Question

1) Which is a binomial factor of 8x2 + 26x + 15?
A) x − 5
B) 2x − 5
C) 2x + 3
D) 4x + 3

2) Factor x2 + 5x - 24
A) (x + 8)(x - 3)
B) (x + 3)(x - 8)
C) (x + 6)(x + 4)
D) (x + 2)(x - 12)

3) Factor the polynomial. 8x2 - 50
A) 2(4x - 5)(x - 5)
B) 2(2x - 5)(2x - 5)
C) 2(2x + 5)(2x + 5)
D) 2(2x - 5)(2x + 5)

4)
Which binomial is a factor of the polynomial? 3x2 + 7x + 2
A) (x − 1)
B) (x − 2)
C) (x − 2)
D) (3x + 1)

5)
Solve. x2 − 5x = 14

A) x = 0, x = 5
B) x = 0, x = −5
C) x = 2, x = −7
D) x = 7, x = −2

6)
Factor x2 + 5x - 50

A) (x + 25)(x - 2)
B) (x - 5)(x + 10)
C) (x - 10)(x + 5)
D) (x + 2)(x - 25)

7)
Factor 16x2 + 24x + 9.

A) (4x + 3)2
B) (4x - 3)2
C) (4x + 2)2
D) (8x + 4.5)2

8) Factor Completely: 32x2 - 50

A) (4x - 5)(4x + 5)
B) 2(4x - 5)(4x + 5)
C) (4x - 25)(8x + 2)
D) 2(4x - 5)(4x - 5)

9)
Select one of the factors of the quadratic expression.
x2 + 7x - 18

A) (x + 2)
B) (x + 6)
C) (x - 2)
D) (x - 6)

10)
Select one of the factors of the quadratic expression.

x2 + 5x - 14

A) (x + 14)
B) (x + 2)
C) (x + 7)
D) (x - 3)

11)
Factor Completely: 25x2 - 64

A) 5(x - 8)(x + 8)
B) 5(x - 8)(x - 8)
C) (5x - 8)(5x + 8)
D) (25x - 1)(x + 64)

12) Factor Completely: x2 - 81

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

13) Solve the quadratic equation.

8x2 + 16x + 8 = 0

A) 1
B) -1
C) 1 and 8
D) 1 and -1

14) Solve the equation.
x2 − x − 12 = 0

A) x = 4
B) x = −3
C) x = −3 or x = 4
D) x = −4 or x = 3

15) Find the factors and zeros of 6x2 + 8x - 28 = 2x2 + 4.


A) 2(x + 4)(x + 2); {-4, -2}
B) 4(x + 4)(x - 2); {-4, 2}
C) 4(x - 4)(x + 2); {4, -2}
D) 4(x - 4)(x - 2); {4, 2}

16)
Factor completely:

6z2 + 18z

A) 24z3
B) 6z(z + 3)
C) z(6z +18)
D) 6(z2 + 3z)

Answer 1

Answer:

all work is shown and pictured

Answer 2

Following are the calculation to the given points:

For point 1:

$\bold{8x^2+26x+15}\\\\\bold{8x^2+(20+6)x+15}\\\\\bold{8x^2+20x+6x+15}\\\\\bold{4x(2x+5)+3(2x+5)}\\\\\bold{(2x+5)(4x+3)}$

Therefore, the answer is "Option D".

For point 2:

$\bold{x^2 + 5x - 24}\\\\\bold{x^2 + (8-3)x - 24}\\\\\bold{x^2 + 8x-3x - 24}\\\\\bold{x(x + 8)-3(x +8)}\\\\\bold{(x + 8) (x-3)}$

Therefore, the answer is "Option A".

For point 3:

$\bold{8x2 - 50}\\\\\bold{2(4x2 - 25)}\\\\\bold{2((2x)^2 - 5^2)}\\\\\therefore \ \ x^2-y^2=(x+y) (x-y)\\\\\bold{2((2x - 5)(2x+5)}$

Therefore, the answer is "Option D".

For point 4:

$\bold{3x^2 + 7x + 2}\\\\\bold{3x^2 +(6+1)x + 2}\\\\\bold{3x^2 +6x+1x + 2}\\\\\bold{3x(x +2)+1(x + 2)}\\\\\bold{(x +2) (3x+1)}$

Therefore, the answer is "Option D".

