Free Printable Completing the Square

1.

What is a perfect square trinomial?

a)

a trinomial where every number is a perfect square

b)

a trinomial that has two different factors

c)

a trinomial that factors as one factor squared

d)

a trinomial with perfect square solutions

2.

Are all trinomials perfect square trinomials?

a)

yes

b)

no

3.

What do we call the process of adding in a new 'c' value to a binomial to create a perfect square trinomial?

a)

adding c

b)

factoring

c)

making things up

d)

completing the square

4.

For the binomial $x^2+bx$ , what 'c' value should we add to complete the square?

a)

$17$

b)

$-\frac{b}{2a}$

c)

$\frac{b}{2}$

d)

$\left(\frac{b}{2}\right)^2$

5.

By adding $\left(\frac{b}{2}\right)^2$ to the binomial $x^2+bx$ , how will the new perfect square trinomial $x^2+bx+\left(\frac{b}{2}\right)^2$ factor?

a)

$\left(x+\frac{b}{2}\right)^2$

b)

$\left(x+\frac{b}{2}\right)\left(x-\frac{b}{2}\right)$

c)

$\left(x+b\right)\left(x-b\right)$

d)

$\left(x+b\right)^2$

6.

What is the first step to completing the square on the left side of the equation $x^2+8x-9=0$ ?

a)

factor the left

b)

add 9

c)

subtract 9

d)

divide by 8

7.

After adding 9 to both sides of the previous equation, we have $x^2+8x=9$ . What is the next step to complete the square?

a)

subtract $8x$

b)

use square roots

c)

add $\left(\frac{b}{2}\right)^2$ to both sides of the equation

d)

add $\left(\frac{b}{2}\right)$ to both sides of the equation

8.

What is $\left(\frac{b}{2}\right)^2$ for the equation $x^2+8x=9$ ?

a)

4

b)

8

c)

12

d)

16

9.

After adding 16 to both sides of the equation $x^2+8x=9$ , what will the equation look like?

a)

$x^2+24x=25$

b)

$x^2+8x+16=9$

c)

$x^2+8x+16=25$

d)

$x^2+8x=25$

10.

Now that we've completed the square in the equation $x^2+8x+16=25$ , what is the next step we should use to solve the equation?

a)

subtract 16

b)

subtract 25

c)

factor the left hand side of the equation

d)

take square roots

11.

After factoring the left hand side of the equation $x^2+8x+16=25$ , what will the equation look like?

a)

$\left(x+4\right)^2=5$

b)

$\left(x+4\right)^2=25$

c)

$\left(x+8\right)^2=25$

d)

$\left(x+4\right)\left(x-4\right)=25$

12.

What operation do we use to cancel squares?

a)

square roots

b)

square roots

c)

square roots

d)

square roots

13.

How do we cancel the square in the equation $\left(x+4\right)^2=25$ ?

a)

square roots

b)

square roots

c)

square roots

d)

square roots

14.

When we use square roots to cancel the square in the equation $\left(x+4\right)^2=25$ , what will the equation look like?

a)

$x+4=0$

b)

$x+4=25^2$

c)

$x+4=\sqrt{25}$

d)

$x+4=\pm\sqrt{25}$

15.

What is the square root of 25?

a)

$\sqrt{25}=5$

b)

$\sqrt{25}=12.5$

c)

$\sqrt{25}=2.5$

d)

$\sqrt{25}=50$

16.

After seeing that the square root of 25 is 5, our previous equation becomes $x+4=\pm5$ , what is the next step we should use to solve for $x$ ?

a)

add 4

b)

subtract 4

c)

add 5

d)

subtract 5

17.

After subtracting 4 from both sides of the equation $x+4=\pm5$ , what will the equation look like?

a)

$x=\pm1$

b)

$x=4\pm5$

c)

$x=\pm9$

d)

$x=-4\pm5$

18.

What two solutions do we get from $x=-4\pm5$ ?

a)

1 and -9

b)

0 and 0

c)

9 and -1

d)

1 and -1

19.

We've just solved the equation $x^2+8x-9=0$ by completing the square and taking square roots. What other methods could we have use to solve?

a)

graphing

b)

factoring

c)

quadratic formula

d)

Photomath

20.

