Chapter 8.3, Problem 28PPS

To determine

To find: The product $\left(x^2+5x-1\right)\left(5x^2-6x+1\right)$

Answer to Problem 28PPS

  $5x^4+19x^3-34x^2+11x-1$

Explanation of Solution

Given:

  $\left(x^2+5x-1\right)\left(5x^2-6x+1\right)$

Calculation:

Multiply each term of the first polynomial with the each term of the second polynomial

  $\begin{array}{l}\left(x^2+5x-1\right)\left(5x^2-6x+1\right)\\ =x^2\cdot 5x^2+x^2\cdot \left(-6x\right)+x^2\cdot 1+5x\cdot 5x^2+5x\cdot \left(-6x\right)+5x\cdot 1-1\cdot 5x^2-1\cdot \left(-6x\right)-1\cdot 1\\ =5x^4-6x^3+x^2+25x^3-30x^2+5x-5x^2+6x-1\\ =5x^4+19x^3-34x^2+11x-1\end{array}$

So, the product of the polynomial is $5x^4+19x^3-34x^2+11x-1$