Q. 156 - Intermediate Algebra

Question

 Tommy factored $x^2-x-20$as $(x + 5)(x - 4).$Sara factored it as $(x + 4)(x - 5).$ Ernesto factored it as $(x - 5)(x - 4).$ Who is correct? Explain why the other two are wrong.

Step-by-Step Solution

Answer

The factors done by Sara's is correct.

Step 1. Given Information

Tommy, Ernesto and Sara factored quadratic polynomial $x^2-x-20.$

We need to identify who is correct.

Step 2. Tommy's work

Tommy did as $x^2-x-20=\left(x+5\right)\left(x-4\right)$

The factors done by Tommy is incorrect because sum of $5 and -4$ is wrong.

It should be $-1.$

Step 3. Sara's work

$x^2-x-20=\left(x+4\right)\left(x-5\right)$

These factors are correct because the sum of $4 and -5$is $-1.$

The product is also correct because $4\times -5=-20$ 

Step 4. Ernesto's work

$x^2-x-20=\left(x-5\right)\left(x-4\right)$

The factors are incorrect because the sum of $-5 and -4 is -9.$

It should be $-1.$