Quiz about Total Factoring Review

Question 1

Factor by using GCF:
8n³ + 2n²

Accepted Answer

2n²(4n + 1)

Answer

2n2(4n-1)

Answer

n2(8n+2)

Answer

3n(4n+1)

Question 2

8r³ + 16r²

Accepted Answer

8r²(r + 2)

Answer

4r²(2r + 4)

Answer

8(r³ + r²)

Answer

4(r³ + 2r²)

Question 3

Factor by using GCF:
10x² + 15x-5

Accepted Answer

5(2x²+3x-1)

Answer

25(10x³+45x-15)

Answer

5(2x³ + 3x²-x)

Answer

x(10x³+15x-5)

Question 4

Factor
5ab²c¹¹ + 2bc⁵

Accepted Answer

bc⁵(5abc⁶ + 2)

Answer

bc⁵(5ab²c⁶ + 2b)

Answer

b²c⁵(5bc⁶ + 2)

Answer

c4(5a²b²c⁷+ 2bc)

Question 5

3x³+ 9x²- 15x

Accepted Answer

3x(x² + 3x - 5)

Answer

x(3x² + 9x - 15)

Answer

3x(x² - 9x + 15)

Answer

x(3x² -9x + 15)

Question 6

Factor

x²- 2x - 15

Accepted Answer

(x-5)(x+3)

Answer

(x+5)(x-3)

Answer

(x-5)(x-3)

Answer

(x+5)(x+3)

Question 7

Factor

x² + 7x + 12

Accepted Answer

(x + 3)(x + 4)

Answer

(x + 2)(x + 10)

Answer

(x + 4)(x + 5)

Answer

(x + 4)(x + 6)

Question 8

Factor x²+ 7x - 30

Accepted Answer

(x + 10)(x - 3)

Answer

(x + 10)(x - 7)

Answer

(x - 10)(x + 3)

Answer

(x + 10)(x + 3)

Question 9

Factor
x²+ 9x - 36

Accepted Answer

(x + 12)(x - 3)

Answer

(x + 9)(x - 4)

Answer

(x - 12)(x + 3)

Answer

(x - 9)(x - 4)

Question 10

Factor completely:

y² - 7y + 12

Accepted Answer

(y - 3) (y - 4)

Answer

(y + 3) (y - 4)

Answer

(y + 3) (y + 4)

Answer

(y - 2) (y - 6)

Question 11

Factor

x² - 5x + 3

Accepted Answer

prime

Answer

(x + 3) (x + 1)

Answer

(x - 3) (x - 1)

Answer

(x - 3) (x + 1)

Question 12

Factor

b²+ 8b + 7

Accepted Answer

(b + 7)(b +1)

Answer

(b + 4)(b + 3)

Answer

(b + 6)(b + 1)

Answer

prime

Question 13

Factor
x²-16x + 48

Accepted Answer

(x - 12)(x - 4)

Answer

(x + 6)(x - 8)

Answer

(x + 12)(x - 4)

Answer

(x -16)(x - 3)

Question 14

Which is a factor of $$x^2-11x+24?$$

Accepted Answer

$$\left(x-3\right)$$

Answer

$$\left(x+3\right)$$

Answer

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

Answer

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

Question 15

What is the factored form of the expression? $$x^2-16$$

Accepted Answer

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

Answer

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

Answer

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

Answer

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

Question 16

Which shows the polynomial $$8x^2+16x+8$$ completely factored?

Accepted Answer

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

Answer

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

Answer

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

Answer

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

Question 17

If $$\left(x-3\right)$$ is a factor of $$x^2+x-12$$ , then the other factor is?

