Factoring Trinomials?

Question

Is there an easy way to remember how to do these problems?
6x2(squared) +17x+5=()()

6x2(squared)+17x+5= ( ) ( )

Answer 1

6x² + 17x + 5 = 0

The middle term is + 17x

Find the sum of the middle term

Multiply the first term 6 by the last term 5 equals 30 and factor

Factors of 30

1 x 30
2 x 15. . . . .<=. . .use these factors
3 x 10
5 x 6

+ 2 and + 15 satisfy the sum of the middle term

Insert + 2x and + 15x into the equation

6x² + 17x + 5 = 0

6x² + 2x + 15x + 5 = 0

2x(3x + 1) + 5(3x + 1) = 0

(2x + 5)(3x + 1)

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Roots

2x + 5 = 0

2x + 5 - 5 = 0 - 5

2x = - 5

2x / 2 = - 5 / 2

x = - 5/2

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Roots

3x + 1 = 0

3x + 1 - 1 = 0 - 1

3x = - 1

3x / 3 = - 1/3

x = - 1/3

- - - - - - - -s-

Answer 2

remember the equation ax2 + bx + c = 0
find a*c, and it's factors (here a*c is +30, factors are 2,3,5). See if you can get "b" by adding/subtracting the factors. (5*3 + 2 = 17). Be careful, mind the sign (+/- of each, the product of a*c, b, and your factor sum. i.e., if ac is negative, your factor sum should be one negative, one positive, so that when multiplied, will give back the negative product, ac. also, the factor sum should add up to b, in the correct sign again). Then you'll get the equation in the form:
ax2 + b1x + b2x + c = 0 which can be factorised easily.
here: 6x2 + 15x + 2x + 5 = 0
or 3x(2x + 5) + 1(2x + 5) = 0
or (3x + 1)(2x + 5) = 0
therefore, x = -1/3 or x = -5/2
(when the product of any two real quantities is zero, either one or both of them has to be zero.)

Answer 3

No. You just have to guess and check
For example, you look at all the numbers that multiply to make 6 (your first number).
You have 1 and 6, 2 and 3
Next, the only numbers that multiply to make 5 are 1 and 5
So, try both:
(x + 5)(6x + 1)
and
(2x + 5)(3x + 1)
The first, you get 6x^2 + 31x +5. That's not right
The second, you get 6x^2 + 17x + 5
So, the second one is your answer.
:D

Answer 4

i do no longer have faith it truly is factored. If the 40 two replaced into useful, it must be factored. till somebody can locate something I ignored, i won't detect a aspects of -40 two that when elevated by technique of two upload as much as -26.

Answer 5

well 6x2 is 12.
12 squared is 144

so

144+7x+5=()()
okay so it should look like
7x+144+5

7x+149=0

divide by 7.