Question

7.5 - factoring polynomials - part 1
factor this quadratic expression.
$x^2 - 16x + 28$

Explanation:

Step1: Find pair of numbers

We need two numbers that multiply to $28$ and add to $-16$. These numbers are $-2$ and $-14$, since $(-2)\times(-14)=28$ and $(-2)+(-14)=-16$.

Step2: Split middle term

Rewrite the quadratic using the two numbers:
$x^2 - 2x -14x +28$

Step3: Factor by grouping

Group the first two and last two terms, then factor out the GCF from each group:
$x(x - 2) -14(x - 2)$

Step4: Factor out common binomial

Factor out $(x-2)$ from both terms:
$(x - 2)(x - 14)$

Answer:

$(x - 2)(x - 14)$