Chapter 8, Problem 71SGR

To determine

To factorize the given polynomial

Answer to Problem 71SGR

  $(x\sqrt{3}-\sqrt{3})(x\sqrt{3}+\sqrt{3})$

Explanation of Solution

Given:

Polynomial: $3x^2-3$

Formula used:

  $a^2-b^2=(a-b)(a+b)$

Calculation:

Consider the given polynomial,

  $\begin{array}{l}\Rightarrow 3x^2-3\\ $ \Rightarrow {(\sqrt{3}x)}^2-{(\sqrt{3})}^2$\Rightarrow (x\sqrt{3}-\sqrt{3})(x\sqrt{3}+\sqrt{3})[\because a^2-b^2=(a-b)(a+b)]\end{array}$

Conclusion:

Therefore, the factors of the polynomial are $(x\sqrt{3}-\sqrt{3})(x\sqrt{3}+\sqrt{3}).$