Question 1145990: How do you factor this trinomial using the Guess and Check Method 3x^2+16x+5? Thank you for your help.
Found 2 solutions by richwmiller, Theo:
Answer by richwmiller(17219)   (Show Source):
You can put this solution on YOUR website! 3x^2+16x+5
The first term is, 3x^2 its coefficient is 3 .
The middle term is, +16x its coefficient is -16 .
The last term, "the constant", is +5
Step-1 : Multiply the coefficient of the first term by the constant 3 * 5 = 15
Step-2 : Find two factors of 15 whose sum equals the coefficient of the middle term, which is +16 .
15 + 1 = 16
Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above, 15 and 1
3x^2 + 15x + 1x +5
Step-4 : Add up the first two terms, pulling out like factors :
3x * (x+5)
Add up the last two terms, pulling out common factors :
1 * (x+5)
Step-5 : Add up the four terms of step 4 :
(3x+1)*(x+5)
Answer by Theo(13342)  (Show Source):
You can put this solution on YOUR website! guess and check means you take a guess and then check to see if that is a solution.
if it's high, then you adjust the number to get a lower answer.
if it's low, then you adjust the number to get a higher number.
since a solution to the quadratic makes the value of the quadratic equation equal to 0, then we can substitute values to see what value makes the quadratic equation equal to 0.
i tried x = 1 and got 24
i tried x = -1 and got -8.
0 has to be between there, so i started narrowing down.
i tried x = x = 0 and got 5.
the solution had to be between x = 0 and x = -1
i tried x = -.5 and got -2.25
the solution had to be between x = 0 and x = -.5
i tried x = -.25 and got 1.1875
the solution had to be between x = -.25 and x = -.5
it took a while, but i finally narrowed it down to x = -1/3.
that got 0 which means that x = -1.3 is a solution to the quadratic equation.
if x = -1/3 is a solution, then you do the following to get one of the factors.
multiply both sides of this equation by 3 to get 3x = -1
add 1 to both sides of this equation to get 3x + 1 = 0
that means that (3x + 1) is one of the factors.
one of the factors of 3x^2 + 16x + 5 is 3x + 1.
to find the other factor, you can divide 3x^2 + 16x + 5 by (3x + 1) and you will get the other factor equal to x + 5.
the factors of the quadratic are therefore (3x + 1) * (x + 5) = 0 which will get you 3x^2 + 16x + 5 = 0
you could also have used guess and check to get the other factor.
i9 tried x = -2 and got 15
i tried -5 and got 0.
srerendipity - i goe a soluti0on without having to do a lot more work.
since x = -5, find the factor as follows:
start with x = -5
add 5 to both sides of the equation to get x + 5 = 0
x + 5 is the other factor.
guess and check is very inefficient and cumbersome and probably best done with the aid of a computer to narrow the possible solutions down rapidly until they converge on a solution.
it can be used on simple quadratics but is not recommended to use on anything complex.
the quadratic equation given in this problem would probably be considered too complex to try and solve using guess and check.
i got lucky and i cheated a little to see what the answer should be so i didn't spend hordes of time to find the solution using that method.
another source from the web recommends the following:
Guess-and Check Method
i. List the factors of the coefficient of the x2 term
ii. List the factors of the constant term
iii. Test all the possible binomials you can make from these factors
using this recommendation, i did the following.
the factors of the x^2 term are 1 and 3.
the factors of the constant term are 1 and 5.
i listed the possible factors.
3x + 1
3x + 5
x + 1
x + 5
i tried (3x + 1) * (x + 1) and got 3x^2 + 4x + 1.
i tried (3x + 1) * (x + 5) and got 3x^2 + 16x + 5 *****
these are the factors.
this method will not work all the time, especially if the quadratic can't be factored without the use of the quadratic formula.
if all else fails, use the quadratic formula.
it will provide a solution regardless if the solution is real or imaginary or complex.
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