Factor problems 18-20

18. which are the factors of the expression 3x2 + 23x – 8?
a (3x + 1)(x – 8)
b (3x – 8)(x + 1)
c (3x – 1)(x + 8)
d (3x – 1)(x – 8)

19. which of the following is equal to x2 + 4x + 3?
a (x + 1)(x + 3)
b (x + 2)(x + 2)
c (x + 4)(x – 1)
d (x – 4)(x – 1)

20. which shows 3x2 – 8x + 4 completely factored?
a (3x – 2)(x + 2)
b (3x + 4)(x – 1)
c (x + 4)(3x – 1)
d (3x – 2)(x – 2)

show all of your work

18. C (3x -1)(x +8)

19. A (x +1)(x +3)

20. D (3x -2)(x -2)

Step-by-step explanation:

Since you know how to multiply binomials, you can easily check any of the offered answers to see if they work.

(ax +b)(x +c) = ax² +(b+ac)x +bc

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18. All of the constants except for choice D multiply to give -8, so you must check the middle term:

A b+ac = 1-24 = -23 ≠ 23

B b+ac = -8+3 = -5 ≠ 23

C b+ac = -1+24 = 23 . . . . . this is the answer

D already eliminated because bc = 8 ≠ -8

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19. The only answer with constants that multiply to give +3 is A.

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20. The only answer with constants that multiply to give +4 is D.

x = ±sqrt(10)

step-by-step explanation:

5 - 2x² = -15

subtract 5 from each side

5-5 - 2x² = -15-5

-2x^2   = -20

divide by -2 on each side

-2x^2   /-2= -20/-2

x^2 =10

take the square root on each side

sqrt(x^2 )=±sqrt(10)

x = ±sqrt(10)

check:

5 - 2x² = -15

+sqrt(10)

5 - 2(sqrt(10))² = -15

5 -2(10) = -15

5 -20 = -15

-15 = -15

-sqrt(10)

5 - 2(-sqrt(10))² = -15

5 -2(10) = -15

5 -20 = -15

-15 = -15