Accepted Answer

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

Answer

$$\left(4x-3\right)$$

Answer

$$\left(3x-4\right)$$

Answer

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

Question 18

Written in factored form, the trinomial $$2y^2+26y+80$$ is equivalent to:

Accepted Answer

$$2\left(y+5\right)\left(y+8\right)$$

Answer

$$2\left(y-5\right)\left(y-8\right)$$

Answer

$$\left(2y+5\right)\left(y+8\right)$$

Answer

$$\left(y+5\right)\left(2y+16\right)$$

Question 19

When factored completely, $$x^3-9x$$ is equivalent to:

Accepted Answer

$$x\left(x+3\right)\left(x-3\right)$$

Answer

$$x\left(x-3\right)$$

Answer

$$\left(x+3\right)\left(x-3\right)$$

Answer

$$x\left(x+3\right)$$

Question 20

Which expression is the factored form of $$2x^2-2x-12?$$

Accepted Answer

$$2\left(x+2\right)\left(x-3\right)$$

Answer

$$2\left(x+6\right)\left(x-1\right)$$

Answer

$$2\left(x+3\right)\left(x-2\right)$$

Answer

$$2\left(x+1\right)\left(x-6\right)$$

Question 21

If $$\left(x-3\right)$$ and $$\left(x+7\right)$$ are the factors of the trinomial $$x^2+bx-21$$ , what is the value of b?

Accepted Answer

$$4$$

Answer

$$-3$$

Answer

$$-4$$

Answer

$$7$$

Question 22

If $$\left(2x-3\right)$$ and $$\left(x+5\right)$$ are multiplied to form the trinomial $$ax^2+bx+c$$ , what is the value of b?

Accepted Answer

$$7$$

Answer

$$-15$$

Answer

$$2$$

Answer

$$4$$

Question 23

$$3x^2+14x+11$$

Accepted Answer

$$\left(x+1\right)\left(3x+11\right)$$

Answer

$$\left(x+11\right)\left(3x+1\right)$$

Answer

$$\left(x+33\right)\left(3x+1\right)$$

Answer

$$\left(x+1\right)\left(3x+33\right)$$

Question 24

$$5x^2+2x-7$$

Accepted Answer

$$\left(5x+7\right)\left(x-1\right)$$

Answer

$$\left(5x-7\right)\left(x+1\right)$$

Answer

$$\left(5x+1\right)\left(x-7\right)$$

Answer

$$\left(5x-1\right)\left(x+7\right)$$

Question 25

$$7x^2+16x+4$$

Accepted Answer

$$\left(x+2\right)\left(7x+2\right)$$

Answer

$$\left(x-2\right)\left(7x-2\right)$$

Answer

$$\left(x+4\right)\left(7x+1\right)$$

Answer

$$\left(x+1\right)\left(7x+4\right)$$

Question 26

$$4x^2+41x+10$$

Accepted Answer

$$\left(x+10\right)\left(4x+1\right)$$

Answer

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

Answer

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

Answer

$$\left(2x+1\right)\left(2x+10\right)$$

Question 27

$$9x^2+30x+25$$

Accepted Answer

$$\left(3x+5\right)^2$$

Answer

$$\left(3x+25\right)\left(3x+1\right)$$

Answer

$$\left(x+5\right)\left(9x+5\right)$$

Answer

$$\left(x+1\right)\left(9x+25\right)$$

Question 28

$$9x^2+34x+25$$

Accepted Answer

$$\left(x+1\right)\left(9x+25\right)$$

Answer

$$\left(3x+5\right)^2$$

Answer

$$\left(3x+25\right)\left(x+1\right)$$

Answer

$$\left(x+25\right)\left(9x+1\right)$$

Question 29

$$15x^2+4x-4$$

Accepted Answer

$$\left(3x+2\right)\left(5x-2\right)$$

Answer

PRIME

Answer

$$\left(x-1\right)\left(15x+4\right)$$

Answer

$$\left(3x-1\right)\left(5x+4\right)$$

Question 30

Factor: $$x^2-121$$

Accepted Answer

$$\left(x+11\right)\left(x-11\right)$$

Answer

$$\left(x-11\right)^2$$

Answer

$$\left(x-60.5\right)\left(x+60.5\right)$$

Answer

$$\left(x+11\right)^2$$

Question 31

$$k^2-225$$ Factor:

Accepted Answer

$$\left(k\ +15\right)\left(k\ -15\right)$$

Answer

$$\left(k-15\right)^2$$

Answer

$$\left(k\ -25\right)^2$$

Answer

$$\left(k\ +10\right)\left(k\ -10\right)$$

Question 32

$$16x^2-81$$ Factor:

