Question

1. Which of the following is the factored form of the expression: 3x2 – 4x?

A. x(3x - 4)
B. x(3 – 4x)
C. (3x -1) (x -1)
D. (3x +1)(x -1)

2. Which is a completely factored form of the expression: x2 + 21x +20 ?

A. (x + 5)(x + 4)
B. (x + 10)(x + 2)
C. (x + 20)(x + 1)
D. (x + 21)(x - 1)

3. Which expression is factored form of 4x2 -9?

A. 2(x - 3)2
B. (x - 3)2
C. 2(x + 3)(x - 3)
D. (2x + 3)(2x - 3)

4. Below are factored forms of the expression: 12x3 – 36x2 . Which expression has the greatest common factor as the first term?

A. 3x (4x2 – 12x)
B. 4x2(3x -9
C. 12x2(x – 3)
D. 12x(x2 - 3x)
5. Adele’s lawn has an area of (x2 -5x -6) square feet and a length of (x + 1) feet. What is the width of the lawn in feet?

A. (x -6)
B. (x +6)
C. (x2 -4x -5)
D. (x2 -6x -7)

6. The expression below represents the area, in square meters, of a rectangle:
X2 + 5x -24
Which of the following pairs of expressions could represent the length and width, in meters, of the rectangle?

A. (x – 3) and (x + 8)
B. (x – 4) and (x + 6)
C. (x – 6) and (x + 4)
D. (x – 8) and (x + 3)

7. What is the complete factorization of 32 – 8z2?

A. -8(2 + z)(2 –z)
B. 8(2 + z)(2 – z)
C. -8(2 + z)2
D. 8(2 – z)2

8. What is the greatest common factor of: 12x2 , 24x2y2 , and 46xy?

A. 4x
B. 3x
C. 6x
D. 2x
9. Which expression is equivalent to: 2x2 -3x -35?

A. (2x + 7)(x - 5)
B. (2x - 7) (x + 5)
C. (2x - 5)(x + 7)
D. (2x + 5)(x - 7)

10. What are the factors of 81x2 + 36x + 4?

A. (9x + 2)(x +2)
B. (9x +2)(9x +2)
C. (9x -2)(9x -2)
D. (9x +2)(9x -2)

11. The top of a rectangular table has an area of: 18x2+ 69x +60.
The width of the table is 3x + 4. What is the length of the table?
(Show proof by multiplying – show your work)

12. Simplify: (x2 +2x)(5x -3)
A. 11x2 -3
B. 6x3 -6x
C. 5x3 + 7x2 – 6x
D. 5x3 – 13x2 -6x

13. Factor by grouping: 30g5 +24g3h – 35g2h2 - 28h3 Show your work!



14. Which is the correct way to factor the polynomial : x2 -16?

A. (x -4)(x -4)
B. (x -4)(x +4)
C. (x +4)(x -2)(x +2)
D. Not factorable

15. The area of a square painting is: 81p2 + 90p +25. What is the length of one side? Prove by multiplication – show your work.

Answer 1

1. $3x^2-4x=x(3x-4)$ - A.

2. $x^2 + 21x +20=(x-x_1)(x-x_2)$

Find the roots:

$D=21^2-4\cdot 20=441-80=361, \ \sqrt{D}=19,\\ \\x_1=\dfrac{-21-19}{2}=-20, \ x_2=\dfrac{-21+19}{2}=-1$,

then

$x^2 + 21x +20=(x+20)(x+1)$ - C.

3. $4x^2 -9=(2x)^2-3^2=(2x-3)(2x+3)$ - D.

4. $12x^3-36x^2=12x^2(x-3)$ - C.

5. $x^2 -5x -6=(x-x_1)(x-x_2)$

Find the roots:

$D=(-5)^2-4\cdot (-6)=25+24=49, \ \sqrt{D}=7,\\ \\x_1=\dfrac{5-7}{2}=-1, \ x_2=\dfrac{5+7}{2}=6$,

then

$x^2 -5x -6=(x-6)(x+1)$ and the width of the lawn is x-6 - A.

6. Since $x^2 + 5x -24=(x+8)(x-3)$ the length and width are x+8 and x-3 - A.

7. $32 -8z^2=8(4-z^2)=8(2^2-z^2)=8(2-z)(2+z)$ - B.

8. $12x^2=2\cdot 2\cdot 3\cdot x\cdot x, \\24x^2y^2=2\cdot 2\cdot 2\cdot3\cdot x\cdot x\cdot y\cdot y , \\ 46xy=2\cdot 23\cdot x\cdot y$.

So the greatest common divisor is $2\cdot x=2x$ - D.

9. $2x^2 -3x -35=2(x-x_1)(x-x_2)$

Find the roots:

$D=(-3)^2-4\cdot (-35)\cdot 2=9+280=289, \ \sqrt{D}=17,\\ \\x_1=\dfrac{3-17}{2\cdot 2}=-\dfrac{7}{2}, \ x_2=\dfrac{3+17}{2\cdot 2}=5$,

then

$2x^2 -3x -35=2(x+\dfrac{7}{2})(x-5)=(2x+7)(x-5)$ - A.

10. $81x^2 + 36x + 4=(9x)^2+2\cdot 9x\cdot 2+2^2=(9x+2)^2$ - B.

11. $18x^2+ 69x +60=3(6x^2+23x+20)=3\cdot 6(x+\dfrac{5}{2})(x+\dfrac{4}{3})=(6x+15)(3x+4)$, the length is 6x+15.

12. $(x^2 +2x)(5x -3) =x^2\cdot 5x-x^2\cdot 3+2x\cdot 5x-2x\cdot 3=5x^3-3x^2+10x^2-6x=5x^3+7x^2-6x$ - C.

13. $30g^5 +24g^3h- 35g^2h^2 - 28h^3=(30g^5 +24g^3h)-(35g^2h^2+ 28h^3)=6g^3(5g^2+4h)-7h^2(5g^2+4h)=(5g^2+4h)(6g^3-7h^2)$.

14. $x^2 -16=(x-4)(x+4)$ - B.

15. $81p^2 + 90p +25=(9p)^2+2\cdot 9p\cdot 5+5^2=(9p+5)^2$, the length of one side is 9p+5.

Answer 2

Answer:

yes that is right

Step-by-step explanation:

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