NCERT Solutions Class 8 Mathematics Solutions for Exercise 14.3 in Chapter 14 - Factorisation

Question 11 Exercise 14.3

Factorize the expressions and divide them as directed:

\left(5 p^{2}-25 p+20\right) \div(p-1)



When a polynomial is represented as "ax2 + bx + c," where "a," "b," and "c" are just numbers, it is referred to as a "quadratic." Now for factorizing purpose, we can determine the two values that, when multiplied together, will equal the product term "ac" as well as added to get the coefficient on the x-term, "b."

\begin{aligned} &\text { Step 1: Take 5 common from the equation, } 5 p^{2}-25 p+20, \text { we get }\\ &5 p^{2}-25 p+20=5\left(p^{2}-5 p+4\right)\\ &\text { Step } 2: \text { Factorize } \mathrm{p}^{2}-5 \mathrm{p}+4\\ &p^{2}-5 p+4=p^{2}-p-4 p+4=(p-1)(p-4) \end{aligned}Step 3: Solve original equation

\left(5 p^{2}-25 p+20\right)+(p-1)=5(p-1)(p-4) /(p-1)=5(p-4)

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