# TSI Math: Finding Solutions to an Equation through Factoring

Which of the following are the solutions to the equation -4x² + 2x + 6 = 0?

Intermediate Algebra and Functions | Quadratic and Other Polynomial Expressions, Equations, and Functions |

Mathematics and Statistics Assessment | Quadratic and Other Polynomial Expressions, and Functions |

Product Type | TSI |

TSI | Mathematics and Statistics Assessment TSI Math TSI Mathematics |

TSI Math | Intermediate Algebra and Functions |

TSI Mathematics | Intermediate Algebra and Functions |

Test Prep | TSI |

### Transcript

Shed some weight here and let's factor out some well

common factors It's More trouble than it's worth factor with

a negative leading coefficient right Well when negative for x

squared plus two x plus six jumps on the equation

Treadmill The first factor it sweats out is a negative

one there So pull the negative out of each term

by swapping the signs and then that's how we do

it Okay well each coefficient is even so too is

another common factor Let's Move it on out front as

well So we got negative two times This whole thing

in here The extra weight is still hovering around by

both sides of the equation by negative too To shed

it for good If only burning off the dozen donuts

alina here may not have eaten yesterday Were this easy

Don't ask Okay so here we go We got to

x squared minus x minus three is zero Well it

feels good to have a lighter equation to factor and

solved now because what leading coefficient of polynomial is to

the factor to x squared minus Acts minus 3 Well

we'll need to do ah little guessing and checking the

first step of guests and check involves listing all the

factors of the leading term Well in this case we

can guess that the first two terms are ex and

two x The second step is to find the factors

of the constant negative three Well the factors will either

be negative three and one or negative One and three

Right Well now it's Time to do some guessing at

fill in two of the possible factors in the second

term of each of your parentheses There right there Since

we know the outside terms will be multiplied together Well

it's probably a better idea to put a three on

the inside term since we know we're aiming for a

middle term of negative one acts right there Multiplying this

out using foil Get following The first two terms will

multiply two to x squared No surprise there The two

outside terms multiply to be positive Two Acts while the

2 inside terms will apply to a negative three x

and our final term yes is negative three Well again

no Surprise on that last one right there Yeah combined

like terms to see that we've actually hit the nail

on the head out with our first guests Well now

that the equations factored either to x minus three or

x plus one must equal zero for the entire equation

equals zero so we just set Each factor equals zero

and solve here so to x minus three zero two

exes three exes three halves or x plus one a

zero and x is negative one Well after only a

few minutes of solving the equation is cleansed of the

solutions so x equals three halves and x equals negative

one So that's a that's Our answer And we're going

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