which shows the four - term polynomial and factored form of $x^{2}+6x - 27$?\n$x^{2}+3x - 9x - 27=(x + 3)(x…

which shows the four - term polynomial and factored form of $x^{2}+6x - 27$?\n$x^{2}+3x - 9x - 27=(x + 3)(x - 9)$\n$x^{2}+6x - 3x - 27=(x + 6)(x - 3)$\n$x^{2}+9x - 3x - 27=(x + 9)(x - 3)$\n$x^{2}+3x - 6x - 27=(x + 3)(x - 6)$

which shows the four - term polynomial and factored form of $x^{2}+6x - 27$?\n$x^{2}+3x - 9x - 27=(x + 3)(x - 9)$\n$x^{2}+6x - 3x - 27=(x + 6)(x - 3)$\n$x^{2}+9x - 3x - 27=(x + 9)(x - 3)$\n$x^{2}+3x - 6x - 27=(x + 3)(x - 6)$

Answer

Explanation:

Step1: Factor the polynomial $x^{2}+6x - 27$

We need to find two numbers that multiply to $-27$ and add up to $6$. The numbers are $9$ and $- 3$ since $9\times(-3)=-27$ and $9+( - 3)=6$. So we can rewrite the middle - term $6x$ as $9x-3x$. Then $x^{2}+6x - 27=x^{2}+9x-3x - 27$.

Step2: Group and factor by grouping

Group the terms: $(x^{2}+9x)-(3x + 27)$. Factor out the greatest common factor from each group: $x(x + 9)-3(x + 9)$. Then factor out the common binomial factor $(x + 9)$: $(x + 9)(x-3)$.

Answer:

$x^{2}+9x - 3x-27=(x + 9)(x - 3)$