Chapter SH, Problem 14.7.6EP

To determine

To factor: the given polynomial

Answer to Problem 14.7.6EP

The required result is $5p^2\left(2p-7\right)$ .

Explanation of Solution

Given: $10p^3-35p^2$

Find the GCF of $10p^3,35p^2$ .

Write each term as the prime factorization.

  $\begin{array}{l}10p^3=2\times 5\times p\times p\times p\\ 35p^2=7\times 5\times p\times p\end{array}$

GCF is $5\times p\times p=5p^2$ .

Write each term as the product of GCF and its remaining factors.

  $\begin{array}{l}10p^3-35p^2=5p^2.2p-5p^2.7\\ =5p^2\left(2p-7\right)\left(distributiveproperty\right)\end{array}$

Hence, the factorization is $5p^2\left(2p-7\right)$ .

Conclusion:

Hence, the factorization is $5p^2\left(2p-7\right)$ .