Question

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

Explanation:

Step1: Split middle term

We need two numbers that multiply to $-27$ (product of $x^2$ coefficient and constant term) and add to $6$ (middle term coefficient). These numbers are $9$ and $-3$.
So rewrite $x^2+6x-27$ as:
$x^2 + 9x - 3x - 27$

Step2: Factor by grouping

Group first two and last two terms:
$(x^2 + 9x) + (-3x - 27)$
Factor out common terms from each group:
$x(x + 9) - 3(x + 9)$
Factor out $(x+9)$:
$(x + 9)(x - 3)$

Step3: Verify options

Compare with given options to match the correct pair.

Answer:

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