Page 393 - Algebra 1

Example
4
Multiplying a Binomial and a Trinomial
Find the product of (3x + 4)(x2 - 4x - 6). SOLUTION
Method1: UsetheDistributiveProperty. (3x+4)(x2 -4x-6)
Math Language
A trinomial is a polynomial with three terms.
3x(x2 - 4x - 6) = 3x3 - 12x2 - 18x
4(x2 -4x-6)=4x2 -16x-24
3x3 -12x2 -18x+4x2 -16x-24 3x3 - 8x2 - 34x - 24
Multiply the first term of the binomial by each term of the trinomial.
Multiplythesecondtermofthe binomial by each term of the trinomial.
Addtheproducts. Simplify.
Method2: Useverticalmultiplication.
Align like terms. Multiply each term in the first row by the terms in the
second row.
x2 -4x-6 3x + 4
Caution
Write polynomials in descending order before lining them up vertivcally.
4x2 -16x-24 +3x3 -12x2 -18x
4(x2 -4x-6) 3x(x2 -4x-6)
3x3 -8x2 -34x-24
Application: Area of Sandbox
Find the area of a rectangular sandbox that has a width of 2x2 + 5x - 6 inches and a length of 4x + 7 inches.
Example
5
378 Saxon Algebra 1
SOLUTION.
(4x + 7)(2x2 + 5x - 6)
4x(2x2 + 5x - 6) = 8x3 + 20x2 - 24x
7(2x2 + 5x - 6) = 14x2 + 35x - 42
8x3 + 20x2 - 24x + 14x2 + 35x - 42
8x3 + 34x2 + 11x - 42
The area of the sandbox is 8x3 + 34x2 + 11x - 42 in2.
Multiply length times width.
Multiply the first term of the binomial by each term of the trinomial.
Multiply the second term of the binomial by each term of the trinomial.
Add the products. Simplify.