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Chapter 7: Q 7.78 (page 846)

Factor:6g2+19g-20

Short Answer

Expert verified

The factorization of6g2+19g-20is(g+4)(6g-5)

Step by step solution

01

Step 1. Given information

Given expression is6g2+19g-20

02

Step 2. Find the product of a×c

a脳c=6脳(-20)=-120

03

Step 3. Find the last terms of the binomials.

Find the numbers that multiply to -120and add to 19

Factors of -120Sum of factors
24, -524 + (-5) = 19
04

Step 4. Factorization

Use 24and -5as the last terms of the binomials.

6g2+4g-5g-20=6g(g+4)-5(g+4)=(g+4)(6g-5)

05

Step 5. Check

(g+4)(6g-5)=6g2+24g-5g-20=6g2+19g-20

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Most popular questions from this chapter

Watermelon drop A springtime tradition at the University of California San Diego is the Watermelon Drop, where a watermelon is dropped from the seventh story of Urey Hall.

(a) The binomial -16t2+80 gives the height of the watermelon t seconds after it is dropped. Factor the greatest common factor from this binomial.

(b) If the watermelon is thrown down with initial velocity 8 feet per second, its height after t seconds is given by the trinomial-16t2-8t+80.Completely factor this trinomial.

Solve:

(y-2)2=0

Factor Differences of Squares

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A rectangular sign has an area of 30square feet. The length of the sign is one foot more than the width. Find the length and width of the sign.

In the following exercises, factor completely.

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