In Exercises 35–46, determine the constant that should be adde...

Question

In Exercises 35–46, determine the constant that should be added to the binomial so that it becomes a perfect square trinomial. Then write and factor the trinomial. $x squared plus 12 x$

Accepted Answer

Hello everyone in this video we're gonna be looking at this problem, we were trying to change the binomial X squared plus 24 X into a perfect square trin Amiel and then we want to factor that perfect square. Try no meal and show the factored form. So in order to solve this let's see what this problem is asking. So first it's saying that we need to show the constant that we're going to add to the binomial to make it a perfect square taino meal and then we need to show the perfect square. Try no meal and also the factored form. So in order to start solving this, let's remember what a perfect square. Try no meal looks like. So a perfect square. Try no meal follows the form X squared Plus 2 8 x plus eight squared. And when we factor that perfect sports binomial we have X plus a squared. So this is what we're trying to achieve in our perfect square. Try no meal however, we already have X squared plus 24 X. So you can see that part of the tri no meal has already been written for us and we're looking to add the plus A squared and the A squared will also be the constant. So in this case you can see that 24 is equal to two a. So if I set to a equal to 24 I can solve for the value of a. If I divide by two I get a is equal to 12. So using the fact that a is equal to 12, we can determine the constant we need to add Because the constant is a squared. So I can do 12 squared And that gives me 144. So I know that the constant I need to add Is equal to 1 44. So if I rewrite my equation I can get X squared Plus 24 x plus 1 44. And you can see that this form follows the perfect square try no meal form. So I've already determined my constant and my perfect square tray normal equation. Now I need to factor my perfect square tray no meal equation. And to do that you can see that the factored form is X plus A squared. So in this case we know that A. Is 12. So the factored form would be X plus squared and that becomes the final part of our answer. So the constant that we added was 1 44. A perfect square train only equation was X squared plus 24. X plus 1 44. And the factored form of our perfect square equation was X plus 12 squirt. And if we look at the answer choices you can see that answer choice C. Alliance with all of those with the constant being 1 44. Our perfect square try no meal being X squared plus 24. X plus 1 44 and the factored form being X plus 12 squared. So hopefully this video helped and see you next time.

In Exercises 35–46, determine the constant that should be added to the binomial so that it becomes a perfect square trinomial. Then write and factor the trinomial. $x squared plus 12 x$

Key Concepts

Perfect Square Trinomial

Completing the Square

Factoring Quadratic Expressions

Watch next

In Exercises 35–46, determine the constant that should be added to the binomial so that it becomes a perfect square trinomial. Then write and factor the trinomial. x2+12xx^2 + 12x

Key Concepts

Perfect Square Trinomial

Completing the Square

Factoring Quadratic Expressions

Watch next

In Exercises 35–46, determine the constant that should be added to the binomial so that it becomes a perfect square trinomial. Then write and factor the trinomial. $x squared plus 12 x$