what is the factored form of the polynomial?\n$x^{2}-12x + 27$\n$(x + 4)(x + 3)$\n$(x - 4)(x + 3)$\n$(x +…

Explanation:

Step1: Analyze the quadratic form

For a quadratic polynomial $ax^{2}+bx + c$ (here $a = 1$, $b=-12$, $c = 27$), we need to find two numbers that multiply to $ac=1\times27 = 27$ and add up to $b=-12$.

Step2: Find the two - numbers

The two numbers that multiply to 27 and add up to - 12 are - 9 and - 3 since $(-9)\times(-3)=27$ and $-9+( - 3)=-12$.

Step3: Factor the polynomial

We can rewrite the middle term $-12x$ as $-9x-3x$. Then $x^{2}-12x + 27=x^{2}-9x-3x + 27$. Group the terms: $(x^{2}-9x)-(3x - 27)=x(x - 9)-3(x - 9)=(x - 9)(x - 3)$.

Answer:

$(x - 9)(x - 3)$