Question

Helppp plz alg 2 Will give ya brainlisttttt

Answer 1

I dont know what you are doing with that, I assume factoring.

so, we can group into like terms.

not all of them have x's, so grouping that way would be a step backwards. let's see if the numbers have anything in common.

$49 {x}^{3} - 35 {x}^{2} + 56x - 40$
the 49, -35, and 56 can be divided by 7, but -40 can't, so we cannot factor any thing out of the entire expression, but lets look at pairs. -40 is the odd man out, so let's think about the factors of 40.

we have 1 (we ignore it since every number is divisible by 1), 2, 4, 5, 8, 10, 20, and 40.

now, which ones have the same factors?

49 has 7 and 49
35 has 5, 7 and 35
56 has 2, 4, 7, 8, 14, 28, and 56

now, let's look at which numbers pair up with the highest factors. 49 and 35 share 7. 49 and 56 share 7. 35 and 56 share 7. 40 and 49 do not share any. 40 and 35 share 5. and 40 and 56 share 8.

so, we will pair up 40 and 56 since they have the highest factor in common, which means we pair up 49 and 36.

$49 {x}^{3} - 35 {x}^{2} + 56x - 40 \\ (49 {x}^{3} - 35 {x}^{2} ) + (56x - 40)$
now factor out the number factors
$(7 \times 7 \times {x}^{3} - 7 \times 5 \times x) + \\ (8 \times 7 \times x - 8 \times 5) \\ \\ 7(7 {x}^{3} - 5 {x}^{2} ) + 8(7x - 5)$
now, we step back and look at our pairs and see if we can factor out variables. in our first pair, we can factor something else out. can you notice what it is?

$7 {x}^{3} - 5 {x}^{2} = \\ 7 \times x \times x \times x - 5 \times x \times x$
they both have two x's so let's factor that out.
remember we factored out a seven before, so we still need that!
$7(7 \times x \times x \times x - 5 \times x \times x) = \\ 7 \times x \times x(7 \times x - 5) \\ 7 {x}^{2} (7x - 5)$
now our expression looks like this
$7 {x}^{2} (7x - 5) + 8(7x - 5)$
we aren't quite done yet. we have a new "super pair" and they have something in common. notice it?

it is (7x-5) so we need to factor that one out.

$(7x - 5)(7 {x}^{2} + 8)$
now, check to see if there is anything else.... I will wait.

.....

....

......

nope? ok. then we are done factoring.

finally, multiply it out with double distribution, box method, or foil to make sure we did it right.
$7x \times 7 {x}^{2} + 7x \times 8 - 5 \times 7 {x}^{2} - 5 \times 8 \\ 49 {x}^{3} + 56x - 35 {x}^{2} - 40$

move it into proper form (descending exponents)
$49 {x}^{3} - 35 {x}^{2} + 56x - 40$

it matches so we have our answer!