Chapter 5.4, Problem 68S

To determine

To find: the factor of the given algebraic equation.

Answer to Problem 68S

  $\text{b=7,-3}$ .

Explanation of Solution

Given:

  ${\text{b}}^{\text{2}}\text{-4b-21}$ .

Concept used:

Factorization of quadratic polynomial:

1. In order to factorize ${\text{x}}^{\text{2}}\text{+bx+c}$ it had to be find the number $\text{p}$ and $\text{q}$ such that $\text{p+q=b}$ and $\text{pq=c}$ .

After finding $\text{p}$ and $\text{q}$ ,split the middle term in the quadratic as $\text{px+qx}$ and get desired factors by grouping the terms.

Calculation:

  ${\text{b}}^{\text{2}}\text{-4b-21}$ .

Comparing with the equation ${\text{x}}^{\text{2}}\text{+bx+c}$ with $\text{p+q=b}$ and $\text{pq=c}$ .

Let find out $\text{p and q}$ .

Here $\text{p=-7 and q=3}$ .

  ${\text{b}}^{\text{2}}\text{-7b+3b-21}$ .

Taking common outside the bracket:

  $\text{b}\left(\text{b-7}\right)\text{+3}\left(\text{b-7}\right)$ .

Hence, the value of $\text{b=7,-3}$ .