Solve each equation in Exercises 1 - 14 by factoring.

x^2 - 3x - 10 = 0

Question

Solve each equation in Exercises 1 - 14 by factoring.

x^2 - 3x - 10 = 0

Accepted Answer

Hello everyone in this video we're going to be looking at this practice problem where we want to find the value of V in the equation V squared plus 10. V minus 39 by factoring so in this case Because we want to find the value of V5 factoring, we want to consider two terms where this first digit has to multiply to give us V squared. So if we do V as the first term, you can see that when I oil and multiply the first terms together I'll get back V squared. So we'll write V as the first term of our factors. And for the second term We need terms that will multiply to give us -39. This last constant in our equation but they need to add to give us positive so we can try three and negative 13. So three times negative 13 gives us negative 39. And if I add three and -13 I get negative 10. So that's telling me I need to switch the sign of these. And now if I multiply negative three times positive 13 I still get negative 39. But when I add negative three with positive 13 I get positive 10. Now that tells me that negative three and positive 13 are the terms I should use as my second terms. And we can check this by doing the foil method where I have the first terms multiplied together V squared plus 13. V and negative three times V is negative three V and negative three times positive 13 is negative 39. And if I combine the middle terms, I have V squared positive 13 minus -3 is positive 10, V -39. And you can see I get back my original equation. So I know that this factory Ization was good. And because this is still equal to zero, I can have these, I can solve for these factors separately. Where I have V minus three is equal to zero and V plus 13 is equal to zero. And when I solve for V in this first equation, I'll add three, which means V is equal to three. And in the second equation all subtract 13, which means V is equal to negative 13. So that tells me that V has two solutions. I could have -13 or positive three. So it becomes my final answer for this equation. And you can see that that aligns with answer choice B. So hopefully this video hope and see you next time.

Solve each equation in Exercises 1 - 14 by factoring. x^2 - 3x - 10 = 0

Verified Solution

Key Concepts

Factoring Quadratic Equations

Zero Product Property

Quadratic Formula