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.

Short answer

The factors done by Sara's is correct.

Step-by-step solution

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 $5and-4$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 $4and-5$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 $-5and-4is-9.$

It should be$-1.$