Page 534 - Algebra 1

Reading Math
In the polynomial
5bx3 + 5bx2 - 60bx, the coefficient of x3 and x2
is 5. The coefficient of x is -60.
b. 5bx3 + 5bx2 - 60bx
SOLUTION
The GCF is 5bx.
5bx3 + 5bx2 - 60bx
5bx(x2 + x - 12) Factor out the GCF.
Find two numbers that have a product of -12 and a sum of 1. 4 · -3 = -12 and 4 + (-3) = 1
5bx(x2 +x-12)=5bx(x+4)(x-3) So,5bx3 +5bx2 -60bx=5bx(x+4)(x-3).
Rearrange the terms, if necessary, before factoring so that the polynomial is in standard form.
Rearranging Terms Before Factoring
Factor completely.
-105k - 14pk + 7p2k
SOLUTION
Before factoring, write the polynomial in standard form.
-105k - 14pk + 7p2k = 7p2k - 14pk - 105k
7k(p2 - 2p - 15) Factor out the GCF, 7k.
Find two numbers that have a product of -15 and a sum of -2.
-5 · 3 = -15; -5 + 3 = -2
7k(p2 -2p-15)=7k(p+3)(p-5)
So, 7p2k - 14pk - 105k = 7k(p + 3)(p - 5).
Application: Golf
The height of a golf ball hit from an elevated tee 40 meters above the hole is -5t2 + 35t + 40, where t represents time. Factor the expression completely.
SOLUTION
The GCF of the terms is 5 and the leading coefficient is negative, so factor out -5, which is -1 · 5.
-5t2 + 35t + 40
-5(t2 - 7t - 8) Factor out the GCF and -1.
Find two numbers that have a product of -8 and a sum of -7. 1 · -8 = -8 and (1) + (-8) = -7
-5(t2 -7t-8)=-5(t+1)(t-8) So,-5t2 +35t+40=-5(t+1)(t-8).
Example
4
Hint
A polynomial is in standard form when the terms are ordered from greatest to least degree.
Example
5
Math Reasoning
Verify Show that
-5(t + 1)(t - 8) is equal to -5t2 + 35t + 40.
Lesson 79 519