Question

$\text{Simplify:}(5p^2-25p+20)÷(p-4).$

• A. $5(p-2)$
• B. $5(p+1)$
• C. $5(p+2)$
• D. $5(p-1)$

Answer 1

The correct option is D $5(p-1)$

Given, the expression is
$\frac{5p^2-25p+20}{(p-4)}.$
Now, the numerator can be factorized as,
$5p^2-25p+20=5(p^2-5p+4)=5[p^2-p-4p+4]=5\left[p\right(p-1)-4(p-1\left)\right]=5(p-1)(p-4)\text{Hence,}\frac{5p^2-25p+20}{(p-4)}=\frac{5(p-1)(p-4)}{(p-4)}=5(p-1)$