Accepted Answer

$$\left(4x+9\right)\left(4x-9\right)$$

Answer

$$\left(4x-9\right)^2$$

Answer

$$\left(2x-9\right)^2$$

Answer

$$\left(4x\ +\ 9\right)^2$$

Question 33

$$49x^2-144$$ Factor:

Accepted Answer

$$\left(7x-12\right)\left(7x+12\right)$$

Answer

$$\left(7x-12\right)^2$$

Answer

$$\left(7x+12\right)^2$$

Answer

$$\left(4x+11\right)^2$$

Question 34

Factor: $$x^2-18x+81$$

Accepted Answer

$$\left(x-9\right)^2$$

Answer

$$\left(x-9\right)\left(x+9\right)$$

Answer

$$\left(x+9\right)^2$$

Answer

$$\left(x+18\right)\left(x-18\right)$$

Question 35

Factor: $$16y^2-24y+9$$

Accepted Answer

$$\left(4y-3\right)^2$$

Answer

$$\left(4y+3\right)\left(4y-3\right)$$

Answer

$$\left(8y\ +\ 3\right)^2$$

Answer

$$\left(8y-3\right)^2$$

Question 36

Factor: $$49x^2-28x+4$$

Accepted Answer

$$\left(7x-2\right)^2$$

Answer

$$\left(7x+2\right)\left(7x-2\right)$$

Answer

$$\left(7x+2\right)^2$$

Answer

$$\left(3.5x-1\right)^2$$

Question 37

Factor: x² + 24x + 144

Accepted Answer

(x + 12)2

Answer

(x + 9)2

Answer

(x + 15)2

Answer

(x + 13)2

Question 38

Factor: x² - 30x + 225

Accepted Answer

(x - 15)2

Answer

(x + 15)2

Answer

(x + 25)2

Answer

(x - 25)2

Question 39

Factor 28x²+ 63x + 12x + 27 by grouping. Remember to look for common factors first.

Accepted Answer

(7x + 3)(4x + 9)

Answer

(4x + 3)(7x + 9)

Answer

(3x + 7)(4x + 9)

Answer

(9x + 4)(3x + 7)

Question 40

Factor 4y³+ y + 12y²+ 3 by grouping. Remember to look for common factors first.

Accepted Answer

(4y² + 1)(y + 3)

Answer

4y²(y + 3) + 3

Answer

4y³+ 12y²+ y + 3

Question 41

Factor p³- 3p² - 16p + 48

Accepted Answer

(p + 4) (p - 4) (p - 3)

Answer

p² ( p - 3) (p - 3)

Answer

(p² - 16) (p - 3)

Question 42

Decide if (x-3) is a factor of 3x³+10x²-x-12

Accepted Answer

No, it is not a factor

Answer

Yes, it is a factor

Question 43

To factor a trinomial by grouping, start by...

Accepted Answer

multiplying the "a" term times the "c" term and identifying the "b" term

Answer

saying a quick prayer

Answer

multiplying the "b" term times the "c" term and identifying the "a" term

Answer

multiplying the "x" term times the "y" term and identifying the "m" term

Question 44

Factor 5x² -13x + 6

Accepted Answer

(5x -3)(x-2)

Answer

(5x -2)(x-3)

Answer

(5x -13)(x-2)

Answer

(5x +3)(x+2)

Question 45

What are the factors of 7x² + 16x + 4?

Accepted Answer

(7x + 2) (x + 2)

Answer

(7x + 4) (x + 1

Answer

(7x - 2) (x - 2)

Answer

(7x - 2) (x + 2)

Question 46

5x²-27x+10

Accepted Answer

(5x-2)(x-5)

Answer

(5x+2)(x+5)

Answer

(5x+2)(x-5)

Answer

5(x+2)(x-5)

Question 47

7x2+12x+9

Accepted Answer

Prime

Answer

(7x-3)(x-3)

Answer

(7x+3)(x+3)

Answer

(7x+1)(x+9)

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