In Exercises 23–34, determine the constant that should be added t...

Question

In Exercises 23–34, determine the constant that should be added to the binomial so that it becomes a perfect square trinomial. Then write and factor the trinomial.30. x² - 1/3x

Accepted Answer

Welcome back. I am so glad you're here. We are given this practice problem and told by completing the square, identify the constant needed for the given expression to become a perfect square trinomial also write the trinomial and express it as the square of a binomial. All right, the expression that we're given is X squared minus 1/11. X. Our answer choices are the constant term for answer choice A is 2/11. And the trinomial set equal to the square of a binomial is X squared minus 1/11 X plus 2/11 equals X minus the squared of 22 divided by 11. All squared. Answer choice B is for the constant term 1/11 and the trinomial and binomial are X squared minus 1/11 X plus 1/11 equals X minus the squared of 11 divided by all squared. Answer choice C, the constant is one 22nd. And the trinomial and binomial are X squared minus 1/ X plus one 22nd equals X minus the squared of 22 divided by 22 all squared. And answer choice D, the constant is one 484th and the trinomial and binomial are X squared minus 1/11 X plus one, 484th equals X minus one 22nd, all squared. All right. So the first step in determining our constant for a perfect square trinomial is to identify our B term that's going to be the one in front of the X to the first degree or the variable to the first degree, which in this case is X and the B term in front of it is negative 1/11. And what we're going to do is take our B term, divide it by two and square it. So we need to take negative 111th, divide it by two and square it. Let's do the work inside the parentheses here. First, we're taking negative 1/11 divided by two, we can rewrite this as two fractions negative 1/11 and then division simple, divide it by two, which is the same as negative 1/11 multiplied by the reciprocal of the second term. So the reciprocal of two is one half. Now we can multiply straight across negative one, multiplied by one equals negative one and 11, multiplied by 2 is 22. So inside the parentheses here we have negative one 22nd that still needs to be squared. However, I want to pause and take note of this term that is B divided by two, which is negative one 22nd. We'll need that in a few moments. But let's finish figuring out our constant term, we need to square negative one 22nd. So negative one squared is one And 22 squared is 484. And this is our constant term. Now, plugging this in to our trinomial will have our given expression which is X squared minus 1/11 X. Now we add our constant term. So plus one 484th and that is equal to open parentheses. And now we take X and then we're going to add our B divided by two term, which is negative one 22nd. So we can have X minus one 22nd, close parentheses squared. We look at our answer choices and this matches with answer choice. D well done. We'll catch you on the next one.

In Exercises 23–34, determine the constant that should be added to the binomial so that it becomes a perfect square trinomial. Then write and factor the trinomial.30. x² - 1/3x

Key Concepts

Perfect Square Trinomial

Completing the Square

Factoring Quadratics

Watch next