Chapter 8.2, Problem 48STP

To determine

To find: The value of “a”, if expression $9x^3-15x$ can be factored as $ax\left(3x^2-5\right)$ .

Answer to Problem 48STP

The value of “a” is 3.

Explanation of Solution

Given information:

The expression $9x^3-15x$ can be factored as $ax\left(3x^2-5\right)$ .

Concept used:

The two polynomial are equal if the coefficients of like powers of variables are equal.

Calculations:

The expression $9x^3-15x$ can be factored as $ax\left(3x^2-5\right)$ .

  $\Rightarrow 9x^3-15x=ax\left(3x^2-5\right)$

  $\Rightarrow 9x^3-15x=ax\cdot 3x^2-ax\cdot 5$

  $\Rightarrow 9x^3-15x=3a{x}^{2+1}-5ax$

  $\Rightarrow 9x^3-15x=3a{x}^3-5ax$

Thus, we have $9x^3-15x=3a{x}^3-5ax$......(1)

Equating coefficients of like powers of “x” in result (1)

  $3a=9\Rightarrow a=\frac{9}{3}=3$ , and $15=5a\Rightarrow a=\frac{15}{5}=3$ .

Thus, the value of “a” is 3.

Conclusion:

The value of “a” is 3.