Chapter 8.7, Problem 26PPS

To determine

To factor: The given polynomial, if possible. If the polynomial cannot be factored, write prime.

Answer to Problem 26PPS

The polynomial $8x^2+10x-21$ cannot be factorize, i.e., $8x^2+10x-21$ a prime polynomial.

Explanation of Solution

Given information:

The given polynomial is $8x^2+10x-21$ .

Concept used:

To factor expression $a{x}^2+bx+c$ , we find two factors of $a\times c$ such that their sum equals b .

Calculations:

The given polynomial E (say) is $E=8x^2+10x-21$ .

To factor expression $8x^2+10x-21$ , we find two factors of $8\times -21$ such that their sum equals -10.

  $8\times -21=-2\times 2\times 2\times 3\times 7$

  $8\times -21=-2\times 2\times 2\times 3\times 7$

From the factors $-2\times 2\times 2\times 3\times 7$ we cannot find two factors “a ” and “b ” such that $-2\times 2\times 2\times 3\times 7=a\times b$ , and $a+b=10$ .

Hence, the polynomial $8x^2+10x-21$ cannot be factorize, i.e., $8x^2+10x-21$ a prime polynomial.

Conclusion:

The polynomial $8x^2+10x-21$ cannot be factorize, i.e., $8x^2+10x-21$ a prime polynomial.