Chapter 9, Problem 29PT

To determine

To compute the value of $\left(f-g\right)\left(x\right)$ for two given functions.

Answer to Problem 29PT

  $\left(f·g\right)\left(x\right)=12x^4-42x^3+58x^2-41x+8$

Explanation of Solution

Given information :

The function provided is $f\left(x\right)=2x^2-4x+1$ and $g\left(x\right)=-6x^2+9x-8$ .

Formula used :

Use the formula $\left(f·g\right)\left(x\right)=\left(f\right)\left(x\right)\times \left(g\right)\left(x\right)$ .

  $f\left(x\right)=2x^2-4x+1$

  $g\left(x\right)=-6x^2+9x-8$

These are the given functions.

  $=\left(2x^2-4x+1\right)\left(6x^2-9x+8\right)$

Use the property $\left(f·g\right)\left(x\right)=\left(f\right)\left(x\right)\times \left(g\right)\left(x\right)$

  $=2x^2\times 6x^2+2x^2\times -9x+2x^2\times 8-4x\times 6x^2-4x\times -9x-4x\times 8+6x^2-9x+8$

Multiplying each term.

  $=12x^4-18x^3+16x^2-24x^3+36x^2-32x+6x^2-9x+8$

Post this, regroup the like terms.

  $=12x^4-18x^3-24x^3+16x^2+36x^2+6x^2-32x-9x+8$

Add/subtract the terms with the same exponent of x

  $\left(f·g\right)\left(x\right)=12x^4-42x^3+58x^2-41x+8$

This is the answer.