Thread: Polynomial 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)

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

Originally Posted by flwer_13

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)

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.

Originally Posted by flwer_13

Expand and simplify. Express equations in standard form.
1. f(x) = -2(x-1)(x+4)(x+1)(x-3)

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.

Originally Posted by flwer_13

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

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.

Originally Posted by flwer_13

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

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