Question 1

What is the greatest common factor (GCF) of $$900$$ and $$700$$?

Accepted Answer

$$100$$

Question 2

Find the GCF of $$14m^5$$ and $$56m^7.$$

Accepted Answer

$$14m^5$$

Question 3

Factor out the GCF from the polynomial $$6x - 6.$$

Accepted Answer

$$6(x - 1)$$

Question 4

Factor out the GCF from $$5x^8y$$ - $$15x^6.$$

Accepted Answer

$$5x^6(x^2$y - 3)$

Question 5

Factor the four-term polynomial by grouping: $$5xy + 25x + 9y + 45.$$

Accepted Answer

$$(5x + 9)(y + 5)$$

Question 6

Factor the four-term polynomial by grouping: $$xy + 8x - 5y - 40.$$

Accepted Answer

$$(y + 8)(x - 5)$$

Question 7

Factor the trinomial $$x^2 - 8x + 7$ completely.

Accepted Answer

$$(x - 1)(x - 7)$$

Question 8

Factor the trinomial $$x^2 + x - 30$ completely.

Accepted Answer

$$(x - 5)(x + 6)$$

Question 9

Factor the trinomial $$x^2 - 6x - 55$ completely.

Accepted Answer

$$(x - 11)(x + 5)$$

Question 10

Factor the trinomial $$x^2 - x - 54$ completely.

Accepted Answer

prime

Question 11

Factor the trinomial $$7x^2 - 119x + 504$ completely.

Accepted Answer

$$7(x - 8)(x - 9)$$

Question 12

Factor the trinomial $$8x^2 + 17x - 21$ completely.

Accepted Answer

$$(x + 3)(8x - 7)$$

Question 13

Factor the trinomial $$x^2 - 8x + 64$ completely.

Accepted Answer

prime

Question 14

Factor the trinomial $$x^2 + 30x + 225$ completely.

Accepted Answer

$$(x + 15)^2$

Question 15

Factor the binomial $$z^2 - 64$ completely.

Accepted Answer

$$(z + 8)(z - 8)$$

Question 16

Factor the binomial $$49x^2 - 36$ completely.

Accepted Answer

$$(7x + 6)(7x - 6)$$

Question 17

Solve the equation $$(x - 3)(x + 5) = 0.$$

Accepted Answer

$$3, -5$$

Question 18

Solve the equation $$x^2 + 5x - 66 = 0$.

Accepted Answer

$$-11, 6$$

Question 19

Solve the equation $$x^2 - 10x = -24$.

Accepted Answer

$$6, 4$$

Question 20

A triangle is 8 cm wider than it is tall. The area is $$280\ \mathrm{cm}^2. $$What is the width (length of the base)? (Use the formula $$A = \frac{1}{2}bh$$ where $$b = h + 8.)$$

Accepted Answer

$$28\ \mathrm{cm}$$

Solving for the Base of a Triangle Given Area and Relationship to Height

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