Q 170. - Intermediate Algebra

Question

In the following exercises, factor completely using the perfect square trinomials pattern.

$64m^2-34m+1$

Step-by-Step Solution

Answer

The factor of the trinomial is $\left(32m-1\right)\left(2m-1\right)$.

Step 1. Given information.

Consider the given trinomial.

$64m^2-34m+1$

Step 2. Find the product a c .

Compare the given trinomial with $a{x}^2+bx+c$

$a=64, b=-34, c=1$

The product $ac$ is,

$64·1=64$

Step 3. Split the middle term.

The two numbers whose product is $64$and add up to $-34$ are $-32$ and $-2$.

Split the middle term of the trinomial.

$64m^2-32m-2m+1$

 

Step 4. Find the factor.

Factor the trinomial by grouping.

$$\begin{gathered} \left(64m^2-32m\right)-\left(2m-1\right) \\ 32m\left(2m-1\right)-1\left(2m-1\right) \\ \left(32m-1\right)\left(2m-1\right) \end{gathered}$$