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.
34. x²-9/5x

Accepted Answer

Welcome back. I am so glad you're here. We are given this practice problem and we're 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 a square of a binomial. The expression we're given is X squared minus 15 halves, X. Our answer choices are answer choice. A, the constant is 15 halves. And then the trinomial and expression as the square of a binomial is X squared minus 15 halves, X plus 15 halves equals X - The Square Root of 15/2, all squared. Answer choice B the constant is 15 4th. And then the trinomial set equal to the square of a binomial is X squared minus 15 halves, X plus 15 4th equals X minus the square root of 15/2 all squared and answer choice C the constant is 16, 225th. The trinomial given as an expression of the square of a binomial is X squared minus 15 halves, X plus 16, 225th equals X -4 15th, All Squared. Answer choice D, the constant is 225/16 and the trinomial and binomial are X squared minus 15 halves, X plus 225 16th equals X -15/4, all squared. All right, we recall from previous lessons. The first step in completing the square is to identify our B term. The B term is the one in front of our X or our variable to the first degree. And the B term here is negative halves. And what we do is we take our B term, divide it by two and then square it that gives us our constant. So our B term here we take negative 15 halves, we divide that by two and then we'll square it. Let's do the work inside the parentheses here. First, we have negative 15 halves divided by two. We can rewrite that as two fractions, we have negative 15 halves, division symbol divided by two, which is equal to negative 15 halves multiplied by one half, the reciprocal of two. And now we can multiply straight across our numerators. Negative 15, multiplied by one is negative 15 and our denominators two multiplied by two is four. So inside the parentheses up here, we have negative 15 4th and that's what needs to be squared. Want to take note real quick of what's in the parentheses here. This B over two or this negative 15 4th will be needed again in a moment. But for now let's finish finding our constant. So we need to square negative 15 4th. That means we will be squaring both negative 15 and scoring four, negative 15 squared is 225 and four squared is 16. So our constant is 16th. So we can plug that in. We'll have our original expression X squared minus halves X and now we add our constant terms. So plus 225 16th and that is equal to. And now we are going to have our square of a bin, no meal, which will be open parentheses X and this is where our B over two comes in the B divided by two. So this is going to be X minus 4th closed parentheses squared. We look at our answer choices and that 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. 34. x²-9/5x

TextbookSolutions.keyConceptsTitle

Perfect Square Trinomial

Completing the Square

Factoring Quadratics

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