# Which is the Factorization of 8×2 13x 6

## Which is the Factorization of 8×2 13x 6

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Richard J.

Algebra

6 months, 3 weeks ago

## which is the factorization of 8×2 13x – half dozen? (8x – 3)(x 2) (10 – vi)(8x ane) (2x – 2)(4x iii) (4x – ane)(2x vi)

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### Related Question

Gene the expression completely. \$(6 ten+1)(8 x-iii)^{4}-(6 10+1)^{2}(8 x-3)^{iii}\$

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### Video Transcript

when factoring polynomial. Our first step should be to await for Thou C F. Greatest common factor in this trouble, you’ll come across that nosotros actually have 2 factors. All of this is 1 factor in all of this is a factor. And then within those two, you lot may notice that we practise accept things in common. They both take a six X plus one. Then that’s something that we tin can factor out. And fifty-fifty though it’southward a binomial, it’s even so a One thousand c f. And when you lot’re factoring at a G C f, y’all e’er choose the smallest exponents. So this get-go one is as an exponent of 1. So I would just factor out six X plus one to the start power. And so I likewise noticed that both of them have this eight ten minus three. So the smaller of those two exponents is to the third ability. And then nosotros simply need to see what’southward left afterward we factor those out. So if we factored out the Ten plus 1 from this, um term information technology’southward gone, we’re only left with this and if nosotros factored out 3 of them we still have an eight 10 minus iii from that commencement term minus now in the second term if we factored out one of the six x plus ones we had 2 of them we still accept one left half-dozen X plus i. And if nosotros factored out viii x minus three to the third those are all gone and we’re just left with, that’due south six X plus 1. At present delight notice that we use the parenthesis here because this minus has to be distributed. Then when we become to clean this up a petty fleck um the first two terms or first 2 factors I’m sorry are skilful but this last ane we’re going to demand to distribute that negative sign. So we’d have viii x minus 3 minus six x minus 1. And again in that last term we can combine some similar terms, then eight x minus six X is two X and negative iii minus one is negative four. Now it looks like we’re finished simply not quite. This last factor has a g c f in in that location, we tin factor to from this last factor so I’m just gonna stick information technology all the style out here. And so we would take two times 6 Ten plus one times viii x minus three to the third times when I factored blastoff two, I’d have an X minus two left over. So this whole thing is factored completely.

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