Q 169. - Intermediate Algebra

Question

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

$100y^2-52y+1$

Step-by-Step Solution

Answer

The factor of the trinomial is $\left(50y-1\right)\left(2y-1\right)$.

Step 1. Given information.

Consider the given trinomial.

$100y^2-52y+1$

Step 2. Find the product a c .

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

$a=100,b=-52,c=1$

The product $ac$ is

$100·1=100$

Step 3. Split the middle term.

The two numbers whose product is  $100$ and add upto $-52$ are $-50$ and $-2$.

Split the middle term of the trinomial.

$100y^2-50y-2y+1$

Step 4. Find the factor.

Factor the trinomial by grouping.

$$\begin{gathered} \left(100y^2-50y\right)-\left(2y-1\right) \\ 50y\left(2y-1\right)-1\left(2y-1\right) \\ \left(50y-1\right)\left(2y-1\right) \end{gathered}$$