Question

Factorise the expression and divide them as directed: $\left(5p^2-25p+20\right)÷\left(p-1\right)$.

Answer 1

Step 1: Factorize the expression $5p^2-25p+20$.

Take out the common factor from the above expression.

$5\left(p^2-5p+4\right)$

Split the middle term of the expression as $-1p-4p$, and take out the common factor.

$\begin{array}{rcl}& \Rightarrow & 5\left(p^2-1p-4p+4\right)=5\left(p\left(p-1\right)-4\left(p-1\right)\right)\\ & =& 5\left(p-4\right)\left(p-1\right)\end{array}$

Step 2: Divide the expression by $\left(p-1\right)$ to get the final answer.

$\Rightarrow \frac{5\left(p-4\right)\left(p-1\right)}{\left(p-1\right)}=5\left(p-4\right)$

Hence, the required final answer is $5\left(p-4\right)$.