Chapter 12, Problem 48CLR

To determine

To find: The factor of the given polynomial and if it cannot be factorized than write prime.

Answer to Problem 48CLR

The factorized form of the polynomial is $\left(2p-7\right)\left(-5p-4\right)$ .

Explanation of Solution

Given:

The given polynomial is $-10p^2+27p+28$ .

Calculation:

Consider the given polynomial is,

  $-10p^2+27p+28$

Then, the solution is,

  $-10p^2+27p+28$

The first term and the last term of the above expression is the perfect square and the factored form of the polynomial is,

  $\begin{array}{c}-10p^2+27p+28=\left(-10p^2+35p\right)-\left(8p-28\right)\\ =-5p\left(2p-7\right)-4\left(2p-7\right)\\ =\left(2p-7\right)\left(-5p-4\right)\end{array}$