SOLUTION: help me solve equation (3x^2+49x+72) in form (3x+ ) (x+ )

Question 320559: help me solve equation (3x^2+49x+72) in form (3x+ ) (x+ )
Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!

Looking at the expression , we can see that the first coefficient is , the second coefficient is , and the last term is .

Now multiply the first coefficient by the last term to get .

Now the question is: what two whole numbers multiply to (the previous product) and add to the second coefficient ?

To find these two numbers, we need to list all of the factors of (the previous product).

Factors of :
1,2,3,4,6,8,9,12,18,24,27,36,54,72,108,216
-1,-2,-3,-4,-6,-8,-9,-12,-18,-24,-27,-36,-54,-72,-108,-216

Note: list the negative of each factor. This will allow us to find all possible combinations.

These factors pair up and multiply to .
1*216 = 216
2*108 = 216
3*72 = 216
4*54 = 216
6*36 = 216
8*27 = 216
9*24 = 216
12*18 = 216
(-1)*(-216) = 216
(-2)*(-108) = 216
(-3)*(-72) = 216
(-4)*(-54) = 216
(-6)*(-36) = 216
(-8)*(-27) = 216
(-9)*(-24) = 216
(-12)*(-18) = 216

Now let's add up each pair of factors to see if one pair adds to the middle coefficient :

First Number	Second Number	Sum
1	216	1+216=217
2	108	2+108=110
3	72	3+72=75
4	54	4+54=58
6	36	6+36=42
8	27	8+27=35
9	24	9+24=33
12	18	12+18=30
-1	-216	-1+(-216)=-217
-2	-108	-2+(-108)=-110
-3	-72	-3+(-72)=-75
-4	-54	-4+(-54)=-58
-6	-36	-6+(-36)=-42
-8	-27	-8+(-27)=-35
-9	-24	-9+(-24)=-33
-12	-18	-12+(-18)=-30

From the table, we can see that there are no pairs of numbers which add to . So cannot be factored.

===============================================================

Answer:

So doesn't factor at all (over the rational numbers).

So is prime.

Make sure that you have the correct problem.

RELATED QUESTIONS
Please help me solve this equation: {{{ 49x^2 = 28x... (answered by Alan3354)

Please help me solve the foci in this equation... (answered by robertb)

please help me solve this equation: rewrite {{{ x^2= -3x+4 }}} in standard form. then... (answered by stanbon,mananth)

please help me solve this: rewrite {{{ 3x^2+x=-4x+5 }}} in standard form. then solve the... (answered by josgarithmetic)

please help me solve this equation in vertex form y=3x^2-6x+10 (answered by Edwin McCravy)

please help me solve this equation:... (answered by checkley71)

please help me solve this equation: 3x-2=x... (answered by Earlsdon)

Please help me solve this equation: f(x)=1/3x-2, reflection in the... (answered by davidb52)

Please help me solve this equation : {{{ x^2-3x+3=0}}} Find all solutions and express... (answered by ikleyn)