Week 7 in Precalc 11 – Solving Perfect Square Trinomials

This week in Precalculus 11, I learned how to factor Trinomials with perfect squares.

Let’s get started. So first, what is a trinomial with perfect squares?

It is when the first and third numbers are perfect squares (Sometimes the second number may be a perfect square.)

So when we look at this equation, we see that a is a perfect square and 36 is as well. When we are solving these equations, the formula is square root of multiplied by the square root of c, then multiplied by 2. This formula ONLY works when you have a perfect square for and c.

Here is an example we can try to solve for bx. When we are solving these equations, the formula is square root of multiplied by the square root of c, then multiplied by 2.

So we square root both sides, multiply those together then multiply by 2 as seen below.

After we solve bx, we then can factor it.

+ 14x + 49

 

From my previous blog post we know that Product of c, Sum of b. Just by looking, I know that 7×7 is 49 and 7+7 is 14 which matches up with our b value.

So when factored correctly, it should look like this.

(x+7)(x+7)

and we can verify it as well.