Download Multiplying Polynomials

Multiplying Polynomials
Remember: (2x3y5)(-6x4y7) = - 12x7y12
3( x + 2 ) = 3x + 6
Multiplying a polynomial by a monomial is just distributing
3x(x2 + 5x - 7) = 3x3 + 15x2 - 21x
Multiplying a binomial by a binomial is really just double distributing
(x + 2)(x + 5)
Distribute the x over the second parentheses x2 + 5x
Distribute the 2 over the second parentheses
2x + 10
2
Combine like terms
x + 7x + 10
Some people memorize this as F.O.I.L.
First
(x
)(x
Outer
(x
)( + 5) = +5x
Inner
( + 2 )( x ) = +2x
Last
( + 2 )( + 5) = +10
) = x2
Multiplying a polynomial by a polynomial is usually easier to do if you set it
up like a regular multiplication of numbers problem. It’s actually easier, because
you don’t have to carry.
2x2 + 3x + 6
3x2 + 5x – 2
-----------------4x2 - 6x -12
3
10x +15x2 +30x
6x4 +9x3 +18x2
---------------------------------6x4 +19x3 +33x2 +24x -12
Special Cases
Middle signs flipped
(x + 2)(x – 2) = x2 - 2x + 2x - 4 = x2 – 4
Binomial squared
(x + 4)2 = ( x + 4 )(x + 4) = x2 + 4x + 4x + 16 = x2 +8x +16
(x – 3)2 = (x – 3 )( x – 3) = x2 – 3x – 3x + 9 = x2 – 6x + 9
Write these out and F.O.I.L. them or you’ll lose the middle term!
Multiplying Polynomial Functions
(f . g)(x) = f(x) . g(x)
If you are evaluating the product of functions, you can either:
multiply the functions and evaluate the answer for the given value
or evaluate each function separately and then multiply the answers.
f(x) = 2x + 6 and g(x) = 3x – 2 evaluate (f . g)(4)
you can either multiply f and g and get 6x2 + 14x – 12 and substitute 4 for x
6(4)2 + 14(4) – 12 = 6(16) + 56 – 12 = 96 + 56 – 12 = 152 – 12 = 140
Or you can find f(4) = 2(4) + 6 = 8 + 6 = 14
and g(4) = 3(4) – 2 = 12 – 2 = 10
and then multiply the answers (14)(10) = 140
Strange Birds
f(x) = 2x + 8 find f(x + 2)
f(x + 2) = 2(x + 2) + 8 = 2x + 4 + 8 = 2x + 12