Question

What is the completed factored form of 5x2 – 45?

(Points : 1)
5(x + 3)(x – 3)

5(x – 3)2

5(x2 – 9)

5(x + 9)(x – 9)

Answer 1

@StudyShark2000

Answer 2

5x² - 45
5(x² - 9)
5(x + 3)(x - 3)

Answer 3

@starlord6200

Answer 4

Sorry I was AFK!
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First thing to do is to use the rational root test. That is, since the coefficient in front of the greatest term is 1 and all the coefficients are integers, then any rational root of the equation will be an integer divisor of the last term. That means all the possible rational roots (meaning not involving square roots or cube roots or other such things) will be integer divisors of 45, or rather that 45 / n = an integer.

So all the possible roots are both positive and negative 1, 3, 5, 9, or 15. That narrows down our search quite a bit. Let's start with 5 first:
5^3 - 5(5^2) - 9(5) + 45 =? 0 Yes it does. Therefore 5 is a root of the equation, so we can use long division to factor out that 5:

..........x^2 +0 -9 +0
(x-5) | x^3 -5x^2 -9x +45
.........-x^3 +5x^2
.........0 0 +9x -45
.................................0 0

I hope you can follow what I did above for long division, especially since Y!A doesn't allow very good mathematical drawing. Anyway, that leaves us with x^2 - 9, which is a bit more obvious, and I'll assume that you can spot by eye that the other two roots are 3 and -3.

Therefore, x^3 - 5x^2 - 9x + 45 is equal to (x-5)(x-3)(x+3), QED.

(your answer is A, 5(x + 3)(x – 3) )

Answer 5

thanks for the help