Which of the following is the correct factorization of the polynomial below?
x³-15
A.) (x+3)(x-5)
B.) (x-3)(x+5)
C.) (x+3)(x²-4x+5)
D.) The polynomial is irreducible

Step-by-step explanation:

(x+3)(x-5)

= x²-5x+3x-15 = x²-2x-15

But the given polynomial x³-15

So it is not the correct factorization.

Again, (x-3)(x+5)

= x²+2x-15

But the given polynomial x³-15

So it is not the correct factorization.

Again , (x+3)(x²-4x+5)

= x³-4x²+5x+3x²-12x+15

= x³-x²-7x+15

But the given polynomial x³-15

So it is not the correct factorization.

So , optionD is the correct answer

the polynomial is a perfect square trinomial of the form a^2-2ab+b^2:

option a. true

step-by-step explanation:

9x^2-12x+4

comparing with the form a^2-2ab+b^2

1.) a^2=9x^2

solving for a: square root both sides of the equation:

sqrt(a^2)=sqrt(9x^2)

a=sqrt(9) sqrt(x^2)

a=3x

2.) b^2=4

solving for b: square root both sides of the equation:

sqrt(b^2)=sqrt(4)

b=2

to be a perfet square trinomial 2ab must be equal to 12x. let's check:

2ab = 2 (3x) (2)

2ab = 12x

correct