Expand and simplify. Express equations in standard form.

1. f(x) = -2(x-1)(x+4)(x+1)(x-3)

2. f(x) = (x+2)(x+1)(x+4)

3.f(x) = x(x-6)

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- May 10th 2009, 06:17 PMflwer_13Polynomial functions
Expand and simplify. Express equations in standard form.

1. f(x) = -2(x-1)(x+4)(x+1)(x-3)

2. f(x) = (x+2)(x+1)(x+4)

3.f(x) = x(x-6) - May 11th 2009, 12:03 PMSENTINEL4
I'm not sure what you have to do... They seem in a pretty simple form. Maybe you want something like the following..

3.f(x) = x(x-6)

x(x-6) = $\displaystyle x^2$-6x = $\displaystyle x^2$-6x+9-9 = ($\displaystyle x^2$-6x+9)-9 = $\displaystyle (x-3)^2$-9 - May 11th 2009, 02:57 PMpickslides
consider these general forms

$\displaystyle a(b+c) =ab+ac $

$\displaystyle (a+b)(c+d) =ac+ad+bc+bd $

$\displaystyle (a+b)(c+d)(e+f) =eac+ead+ebc+ebd+fac+fad+fbc+fbd$

$\displaystyle (a+b)(c+d)(e+f)(g+h) $

$\displaystyle =geac+gead+gebc+gebd+gfac+gfad+gfbc+gfbd$

$\displaystyle +heac+head+hebc+hebd+hfac+hfad+hfbc+hfbd$

You must group like terms. - May 12th 2009, 05:57 AMstapel
For this one, note first that (x - 1)(x + 1) = x^2 - 1. Then multiply this by the product of the other two linear factors, x^2 + x - 12. Multiply

*that*through by the -2, and you're done. (Wink)

You can**multiply the polynomial factors**in any order you like, but it might be quickest to multiply the x + 2 by the x + 4, and then multiply the result by the x + 1.

Take the x**through the parentheses**, and you're done. :D