To
multiply polynomials, follow these steps:
P(x) =
2x2 − 3 Q(x) = 2x3 − 3x2 +
4x
1.
Multiply all monomials from the first polynomial by all of the monomials in the
second polynomial.
P(x) ·
Q(x) = (2x2 − 3) · (2x3 − 3x2 + 4x) =
= 4x5
− 6x4 + 8x3 − 6x3 + 9x2 − 12x =
2.Add the
monomials of the same degree:
= 4x5
− 6x4 + 2x3 + 9x2 − 12x
The
multiplication of polynomials is another polynomial
whose degree is the sum of the
degrees of the polynomials.
Also,
polynomials can be multiplied as follows:
Example
Multiply the polynomials using two different methods:
P(x) = 3x4 + 5x3 − 2x + 3 and Q(x) = 2x2
− x + 3
P(x) · Q(x) = (3x4 + 5x3 − 2x + 3) · (2x2
− x + 3) =
= 6x6 − 3x5 + 9x4 + 10x5 −
5x4 + 15x3 −
− 4x3 + 2x2 − 6x + 6x2 − 3x + 9 =
= 6x6 + 7x5 + 4x4
+ 11x3 + 8x2 − 9x + 9
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