Use Choices A–D to answer each question. A. 3x^2 - 17x - 6 = 0 B....

Question

Use Choices A–D to answer each question. A. 3x^2 - 17x - 6 = 0 B. (2x + 5)^2 = 7 C. x^2 + x = 12 D. (3x - 1)(x - 7) = 0 Which equation is set up for direct use of the zero-factor property? Solve it

Accepted Answer

Hey, everyone here, we are asked to select one of the given equations that can be directly solved by using the zero factor property. And then we need to work out the values of X. So before we take a look at our given equations, we first need to recall the formula for the zero factor property, which is the quantity of A times the quantity of B is equal to zero. So now we just need to compare this formula with our equations to see which one is the best match. So it looks like from our list of equations that our fourth equation is our best match to the formula. So our fourth equation, we have the quantity of nine X minus four times the quantity of X minus five and this is equal to zero. So we can see comparing our formula to this fourth equation that both the formula and equation are equal to zero. And then both the formula and the equation have two expressions which are grouped into, into two different sets of parentheses. So we can see that we have a perfect match here. So with our fourth equation, we can directly solve for X by using the zero factor property. And now the zero factor property tells us that we can set each individual expression in each set of parentheses equal to zero. So we can start with our first set of parentheses which is nine X minus four. And again, we set this equal to zero and solve for X. So first, we need to add four to both sides and this gives us nine X is equal to four. And now we need to get rid of this coefficient for X. So we just need to divide both sides by nine. And we see that one of our solutions for X is four nights. And now we can repeat this process with the second set of parentheses where we have X minus five and we set this expression equal to zero. And now again, solving for X, we just need to move this negative five to the right hand side. So we just add five to both sides. And we see that our second solution for X is just five. So now summarizing, we see that our two solutions for X are four nights and five. And we got these two solutions by using the zero factor property for equation four. So with this, we are left with answer choice age. Thanks for watching. I hope you found this video helpful and I'll see you again next time.

Struggling with College Algebra?

Use Choices A–D to answer each question. A. 3x^2 - 17x - 6 = 0 B. (2x + 5)^2 = 7 C. x^2 + x = 12 D. (3x - 1)(x - 7) = 0 Which equation is set up for direct use of the zero-factor property? Solve it

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