# Thread: Factoring Polynomials

1. ## Factoring Polynomials

I have a test over factoring polynomials tomorrow. Most of it i have fairly well understood, but there's an extra credit section with problems we haven't discussed yet. I am not doing fantastic in math right now, so i could really use the bonus points. Can someone help explain them?

Factor Completely. (Bi) (Bi)

$\displaystyle 2x^2 - 7x - 4$

$\displaystyle 24x^2 + 47x - 2$

$\displaystyle 18c^4 - 3c^2 - 10$

$\displaystyle 16 - 9x + 15x^2$

Also, how can you determine in an answer in the format of (x + 1)(x - 2) whether it will be a +-, -+, ++, or -- answer?

2. $\displaystyle 2x^{2}-7x-4$

$\displaystyle (2x+1)(x-4)$

$\displaystyle x=-\frac{1}{2} , x=4$

$\displaystyle 15x^{2}-9x+16$

$\displaystyle b^{2}-4ac=<0$ (less than 0, no roots)

Also, how can you determine in an answer in the format of (x + 1)(x - 2) whether it will be a +-, -+, ++, or -- answer?
Example

$\displaystyle 2x^{2}-7x-4$

If the sign after '-7x' is negative, it means the signs within the two brackets will be different.
ie. (2x + 1)(x - 4)

If the sign was positive, it means the signs will be the same for both brackets. This sign used would be the sign after the squared term.
ie. $\displaystyle 12x^{2}-20x+3$
(2x - 3)(6x - 1)

3. Originally Posted by Forkmaster
I have a test over factoring polynomials tomorrow. Most of it i have fairly well understood, but there's an extra credit section with problems we haven't discussed yet. I am not doing fantastic in math right now, so i could really use the bonus points. Can someone help explain them?

Factor Completely. (Bi) (Bi)

$\displaystyle 2x^2 - 7x - 4$

$\displaystyle 24x^2 + 47x - 2$

$\displaystyle 18c^4 - 3c^2 - 10$

$\displaystyle 16 - 9x + 15x^2$

Also, how can you determine in an answer in the format of (x + 1)(x - 2) whether it will be a +-, -+, ++, or -- answer?
$\displaystyle 2x^2 - 7x - 4 = (2x +1)(x-4)$

$\displaystyle 24x^2 + 47x - 2 = (24x - 1)(x + 2)$

$\displaystyle 18c^4 - 3c^2 - 10 = (3c^2 + 2)(6c^2 - 5)$

$\displaystyle 16 - 9x + 15x^2$ cannot be factored.

And, to answer your final question, the way to tell ++ from -- is the middle term. Assuming the last term is positive: if the middle term is positive, then you have ++, and if the middle term is negative you have --. If the last term is negative, though, you just know that one of the roots will be positive and the other negative.

4. +- is the same as -+ because AB = BA

++ when A, B and C are positive

+- when A positive, C negative

-- when A positive, B negative, C positive.

2x^2 - 7x - 4 = (2x + 1)(x - 4)

24x^2 + 47x - 2 = (24x - 1)(x + 2)

18c^4 - 3c^2 - 10 = (6c^2 - 5)(3c^2 + 2)

15x^2 - 9x + 16 has no real roots because 81 - 4*15*16 < 0