Question

3 is a zero of f(x)=x^3-x^2-7x+3. Express f(x) as a product of linear factors.

Answer 1

you need to divide the cubic by x-3

Answer 2

i would google long division of polynomials its not so easy to give examples in latex, and I cant use the draw option on this computer..

Answer 3

http://www.purplemath.com/modules/polydiv2.htm

Answer 4

that comes out to f(x)=x^2-2x-1. Then what? That's where I get lost.

Answer 5

now factor x^2-2x-1

Answer 6

your answer will be like this

(x-3)(x+a)(x+b) for some a and b

Answer 7

hmm u sure thats right?

Answer 8

Um I just saw that, one sec. Because that's not factorable

Answer 9

f(x)=x^2+2x-1

Answer 10

you have to factor using i or something?

Answer 11

-(-x+sqrt(2)-1)(x+sqrt(2)+1)

Answer 12

\(x^2+2x-1=0\iff (x+1)^2=1+1\iff x+1=\pm\sqrt{2}\iff x=\pm\sqrt{2}-1\)

Answer 13

\(x^2+2x-1=0\iff (x+1)^2=1+1\iff x+1=\pm\sqrt{2}\iff x\\=\pm\sqrt{2}-1\)

Answer 14

so we get \((x-(\sqrt{2}-1)(x-(-\sqrt{2}-1))\)

Answer 15

I factored by completing the square...

Answer 16

thus we get \((x-3)(x-\sqrt{2}+1)(x+\sqrt{2}+1)\)

Answer 17

how do you get " -(-x+sqrt(2)-1)(x+sqrt(2)+1)"? I completed the square for f(x)=x^2+2x-1 and got (x+1)^2-2