Chapter 8, Problem 81SGR

To determine

To factorize the given polynomial

Answer to Problem 81SGR

  $-3(x+2)(x+2)$

Explanation of Solution

Given:

Polynomial: $-3x^2-12x-12$

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 given polynomial,

  $\begin{array}{l}\Rightarrow -3x^2-12x-12\\ \Rightarrow -3(x^2+4x+4)\end{array}$

Substituting in the above formula where $a=1,b=4,c=4$

  $\begin{array}{l}\Rightarrow x=\frac{-4\pm \sqrt{4^2-4(1)(4)}}{2(1)}\\ \Rightarrow x=\frac{-4\pm \sqrt{16-16}}{2}\\ \Rightarrow x=\frac{-4\pm 0}{2}\\ \Rightarrow x=-2\pm 0\\ \Rightarrow x=-2,-2\end{array}$

The roots are,

  $\Rightarrow x_1=x_2=-2$

The roots of the quadratic polynomial $-3x^2-12x-12=-3(x+2)(x+2).$

Conclusion:

Therefore, the factors of the polynomial is $-3(x+2)(x+2).$