Chapter 4.3, Problem 9CYU

To determine

To calculate: The factors of the polynomial $16x^2-16x+3$ .

Answer to Problem 9CYU

The polynomial is factored as $\left(4x-3\right)\left(4x-1\right)$ .

Explanation of Solution

Given information:

The polynomial $16x^2-16x+3$ .

Formula used:

To factor a polynomial split the middle term in such a way that sum of two numbers is the middle term and product of two numbers is same is product of first and last term.

Calculation:

Consider the polynomial $16x^2-16x+3$ .

Recall that to factor a polynomial split the middle term in such a way that sum of two numbers is the middle term and product of two numbers is same is product of first and last term.

For the above polynomial $-12$ and $-4$ are two numbers such that their sum is $-16$ and product is $48$ .

Apply it, first the group the similar terms,

  $\begin{array}{c}16x^2-16x+3=16x^2-12x-4x+3\\ =4x\left(4x-3\right)-1\left(4x-3\right)\\ =\left(4x-3\right)\left(4x-1\right)\end{array}$

Thus, the polynomial is factored as $\left(4x-3\right)\left(4x-1\right)$ .