how do you factor the trinomial 5+34x-7x^2?

Answer 1

Well first put it in standard form

7x^2 - 34x - 5

Then you have to do the four step method since the leading coeffecient is 7 instead of 1.

Multiply the a value (7) by the c (-5) value. = -35

You are going to replace the b value (34) with two numbers that add to 34 and multiply to -35 like you would in an easier trinomial factoring problem.

The two numers that you should find are -35 and +1. Then put those numbers with the x in replacing the -34x.

7x^2 -35x + 1x - 5

Now you use the grouping method. Seperate the first two terms and the second two terms

7x^2 -35x <> + 1x - 5

Simply factor the first part (factor out the 7x):
7x^2 -35x factors to 7x (x - 5)

And the second part:

1x - 5, which is already factored.

Now you have 7x (x - 5) + 1 (x - 5)

Now you combine these to get two binomials, which is the final answer.

(7x + 1)(x - 5)

Answer 2

If we were to factor 5+34x-7x^2 into (ax+b)(cx+d), we see that bd = 5 (as this is the only non-x term).

The factors of 5 are 1,5,-1,-5

We see that a*c*x^2 = -7x^2, thus ac = -7. The factors of -7 are 1,7,-1,-7.

We also see that (ad+bc)x = 34x or (ad+bc) = 34.

Given the above factors of 5 and 7, we easily notice that 34 = 5*7-1*1 or (-5)(-7)-1*1. From this, we deduce that the factorization is:

(-7x-1)(x-5)

We can also factor out the -1 from the first term, giving:

-(7x+1)(x-5)

Answer 3

you would put it in standard form which would be -7x^2+34x+5
then times -7 and 5 and you get 35 and you want to find something that the product would be -35 and the sum would be 34 hich would be 35 and -1 so then rewrite it as -7x^2+35x-1x+5 then factor 7x(-x+5)(-1x+5) so it would be
(-x+5)(7x+1)

Answer 4

switch it around -7x^2+34x+5
remove negative sign -(7x^2-34x-5)
then factor out -(7x+1)(x-5)
how i did it: 7x^2 cant be split up so one side needs to be 7x while the other is just x. then figure out how to get -34. 7*5=35, but since the last part is -5, which you get by 5*-1. basically you need to find numbers that multiply to -34 but also -5.

Answer 5

Follow trinomial factoring rules and you will end up with a final answer of::

(5-1)(1+7x)

Answer 6

-7x^2 + 34x + 5

find two numbers that multiply to -35 and add to 34

the two numbers are 35 and -1

-7x^2 - x + 34x + 5

factor by groups

(-7x^2 - x ) + (35x + 5)

take out -7x and 5

-x (7x + 1) + 5(7x + 1)

(7x + 1) (-x + 5)

you can take out the negative if you want

- (7x + 1) (x - 5)

Answer 7

5 x -7 = -35, -1 x 35 = -35 and -1 + 35 = 34, so rewrite as

5 - x + 35x - 7x^2
Group the terms into the sum of two binomials:

(5 - x) + (35x - 7x^2)
This is the same as 1(5 - x) + 7x(5 - x) or (1 + 7x)(5 - x)

Answer 8

-7x^2+34x+5

(7x+1)*(-x+5)

Answer 9

put it in standard form first

-7x^2+34x+5

Then factor.(you can do that by yourself)

Answer 10

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