# Factoring

> TSI Math Test Study Guide · Hightower High School P-TECH (2023)
>
> Source: [complete Markdown guide](../TSI-Math-Test-Study-Guide.md) · [original PDF](../1062198634-Hightower-TSI-Test-Study-Guide-v2-MATH.pdf)


#### I. Factor by GCF

#### 1. $4(x + 5) + 4x + 8$ Which of the following expression is equivalent to the expression above?

**A.** $4(2x + 7)$

**B.** $8(x + 4)$

**C.** $5x + 17$

**D.** $8x + 13$


#### 2. Which expression is not equal to $24y - 12$?

**A.** $2(12y - 12)$

**B.** $2(12y - 6)$

**C.** $4(6y - 3)$

**D.** $12(2y - 1)$


#### 3. Which below choice is equivalent to $24x - 18$?

**A.** $6(4x - 3)$

**B.** $6(3x-4)$

**C.** $4(6x - 4)$

**D.** $12x - 9$


#### 4. Which is equivalent to expression $6x + 9y$?

**A.** $6(x + 3y)$

**B.** $3(2x + 3y)$

**C.** $9x + 6y$

**D.** $6x - 9y$


#### 5. Which is equivalent to $12x + 8$?

**A.** $4(3x + 2)$

**B.** $4(3x + 8)$

**C.** $4(3x + 2x)$

**D.** \$20x$


#### 6. Which is equivalent to $3x - 36$?

**A.** $3x + 36$

**B.** $3 (12 - x)$

**C.** $3 (3x - 12)$

**D.** $3 (x - 12)$


#### 7. Which is equivalent to $12xy + 15x$?

**A.** $12xy - 15x$

**B.** $3x (4y + 5)$

**C.** $3x (5y + 4)$

**D.** $12yz + 15x$


#### 8. Which is equivalent to $2x + 4$?

**A.** $2 + 4x$

**B.** $x (2 + 4)$

**C.** $2 (x + 2)$

**D.** $4 (x + 2)$


#### 9. Which below is equivalent to $x^3 - 7x$?

**A.** $(x-7)(x^2 - x)$

**B.** $(x-7)(x^2 + 1)$

**C.** $x(x^2 - 7)$

**D.** $x^2 (x - 7)$


#### 10. Which is equivalent to $x^3 - 13x$?

**A.** $(x-7)(x^2 - 13)$

**B.** $(x-7)(x^2 + 13)$

**C.** $x(x^2 - 13)$

**D.** $x^2 (x - 13)$


#### 11. Which is equivalent to $5x(4x^3 + x - 7)$?

**A.** $20x^4 - 5x^2 - 35x$

**B.** $20x^4 + 5x^2 - 35x$

**C.** $20x^4 + x - 7$

**D.** $9x^4 + 6x^2 - 12x$


#### 12. Simplify: (xy + y) / y =

**A.** $x + 1$

**B.** $\frac{x(y+1)}{y}$

**C.** $x$

**D.** $x + y$


#### II. Factor Trinomials

#### 1. Which function is equivalent to $f(x) = x^2 - 3x - 18$?

**A.** $f(x) = (x + 3)(x - 6)$

**B.** $f(x) = (x + 6)(x - 3)$

**C.** $f(x) = (x + 6)(x + 3)$

**D.** $f(x) = (x - 3)(x + 6)$


#### 2. Which function is equivalent to $f(x) = x^2 - 7x + 10$?

**A.** $f(x) = (x - 3)(x - 7)$

**B.** $f(x) = (x + 7)(x + 3)$

**C.** $f(x) = (x - 2)(x - 5)$

**D.** $f(x) = (x - 2)(x + 5)$


#### 3. Which function is equivalent to $f(x) = x^2 - 7x - 8$?

**A.** $f(x) = (x - 1)(x - 8)$

**B.** $f(x) = (x + 1)(x + 8)$

**C.** $f(x) = (x - 1)(x + 8)$

**D.** $f(x) = (x + 1)(x - 8)$


#### 4. Which expression is a factor of $x^2 - 5x - 6$?

**A.** $x - 6$

**B.** $x + 6$

**C.** $x - 3$

**D.** $x - 1$


#### 5. Which of the following is factor of $u^2 + u - 2v^2$?

**A.** $(u - v)$

**B.** $(u - 2v)$

**C.** $(2u + v)$

**D.** $(u + v)$


#### 6. If $a^2 + n + 2b^2 = (a + b)(a + 2b)$, what is the value of n?

**A.** $a^2 b$

**B.** \$3a$

**C.** $ab + ba$

**D.** $3ab^2$


#### 7. Which function is equivalent to $f(x) = x^2 - 3x - 10$?

**A.** $f(x) = (x - 6)(2x + 4)$

**B.** $f(x) = (x - 5)(x + 2)$

**C.** $f(x) = (2x - 3)(x + 4)$

**D.** $f(x) = (x + 5)(x - 2)$


#### 8. Which function is equal to $f(x) = x^2 - 12x + 11$?

**A.** $f(x) = (x + 11)(x + 1)$

**B.** $f(x) = (x - 11)(x + 1)$

**C.** $f(x) = (x + 11)(x - 1)$

**D.** $f(x) = (x - 11)(x - 1)$


#### 9. Which expression is a factor of $2x^2 - x - 6$?

**A.** $3x + 2$

**B.** $2x - 3$

**C.** $x + 2$

**D.** $2x + 3$


#### 10. Which expression is a factor of $2x^2 - 3x - 5$?

**A.** $(2x - 1)$

**B.** $(x - 1)$

**C.** $(2x - 5)$

**D.** $(2x + 5)$


#### 11. Factor $x^2 - 7x + 10$

> Added practice choices; these options were not printed in the original PDF.

