Question

q13) $4x^2 - x - 5$

Explanation:

Step1: Identify coefficients

For $4x^2 - x - 5$, $a=4$, $b=-1$, $c=-5$

Step2: Find factor pairs

Find two numbers: product $4\times(-5)=-20$, sum $-1$. The numbers are $4$ and $-5$.

Step3: Split middle term

Rewrite $-x$ as $4x-5x$:
$4x^2 + 4x - 5x - 5$

Step4: Factor by grouping

Group terms: $(4x^2 + 4x) + (-5x - 5)$
Factor out GCFs: $4x(x+1) -5(x+1)$
Factor out $(x+1)$: $(4x-5)(x+1)$

Answer:

$(4x - 5)(x + 1)$