Factor each polynomial?

Question

Factor each polynomial

b^2 + 5b – 24

v^2 – 22v – 75

Answer 1

b^2+5b-24
=b^2+8b-3b-24
=b(b+8)-3(b+8)
(b+8)(b-3)

v^2-25v+3v-75
v(v-25)+3(v-25)
(v_25)(v+3)

Answer 2

b^2 + 5b – 24
(b+8)(b-3)

v^2 – 22v – 75
(v-25)(v+3)

Answer 3

b^2 + 5b - 24 = (b - 3)(b + 8)

v^2 - 22v - 75 = (v - 25)(v + 3)

Answer 4

b² + 5b - 24

(b + 8)(b - 3)

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Check

FOIL method

(b + 8)(b - 3) = b² + 8b - 3b - 24= b² + 5b - 24

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v² - 22v - 75

(v - 25)(v + 3)

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Check

FOIL Method

v - 25)(v + 3) = v² -25v + 3b - 75 = v² - 22v - 75

Answer 5

factor x^2 + 5x - 24

we need to get something like:

(ax+c)(bx+d)
to reach that we should develop the above to get:
abx^2 + adx + bcx + cd = abx^2 +(ad + bc) x + cd

coefficient of x^2 is 1 so ab = 1
then x^2 + (c + d)x + cd
c+d = 5 and cd = -24 so c=8 and d = -3

finally we will have (x+8)(x-3)


x^2 - 22x - 75
c + d = -22 c=-25 and d=3
cd = -75

(x-25)(x+3)

Answer 6

Yes. Multiplication is commutative, like addition, meaning the order in which it is done is not important. 2+ 3 and 3 + 2 are both same. 2 x 4 and 4 x 2 are same as well. Similarly, (a-2) x (a+2) is the same as (a+2) x (a-2)