# ACT Aspire Math: Factoring Polynomials

What is the fully factored form of the polynomial -16x⁶ + 81x²?

ACT Aspire | Math |

ACT Aspire Math | Algebra |

Math | Algebra |

Product Type | ACT Aspire |

Test Prep | ACT Aspire ACT Aspire Math |

### Transcript

too bad of a problem if we take it step

by step So we start by factoring out negative one

to make the leading term positive and just looks like

that And sixteen and eighty one don't have any common

factors But we can factor out x squared from the

next in the sixth and the square there Right So

now notice that both sixteen x the fourth and anyone

are perfect squares Yes your hunch was right since four

x squared then squared is sixty next the fourth and

nine squares Eighty one Well they follow the pattern of

a difference of squares problem And when we see terms

that fit into the pattern a squared minus b squared

well we can factor to a plus b and an

a minus b that looks like that That means we

didn't factor that last term Sixteen x the fourth minus

eighty one And it'll look like that negative x squared

for tripolis nine for its foreign minus nine And finally

we noticed that now we have another difference Of squares

in the last binomial term Therefore x squared minus nine

Since you know to x squared is for x squared

and three export is nine Right So we have ah

for x squared there and well yeah three squared is

nine All right Time to factor yet again Well what

does that give us That gives us negative x squared

over here Times quantity for x where plus nine times

quantity to explode three times quantity to x minus three

While poly means many and no meal means well my

mother said no dinner until we finish studying Right Well

we're one step closer to father bears a scarier than

a polynomial meatloaf with this answer So whatever That's the 00:01:49.12 --> [endTime] answer Yo Whoa