what is the factored form of $x^{2}-9x + 20$?\na. $x(x - 9)+20$\nb. $(x - 4)(x + 5)$\nc. $(x - 4)(x…

Explanation:

Step1: Identify the form

For a quadratic expression $ax^{2}+bx + c$ (here $a = 1$, $b=-9$, $c = 20$), we need to find two numbers that multiply to $ac=1\times20 = 20$ and add up to $b=-9$.

Step2: Find the two - numbers

The two numbers that multiply to 20 and add up to - 9 are - 4 and - 5 since $(-4)\times(-5)=20$ and $-4+( - 5)=-9$.

Step3: Factor the quadratic

We can rewrite the middle term $-9x$ as $-4x-5x$. Then $x^{2}-9x + 20=x^{2}-4x-5x + 20$. Group the terms: $(x^{2}-4x)-(5x - 20)=x(x - 4)-5(x - 4)=(x - 4)(x - 5)$.

Answer:

C. $(x - 4)(x - 5)$