**A.** $(x + 5)(x + 2)$


**B.** $(x - 10)(x + 1)$


**C.** $(x - 5)(x - 2)$


**D.** $(x - 7)(x - 10)$


#### 12. Factor $x^2 + 6x + 8$

> Added practice choices; these options were not printed in the original PDF.

**A.** $(x + 2)(x + 4)$


**B.** $(x - 2)(x - 4)$


**C.** $(x + 6)(x + 2)$


**D.** $(x - 6)(x - 2)$


#### 13. Factor $2x^2 - 14x + 16$?

> Added practice choices; these options were not printed in the original PDF.

**A.** $2(x - 2)(x - 4)$


**B.** $2(x^2 - 7x - 8)$


**C.** $(2x - 4)(x - 4)$


**D.** $2(x^2 - 7x + 8)$


#### 14. Factor $2x^2 + 5x - 12$

> Added practice choices; these options were not printed in the original PDF.

**A.** $(2x + 3)(x - 4)$


**B.** $(2x - 3)(x + 4)$


**C.** $(2x + 4)(x - 3)$


**D.** $(x - 3)(x + 4)$


#### III. Factor by Formulas

#### 1. Which function is equivalent to $f(x) = x^2 - 9$?

**A.** $f(x) = (x - 9)(x + 9)$

**B.** $f(x) = (9 - x)(9 + x)$

**C.** $f(x) = (x - 3)(x + 3)$

**D.** $f(x) = (3 - x)(3 + x)$


#### 2. Which expression is a factor of $x^2 - 36$?

**A.** $3x - 6$

**B.** $6 - x$

**C.** $9x - 36$

**D.** $x + 6$


#### 3. Which function is equivalent to $a^2 - 25$?

**A.** $(a - 25)(a + 25)$

**B.** $(a - 5)(a - 5)$

**C.** $(a + 5)(a - 5)$

**D.** $(a + 5)(a + 5)$


#### 4. Which expression is a factor of $9x^2 - 1$?

**A.** $(3x + 1)$

**B.** $(1 - 3x)$

**C.** $(x - 3)$

**D.** $(x + 3)$


#### 5. Which function is equivalent to $2k^2 - 18$?

**A.** $2(k - 3)(k - 3)$

**B.** $2(k + 3)(k + 3)$

**C.** $2(k + 3)(k - 3)$

**D.** $(2k + 3)(k - 3)$


#### 6. Which function is equivalent to $a^2 - b^2$?

**A.** $(a - b)(a + b)$

**B.** $(a - b)(a - b)$

**C.** $(a + b)(b - a)$

**D.** $(a + b)(a + b)$


#### 7. Which expression is a factor of $36x^2 - 1$?

**A.** $18x - 7$

**B.** $6x - 1$

**C.** $1 - 6x$

**D.** $6x - 7$


#### 8. Which function is equivalent to $a^2 - 25b^2$?

**A.** $(a - 25b)(a + 25b)$

**B.** $(a - 5b)(a - 5b)$

**C.** $(a + 5b)(a - 5b)$

**D.** $(a + 5b)(a + 5b)$


#### 9. Which expression is a factor of $81x^4 - 4t^2$?

**A.** $4x - 7$

**B.** $9x^2 - 2t$

**C.** $2x + 7$

**D.** $7 - 2x$


#### 10. Which is equivalent to $(13 + 2) (13 - 2)$?

**A.** $15^2 + 11^2$

**B.** $15^2 - 11^2$

**C.** $13^2 + 2^2$

**D.** $13^2 - 2^2$


#### 11. Factor $x^2 - 4$

> Added practice choices; these options were not printed in the original PDF.

**A.** $(x - 4)(x + 1)$


**B.** $(x - 2)(x + 2)$


**C.** $(x - 2)^2$


**D.** $(x + 4)(x - 1)$


#### 12. Factor $144 - 5x^2$

> Added practice choices; these options were not printed in the original PDF.

**A.** $(12 - 5x)(12 + 5x)$


**B.** $(144 - \sqrt{5x})(144 + \sqrt{5x})$


**C.** $(12 - 5x^2)(12 + 5x^2)$


**D.** $(12 - \sqrt{5x})(12 + \sqrt{5x})$


#### 13. Factor $196c^2 - 144$

> Added practice choices; these options were not printed in the original PDF.

**A.** $4(7c - 6)(7c + 6)$


**B.** $(14c - 12)(14c + 12)$


**C.** $4(14c - 12)(14c + 12)$


**D.** $(7c - 6)(7c + 6)$


#### 14. Factor $180k^2 - 5$

> Added practice choices; these options were not printed in the original PDF.

**A.** $5(6k - 1)(6k + 1)$


**B.** $(18k - 5)(10k + 1)$


**C.** $5(6k - 1)^2$


**D.** $(6k - 5)(6k + 1)$


#### 15. Factor $81x^4 - 4t^2$?

> Added practice choices; these options were not printed in the original PDF.

**A.** $(9x^2 - 4t)(9x^2 + 4t)$


**B.** $(81x^2 - 2t)(81x^2 + 2t)$


**C.** $(9x - 2t)(9x + 2t)$


**D.** $(9x^2 - 2t)(9x^2 + 2t)$


#### 16. Factor $a^2 - 25b^2$

> Added practice choices; these options were not printed in the original PDF.

**A.** $(a - 25b)(a + 25b)$


**B.** $(a - 5b)(a + 5b)$


**C.** $(a - 5b)^2$


**D.** $(a + 25b)(a - 25b)$