Chapter 7: Q 133. (page 833)

Will factored $x^{2} - x - 20$ as $(x + 5) (x - 4)$ . Bill factored it as $(x + 4) (x - 5)$ . Phil factored it as $(x - 5) (x - 4)$ . Who is correct? Explain why the other two are wrong.

Short Answer

Expert verified

The correct factorization of $x^{2} - x - 20$ is, $(x - 5) (x + 4)$ .

Step by step solution

Step 1. Given information

Given expression is $x^{2} - x - 20$ .

Step 2. Find the last terms of the binomials

Write the factors as two binomials with the first terms $x$ .

$(x) (x)$

Find two numbers that multiply to $- 20$ and add to $- 1$ .

Factors of -20	Sum of factors
-1, 20	-1 + 20 = 19
-2, 10	-2 +10 = 8
-4, 5	-4 + 5 = 1
-5, 4	-5 + 4 = -1*
-10, 2	-10 + 2 =-8
-20, 1	-20+1 = -19

Step 3. Factorization

Use $- 5$ and $4$ as the last terms of the binomials.

$x^{2} - x - 20 = (x - 5) (x + 4)$

Step 4. Check

$(x - 5) (x + 4) = x^{2} - 5 x + 4 x - 20 = x^{2} - x - 20$

It has been proven that the correct value of $x^{2} - x - 20 = (x - 5) (x + 4)$ .

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Will factored $x^{2} - x - 20$ as $(x + 5) (x - 4)$ . Bill factored it as $(x + 4) (x - 5)$ . Phil factored it as $(x - 5) (x - 4)$ . Who is correct? Explain why the other two are wrong.

Short Answer

Step by step solution

Step 1. Given information

Step 2. Find the last terms of the binomials

Step 3. Factorization

Step 4. Check

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Will factored x2-x-20as (x+5)(x-4). Bill factored it as(x+4)(x-5). Phil factored it as (x-5)(x-4). Who is correct? Explain why the other two are wrong.

Short Answer

Step by step solution

Step 1. Given information

Step 2. Find the last terms of the binomials

Step 3. Factorization

Step 4. Check

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Mechanics Maths

Probability and Statistics

Theoretical and Mathematical Physics

Statistics

Applied Mathematics

Discrete Mathematics

Study anywhere. Anytime. Across all devices.

Will factored $x^{2} - x - 20$ as $(x + 5) (x - 4)$ . Bill factored it as $(x + 4) (x - 5)$ . Phil factored it as $(x - 5) (x - 4)$ . Who is correct? Explain why the other two are wrong.