Question

Factor the polynomial. p^3 - 3p^2 + 5p - 15

Answer 1

\[\mathrm{p^3 - 3p^2 + 5p - 15=(p-3)(p^2+5)}\]

Answer 2

How did you come up with that?

Answer 3

because 3 is a root of p^3 - 3p^2 + 5p - 15

Answer 4

sorry it's been awhile since I've done these. what do you mean 3's a root.

Answer 5

p^3 - 3p^2 + 5p - 15


(p^3 - 3p^2) + 5p - 15

p^2 ( p - 3) + 5(p-3)

(p-3) (p^2+5)

Answer 6

\[\mathrm{P(x)=p^3 - 3p^2 + 5p - 15\\\textrm{3 is a root of P(x) if }P(3)=0}\\\]
So (p-3) is a factor of P(x)

Answer 7

can you guys help with one more? Solve by factoring or by finding a square root. 2x^2 -11x + 5 = 0

Answer 8

You can also sometimes think of the simple factors of 15. 15 = 3 * 5. And then figure the rest out. But it doesn't always work.

Answer 9

The most simple factors of 5 are 5 and 1 (5 = 5*1).

So you might be able to have (2x ? 1 ) ( x ? 5 ) Where the ? is a plus or minus.

Answer 10

got it. thanks. wasn't thinking right on that one.

Answer 11

\[\mathrm{2x^2 -11x + 5 = 0\\
2(x^2-\frac{11}{2}x+\frac{121}{16})-2\times\frac{121}{16}+5=0\\
2(x-\frac{11}{4})^2-\frac{81}{8}=0\\(x-\frac{11}{4})^2=\frac{81}{16}=(\frac{9}{4})^2\\x-\frac{11}{4}=\frac{9}{4}\\x=5}\]