how do you factor 6x^2+49x-45

Question

they all have a common factor of 1 but you wouldn't need to do that here so cant you just go ahead and factor the equation out?

Answer 1

Try using the quadratic equation formula

 

-b+-square root of b^2-4(a)(c)/2(a)

 

where a=6, b=49 and c=-45

 

-49+-square root of 

 

49^2-4(6)(-45)

2401-4(-270)

2401-(-1080)

=3481...find square root 

square root of 3481=59

 

(-49+59)/12=10/12=5/6=0.8333

(-49-59)/12=-9

 

x=0.8333,x=-9

 

these are the factors

Answer 2

your expression is 6x²+49x-45

FIRST look for greatest common factors. Do you see any (1 is not useful as a factor)? I don't.

SECOND look for special, recognizable cases, to save time. These are like a²+2ab+b² or a²-b², etc. I don't see any of these either.

Next, I like a method I call the product-sum method. I find factors of a*c that sum to to b.

Since our expression is in standard form, a=6, b=49, and c=-45.

I want factors of a*c=(6)*(-45)=-270

FACTORS OF -270:

2     -135

3      -90

5      -54

6      -45

9      -30

10    -27

15    -18

18    -15

27    -10

30     -9

45     -6

54     -5

90     -3

135   -2

 

Those are all the factor pairs I can find. Once you get used to this method you won't actually have to list them all. Do you see a pair that sums to b? Remember, b=49

I see that (54)+(-5)=49, so let's use that. We're going to split our middle term b into those two terms, which doesn't change anything but allows us to factor by grouping.

6x²+49x-45

6x²+54x-5x-45

Take a close look at how I split that middle term, how I didn't really change the value of the expression, and where I got those numbers.

Now, factor by grouping.

(6x²+54x)+(-5x-45)

What is the largest thing I can factor out of the first two terms? the last two terms?

6x(x+9)-5(x+9)

Now I can factor out the binomial (x+9) from both terms

(6x-5)(x+9)

 

Double check that this is the correct factorization by distributing these two binomials.

Answer 3

6x² + 49x - 45 = (6x-5)(x+9)

 

Basically, the x terms need to multiply to 6x² and the constant terms need to multiply to -45.  The difficult part is to find the right factors of 6 (6*1 and 3*2) and -45 (45*(-1), -45*1, 9*(-5), -9*5) to yield the +49x term.  Some trial and error using different factor combinations is usually needed until you find the right combination.