Chapter 8.7, Problem 40PPS

To determine

To factor the given polynomial

Answer to Problem 40PPS

Prime

Explanation of Solution

Given:

Polynomial: $g^2+2g-3h^2+4h$

Concept used:

Finding common factor in each term and factoring using grouping method.

Calculation:

Consider the given polynomial,

  $\Rightarrow g^2+2g-3h^2+4h$

Group the like terms and find common factor.

  $\Rightarrow (g^2+2g)-(3h^2-4h)$

Find out common terms in the above expression.

  $\Rightarrow g(g+2)-h(3h-4)$

The polynomial cannot be factored further since there is no common factor.

Conclusion:

Therefore, the polynomial is prime.