Question

(6x 2 +11x - 35) (3x - 5)

Answer 1

2x + 7

Explanation:

Simplify

6x2 + 11x - 35 / 3x - 5

2.1 Factoring 6x2 + 11x - 35

The first term is, 6x2 its coefficient is 6 .

The middle term is, +11x its coefficient is 11 .

The last term, "the constant", is -35

Step-1 : Multiply the coefficient of the first term by the constant 6 • -35 = -210

Step-2 : Find two factors of -210 whose sum equals the coefficient of the middle term, which is 11 .

-210 + 1 = -209

-105 + 2 = -103

-70 + 3 = -67

-42 + 5 = -37

-35 + 6 = -29

-30 + 7 = -23

-21 + 10 = -11

-15 + 14 = -1

-14 + 15 = 1

-10 + 21 = 11 That's it

Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above, -10 and 21

6x2 - 10x + 21x - 35

Step-4 : Add up the first 2 terms, pulling out like factors :

2x • (3x-5)

Add up the last 2 terms, pulling out common factors :

7 • (3x-5)

Step-5 : Add up the four terms of step 4 :

(2x+7) • (3x-5)

Which is the desired factorization

2.2 Cancel out (3x-5) which appears on both sides of the fraction line.

Final result : 2x + 7

Answer 2

When doing this kind of problem, one thing that we would have to consider first would be the fact that we would have to simplify this. We're not just clearly giving a simple answer as "6" or something of that case, but we would be narrowing this expression above down to the most that we can.

Let's begin!


`(((2*3x^2) + 11x) - 35) * (3x - 5) \\ \\`

Then after doing this part of the section, the next thing that we would do in this case would be the fact of factoring the problem down.


`\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \downarrow \ \ \ \ \ \ \downarrow \ \ \ \ \ \ \ \ \downarrow \\ Factoring \: 6x^2+11x-35`

As we can see above, this would be the numbers that we were practically factoring.So, the next step that we would do would be the following.


`6x^2 - 10x + 21x - 35 \\ \\`

We then would pull out the like factors.


`2x * (3x-5)`

Then, the following would show us on how we would add up all of the "like terms" all together.


`\boxed{ (2x+7) * (3x-5)}`

But that would not be the answer quite yet. By simplifying this down once again, our answer would be the following:


`YOUR \ ANSWER: \ \boxed{\boxed{\bf{ (3x - 5)^2 * (2x + 7)}}}`