Free Printable Test 3 Review - Solving Quadratics

1.

Factor 4x²-9

a)

(4x-9)(4x+9)

b)

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

c)

2x-3

d)

(2x-4.5)(2x+4.5)

2.

Factor x²-25

a)

( x + 5 ) ( x - 5 )

b)

( x - 5 ) ( x - 5 )

c)

( x + 5 ) ( x + 5 )

d)

Prime

3.

Factor $p^{2\ }+24p\ +\ 144$

a)

$\left(p\ +\ 12\right)^2$

b)

$\left(p\ -12\right)^2$

c)

$\left(p\ -\ 12\right)\left(P\ +\ 12\right)$

d)

$\left(p\ -12\right)\left(p-12\right)$

4.

Factor: 9x²+6x +1

a)

(x-3)²

b)

(x+3)²

c)

(3x+1)²

d)

(3x-1)²

5.

7r³-8r²+42r-48

a)

(r²+6)(7r+8)

b)

(r²+6)(7r-8)

c)

(r²+6)(r²+8)

d)

(r²+6)(7r+6)

6.

30x³+15x²-18x-9

a)

(5x²-3)(6x+1)

b)

(5x²-3)(6x+3)

c)

3(5x²+3)(2x-1)

d)

3(5x²-3)(2x+1)

7.

Factor: x³+ 1

a)

(x + 1)³

b)

(x+1)(x²- x + 1)

c)

(x - 1) (x² + x - 1)

d)

(x + 1)(x² - 2x + 1)

8.

Factor: 27x³ + 8

a)

(3x + 2)(9x² - 6x + 4)

b)

(9x + 2)(3x² + 18x + 4)

c)

(3x²+4)(9x + 2)

d)

(27x + 8)(x² - 216x + 64)

9.

Fully Factor the Following
8x³-27

a)

(2x+3)(4x²-6x+9)

b)

(2x-3)(4x²+6x+9)

c)

(2x-3)(4x²+6x-9)

d)

(2x-3)(2x²+6x+9)

10.

Factor $x^2-7x+10$

a)

(x+5)(x+2)

b)

(x+5)(x-2)

c)

(x-5)(x-2)

d)

(x-5)(x+2)

11.

Solve the equation $x^2-10x\ =\ 0$

a)

10 and -10

b)

0 and 10

c)

0 and -10

d)

10

12.

What is the greatest common factor of the terms of the polynomial $-24x^3y^2+30x^2y^3+12x^2y^4$ ?

a)

$12x^2y^2$

b)

$-6x^2y^2$

c)

$30x^3y^4$

d)

xy

13.

Factor out the GCF from the terms of the polynomial 8x³ + 12x² - 4x?

a)

2x(4x² + 6x - 2)

b)

3x(2x² + 3x - 1)

c)

4x(2x² - 3x + 1)

d)

4x(2x² + 3x - 1)

14.

Factor Trinomial Completely:
2x² + 12x + 16

a)

2(x + 8)(x + 6)

b)

(2x + 4)(2x + 2)

c)

2(x + 2)(x + 4)

d)

2(x² + 6x + 8)

15.

Factor completely.
3x²- 9x -120

a)

3(x - 8)(x + 5)

b)

3(x + 8)(x - 5)

c)

(3x + 8)(x - 5)

d)

(3x - 8)(x + 5)

16.

Factor the trinomial.

a)

6(x-7)(x-1)

b)

(x-7)(x-1)

c)

(x-6)(x-1)

d)

6(x-6)(x-1)

17.

Factor to solve the equation $4x^2-5x-9=0$ .

a)

x=-1 or x=9/4

b)

x=1 or x=9/4

c)

x=2 or x=3

d)

x=-2 or x=-3

18.

Solve the following for x by using the Quadratic Formula

2x²+6x=7

a)

b)

c)

19.

Solve by the Square Root method: (x - 2) ² = 49

a)

9 or -5

b)

± 9

c)

± 5

d)

± 7

20.

Solve the quadratic using the square root method.

$-4x^2+84=4$

Simplify your answer completely.

a)

$x=\pm\sqrt[]{22}$

b)

$x=\pm\sqrt[]{20}$

c)

$x=\pm4\sqrt[]{5}$

d)

$x=\pm2\sqrt[]{5}$

e)

$No\ solution.$

21.

Solve to find the values of y :
$y^2=-9-9y$

a)

$\frac{-9\pm\sqrt{117}}{2}$

b)

$\frac{9\pm\sqrt{45}}{2}$

c)

$\frac{-9\pm3\sqrt{5}}{2}$

d)

$\frac{9\pm5\sqrt{3}}{2}$

22.

Solve using the quadratic formula.
2x² - 9x - 35 = 0

a)

x = 7/2, x = -6

b)

x = -5/2, x =5

c)

x = -3/7, x =6

d)

x = -5/2, x = 7

23.

$2x^2+2x+5=0$

a)

$\frac{-1\pm3i}{2}$

b)

$\frac{-1\pm i\sqrt{11}}{2}$

c)

$\frac{2\pm\sqrt{40}}{4}$

d)

$\frac{-1\pm i\sqrt{6}}{2}$

24.

Solve.

a)

no solution

b)

6

c)

3

d)

4

25.

Solve.

a)

8

b)

-8

c)

0

d)

no solution

Test 3 Review - Solving Quadratics

Total questions: 25

Worksheet time: 2hrs 55mins

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