Question

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

Explanation:

Step1: Split middle term correctly

We need two numbers that multiply to $-27$ and add to $6$. These numbers are $9$ and $-3$. So rewrite the polynomial:
$x^2 + 9x - 3x - 27$

Step2: Factor by grouping

Group terms and factor out GCF:

$$\begin{align} x^2 + 9x - 3x - 27 &= x(x+9) - 3(x+9) \\ &= (x+9)(x-3) \end{align}$$

Step3: Verify other options

• Option1: $x^2+3x-9x-27=x^2-6x-27

eq x^2+6x-27$

• Option2: $x^2+6x-3x-27=x^2+3x-27

eq x^2+6x-27$

• Option4: $x^2+3x-6x-27=x^2-3x-27

eq x^2+6x-27$

Answer:

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