SOLUTION: What is the completely factored form of {{{ f(x) = x^3 + 5x^2 + 4x - 6? }}} The equation is in the link here: https://prnt.sc/ldtqsv Is my answer correct? I'm not sure. I tri

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: What is the completely factored form of {{{ f(x) = x^3 + 5x^2 + 4x - 6? }}} The equation is in the link here: https://prnt.sc/ldtqsv Is my answer correct? I'm not sure. I tri      Log On


   

Question 1127897: What is the completely factored form of +f%28x%29+=+x%5E3+%2B+5x%5E2+%2B+4x+-+6%3F+
The equation is in the link here: https://prnt.sc/ldtqsv
Is my answer correct? I'm not sure. I tried many times to provide the answers through the formula system, so I decided to attach an image of the equation and answers provided.
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!

You have the correct answer. It is choice A. Nice work.

To prove that (x+3) is a factor, plug x = -3 into f(x) and you should get 0 as a result. This is using the remainder theorem.

If you were to divide f(x) over (x+3), you should get x^2+2x-2 as the quotient. Solve x^2+2x-2=0 through the quadratic formula and you should get the following:
x+=+%28-b%2Bsqrt%28b%5E2-4ac%29%29%2F%282a%29 or x+=+%28-b-sqrt%28b%5E2-4ac%29%29%2F%282a%29
x+=+%28-2%2Bsqrt%28%282%29%5E2-4%281%29%28-2%29%29%29%2F%282%281%29%29 or x+=+%28-2-sqrt%28%282%29%5E2-4%281%29%28-2%29%29%29%2F%282%281%29%29
x+=+%28-2%2Bsqrt%2812%29%29%2F%282%29 or x+=+%28-2-sqrt%2812%29%29%2F%282%29
x+=+%28-2%2Bsqrt%284%2A3%29%29%2F%282%29 or x+=+%28-2-sqrt%284%2A3%29%29%2F%282%29
x+=+%28-2%2Bsqrt%284%29%2Asqrt%283%29%29%2F%282%29 or x+=+%28-2-sqrt%284%29%2Asqrt%283%29%29%2F%282%29
x+=+%28-2%2B2%2Asqrt%283%29%29%2F%282%29 or x+=+%28-2-2%2Asqrt%283%29%29%2F%282%29
x+=+-1%2Bsqrt%283%29 or x+=+-1-sqrt%283%29
which help set up the other factor of the answer

Note: if x = k is a root, then x-k is a factor
So if x+=+-1%2Bsqrt%283%29 is a root, then x+-%28+-1%2Bsqrt%283%29%29 is a factor