# 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 AspireACT Aspire Math

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too bad of a problem if we take it step

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by step So we start by factoring out negative one

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to make the leading term positive and just looks like

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

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factors But we can factor out x squared from the

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next in the sixth and the square there Right So

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now notice that both sixteen x the fourth and anyone

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are perfect squares Yes your hunch was right since four

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x squared then squared is sixty next the fourth and

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nine squares Eighty one Well they follow the pattern of

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a difference of squares problem And when we see terms

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that fit into the pattern a squared minus b squared

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well we can factor to a plus b and an

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a minus b that looks like that That means we

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

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

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for tripolis nine for its foreign minus nine And finally

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we noticed that now we have another difference Of squares

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in the last binomial term Therefore x squared minus nine

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Since you know to x squared is for x squared

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and three export is nine Right So we have ah

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for x squared there and well yeah three squared is

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nine All right Time to factor yet again Well what

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does that give us That gives us negative x squared

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over here Times quantity for x where plus nine times

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quantity to explode three times quantity to x minus three

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While poly means many and no meal means well my

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mother said no dinner until we finish studying Right Well

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

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