^4$

b)

$x^5$

c)

$x^{13}$

d)

$x^{20}$

19.

When the variables have coefficients, you have to apply both rules. For coefficients, you are looking for the smallest number that divides evenly into ALL coefficient. For the variables, you are looking for the smallest exponent.
For example, in the quadratic $3x^4+6x^3-12x^2$ the GCF is $3x^2$ . Getting fancy. Factored form then would be $3x^2\left(x^2+2x-4\right)$
What is the GCF of $5x^3+15x^2-10x$ ?

a)

5

b)

5x

c)

$5x^2$

d)

$5x^3$

20.

$8x^3-4x^2+2x$ Last one here, can you find the GCF AND rewrite the following in factored form?

a)

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

b)

$2\left(4x^2-2x+x\right)$

c)

$2x\left(4x^2-2x+1\right)$

d)

$4x\left(2x^2-x+\frac{1}{2}\right)$

EXPLAIN: Factoring Quadratics (Leading Coefficient 1)

Total questions: 20

Worksheet time: 12mins

Similar Resources on Wayground