Chapter 8.7, Problem 39PPS

To determine

To factor the given polynomial

Answer to Problem 39PPS

  $2cd(c^2+d^2)(2c-5)$

Explanation of Solution

Given:

Polynomial: $4c^{4}d-10c^{3}d+4c^2{d}^3-10c{d}^3$

Formula used:

Roots of the polynomial of the form $a{x}^2+bx+c=a(x-x_1)(x-x_2)$ are

  $x=\frac{-b\pm \sqrt{b^2-4ac}}{2a}$

Calculation:

Consider the polynomial,

  $4c^{4}d-10c^{3}d+4c^2{d}^3-10c{d}^3$

Find the common term in each term,

  $\begin{array}{l}\Rightarrow 4c^{4}d-10c^{3}d+4c^2{d}^3-10c{d}^3\\ \Rightarrow 2c^{3}d(2c-5)+2c{d}^3(4c-5)\\ \Rightarrow (2c^{3}d+2c{d}^3)(2c-5)\\ \Rightarrow 2cd(c^2+d^2)(2c-5)\end{array}$

Thus, the factors of the equation are $4c^{4}d-10c^{3}d+4c^2{d}^3-10c{d}^3=2cd(c^2+d^2)(2c-5).$

Conclusion:

Therefore, the factors of the given equation are $2cd(c^2+d^2)(2c-5).$