Question

1. what are the factors of the expression x² + x - 20? 1) (x + 5) and (x + 4) 2) (x + 5) and (x - 4) 3) (x - 5) and (x + 4) 4) (x - 5) and (x - 4) 2) what are the factors of x² - 5x + 6? 1) (x + 2) and (x + 3) 2) (x - 2) and (x - 3) 3) (x + 6) and (x - 1) 4) (x - 6) and (x + 1)

Explanation:

Step1: Factorize $x^{2}+x - 20$

We need two numbers that multiply to - 20 and add up to 1. The numbers are 5 and - 4 since $5\times(-4)=-20$ and $5+( - 4)=1$. So $x^{2}+x - 20=(x + 5)(x - 4)$.

Step2: Factorize $x^{2}-5x + 6$

We need two numbers that multiply to 6 and add up to - 5. The numbers are - 2 and - 3 since $(-2)\times(-3)=6$ and $(-2)+(-3)=-5$. So $x^{2}-5x + 6=(x - 2)(x - 3)$.

Answer:

1. 2) $(x + 5)$ and $(x - 4)$
2. 2) $(x - 2)$ and $(x - 3)$