# Polynomial functions

• May 10th 2009, 06:17 PM
flwer_13
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)
• May 11th 2009, 12:03 PM
SENTINEL4
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) = $x^2$-6x = $x^2$-6x+9-9 = ( $x^2$-6x+9)-9 = $(x-3)^2$-9
• May 11th 2009, 02:57 PM
pickslides
Quote:

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

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

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

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

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

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

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

You must group like terms.
• May 12th 2009, 05:57 AM
stapel
Quote:

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. (Wink)

Quote:

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.

Quote:

Originally Posted by flwer_13
3.f(x) = x(x-6)

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