Polynomials
Adding and Subtracting Polynomials
EXAMPLE
Add or subtract the following polynomials.
(a) (8x  4x + 6x) +
(3x
+ 5x
 9x + 8)
Solution
Combine like terms.
(8x  4x + 6x) + (3x + 5x  9x + 8)
= (8x + 3x) + ( 4x + 5x) + (6x 
9x) + 8
= 11x + x 3x + 8
(b) (4x + 6x  9x  12) +
(3x
+ 8x
 11x + 7)
Solution
Combining like terms as before yields .
4x + 3x  x  11x  5
(c) (2x  11x + 8)  (7x  6x + 2)
Solution
Distributing the minus sign yields
(2x
 11x + 8) + (7x + 6x  2)
= 5x  5x + 6
Multiplying Polynomials
The distributive property is also used to multiply
polynomials, along with the fact that For
example,
EXAMPLE
Multiply.
(a) 8x(6x  4)
Solution
8x(6x  4) = 8x(6x)  8x(4)
= 48x  32x
(b) (3p  2)(p + 5p  1)
Solution
(3p  2)(p + 5p  1)
= 3p(p + 5p  1) 2(p + 5p  1)
= 3p(p) + 3p(5p) + 3p(1) 2(p) 2(5p)
2(1)
= 3p + 15p 3p 2p  10p + 2
= 3p + 13p 13p + 2
(c) (x + 2)(x + 3)(x  4)
Solution
(x + 2)(x + 3)(x  4)
= [(x + 2)(x + 3)](x  4)
= (x + 2x + 3x + 6)(x  4)
= (x + 5x + 6)(x  4)
= x + 5x + 6x 4x  20x  24
= x + x  14x  24