What is the first step to completing the square on the left side of the equation $x^2-16x-17=0$ ?

a)

factor the left

b)

add 17

c)

subtract 17

d)

divide by 2

21.

After adding 17 to both sides of the previous equation, we have $x^2-16x=17$ . What is the next step to complete the square?

a)

subtract $8x$

b)

use square roots

c)

add $\left(\frac{b}{2}\right)^2$ to both sides of the equation

d)

add $\left(\frac{b}{2}\right)$ to both sides of the equation

22.

What is $\left(\frac{b}{2}\right)^2$ for the equation $x^2-16x=17$ ?

a)

16

b)

-8

c)

32

d)

64

23.

After adding 64 to both sides of the equation $x^2-16x=17$ , what will the equation look like?

a)

$x^2+48x=17$

b)

$x^2-16x+64=9$

c)

$x^2-16x+64=81$

d)

$x^2+8x=25$

24.

After factoring the left hand side of the equation $x^2-16x+64=81$ , what will the equation look like?

a)

$\left(x+4\right)^2=81$

b)

$\left(x-8\right)^2=81$

c)

$\left(x+8\right)^2=81$

d)

$\left(x+8\right)\left(x-8\right)=81$

25.

When we use square roots to cancel the square in the equation $\left(x-8\right)^2=81$ , what will the equation look like?

a)

$x-8=0$

b)

$x-8=81^2$

c)

$x-8=\sqrt{81}$

d)

$x-8=\pm\sqrt{81}$

26.

After seeing that the square root of 81 is 9, our previous equation becomes $x-8=\pm9$ , what is the next step we should use to solve for $x$ ?

a)

subtract 8

b)

add 8

c)

add 9

d)

subtract 9

27.

What two solutions do we get from $x=8\pm9$ ?

a)

-1 and 17

b)

0 and 0

c)

8 and 9

d)

-72 and 72

28.

What value should we add to the following binomial to complete the square? $x^2+16x$

a)

8

b)

16

c)

32

d)

64

29.

What value should we add to the following binomial to complete the square? $x^2-16x$

a)

-8

b)

-64

c)

32

d)

64

30.

What value should we add to the following binomial to complete the square? $x^2+10x$

a)

25

b)

5

c)

10

d)

100

31.

How does the following perfect square trinomial factor?

$x^2+10x+25$

a)

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

b)

$\left(x+5\right)\left(x-5\right)$

c)

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

d)

$\left(x+10\right)^2$

32.

How does the following perfect square trinomial factor?

$x^2+8x+16$

a)

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

b)

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

c)

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

d)

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

33.

How does the following perfect square trinomial factor?

$x^2-16x+64$

a)

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

b)

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

c)

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

d)

$\left(x+32\right)^2$

34.

What is the next step to complete the square in the following equation?

$4x^2+24x=108$

a)

subtract 108

b)

divide by 4

c)

add 144 to both sides

d)

factor

35.

After dividing by 4 on the previous equation, we end up with

$x^2+6x=27$ . What is the next step to solve the equation?

a)

complete the square

b)

factor

c)

subtract 27

d)

divide by 6

36.

Complete the square and solve the equation

$x^2+6x=27$ . What are the solutions?

a)

$x=3,\ x=9$

b)

$x=6,\ x=-6$

c)

$x=3,\ x=-3$

d)

$x=3,\ x=-9$

37.

Solve the following equation by completing the square.

$3x^2-36x-39=0$

a)

$x=13,\ x=-1$

b)

$x=-13,\ x=1$

c)

$x=13,\ x=-13$

d)

$x=1,\ x=-1$

38.

After taking square roots to cancel the square, you may end up with the square root of a number that is not a perfect square. This does not mean that the square root does not simplify.

For example, simplify the following square root. (Note: 112=16x7)

$\sqrt{112}$

a)

$16\sqrt{7}$

b)

$7\sqrt{4}$

c)

$66$

d)

$4\sqrt{7}$

39.

How confident do you feel about completing the square?

a)

I'm totally confused.

b)

I feel okay, but I still struggle with it.

c)

I feel good, but I still struggle with it.

d)

I KNOW HOW TO COMPLETE THE SQUARE!

Completing the Square

Total questions: 39

Worksheet time: 3hrs 15mins

Similar Resources on Wayground