Chapter 8, Problem 11PFA

To determine

To find the method to factor the given polynomials.

Answer to Problem 11PFA

Factor of perfect square trinomial

Explanation of Solution

Given:

Polynomial: $3x^2+18x+27$

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,

  $\Rightarrow 3x^2+18x+27$

Apply the above formula for $a=3,b=18,c=27$

  $\begin{array}{l}x=\frac{-18\pm \sqrt{{18}^2-4(3)(27)}}{2(3)}\\ x=\frac{-18\pm \sqrt{324-324}}{6}\\ x=\frac{-18}{6}=-3\end{array}$

Therefore, the factors of the equation are $3(x+3)(x+3)$ which is a perfect square trinomial.

Conclusion:

Therefore, to completely factorise the polynomial, the method of perfect square trinomial is used.