For point 5:

$\bold{x^2 - 5x = 14}\\\\\bold{x^2 - 5x -14= 0}\\\\\bold{x^2 - (7-2)x -14= 0}\\\\\bold{x^2 -7x+2x -14= 0}\\\\\bold{x(x -7)+2(x -7)= 0}\\\\\bold{(x -7) (x+2)= 0}\\\\\bold{x -7=0\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ x+2= 0}\\\\\bold{x =7\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ x= -2}$

Therefore, the answer is "Option D".

For point 6:

$\bold{x^2 + 5x - 50}\\\\\bold{x^2 + (10-5)x - 50}\\\\\bold{x^2 + 10x-5x - 50}\\\\\bold{x(x+ 10)-5(x +10)}\\\\\bold{(x+ 10)(x -5)}$

Therefore, the answer is "Option B".

For point 7:

$\bold{16x^2 + 24x + 9}\\\\\bold{16x^2 + (12+12)x + 9}\\\\\bold{16x^2 + 12x+12x + 9}\\\\\bold{4x(4x +3)+3(4x + 3)}\\\\\bold{(4x +3)(4x + 3)}\\\\\bold{(4x +3)^2}$

Therefore, the answer is "Option A".

For point 8:

$\bold{32x^2 - 50}\\\\\bold{2(16x^2 - 25)}\\\\\bold{2((4x)^2 - (5)^2)}\\\\\bold{2((4x-5)(4x+5))}$

Therefore, the answer is "Option B".

For point 9:

$\bold{x^2 + 7x - 18}\\\\\bold{x^2 + (9-2)x - 18}\\\\\bold{x^2 + 9x-2x - 18}\\\\\bold{x(x+ 9)-2(x +9)}\\\\\bold{(x+ 9)(x-2)}$

Therefore, the answer is "Option C".

For point 10:

$\bold{x^2 + 5x - 14}\\\\\bold{x^2 + (7-2)x - 14}\\\\\bold{x^2 + 7x-2x - 14}\\\\\bold{x(x+7)-2(x +7)}\\\\\bold{(x+7)(x -2)}$

Therefore, the answer is "Option C".

For point 11:

$\bold{25x^2 - 64}\\\\\bold{(5x)^2 - (8)^2}\\\\\bold{(5x-8)(5x+8)}$

Therefore, the answer is "Option C".

For point 12:

$\bold{x^2 - 81}\\\\\bold{x^2 - 9^2}\\\\\bold{(x - 9)(x+9)}$

Therefore, the answer is "Option A".

For point 13:

$\bold{8x^2 + 16x + 8 = 0}\\\\\bold{8(x^2 + 2x + 1) = 0}\\\\\bold{(x^2 + 2x + 1) = 0}\\\\\bold{(x^2 + x+x + 1) = 0}\\\\\bold{(x(x +1)1(x + 1)) = 0}\\\\\bold{(x +1)(x + 1) = 0}\\\\\bold{(x +1)^2 = 0}\\\\\bold{x +1 = 0}\\\\\bold{x=-1}$

Therefore, the answer is "Option B".

For point 14:

$\bold{x^2 -x -12 = 0}\\\\\bold{x^2 -(4-3)x -12 = 0}\\\\\bold{x^2 -4x+3x -12 = 0}\\\\\bold{x(x -4)+3(x -4) = 0}\\\\\bold{(x -4) (x+3) = 0}\\\\\bold{(x -4)=0\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ (x+3) = 0}\\\\\bold{x =4\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ x = -3}$

Therefore, the answer is "Option C".

For point 15:

$\bold{6x^2 + 8x - 28 = 2x^2 + 4}\\\\\bold{6x^2 + 8x - 28 - 2x^2 - 4=0}\\\\\bold{4x^2 + 8x - 32=0}\\\\\bold{4(x^2 + 2x - 8)=0}\\\\\bold{(x^2 + 2x - 8)=0}\\\\\bold{(x^2 + (4-2)x - 8)=0}\\\\\bold{(x^2 + 4x-2x - 8)=0}\\\\\bold{(x(x + 4)-2(x +4))=0}\\\\\bold{(x + 4)(x -2)=0}\\\\\bold{(x + 4)=0\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ (x -2)=0}\\\\\bold{x =-4\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ x =2}$

Therefore, the answer is "Option B".

For point 14:

$\bold{6z^2 + 18z}\\\\\bold{6z(z + 3)}$

Therefore, the answer is "Option B".

Learn more:

brainly.com/question/18877132