how do you factor
m^3+5m^2+3m-9
it might be simple i am not seeing it..
please help so i can continue with the problem...thanks
Well, by inspection, I see that m=1 works, so divide m-1 into the polynomial to see what is left.
okey i am confused. We are suppose to solve for what m is equal to...i thought we could factor by grouping...but didn't know exactly how..please explain
one factor is by inspection (m-1)
Divide then m^3+5m^2+3m-9 by (m-1) and you will have the second factor, which I suspect can then be factored easily.
i honestly don't see how u divid it and u get the answer...please explain in detail
You can also use the Rational Roots Theorem. If m = p/q is a solution, then p has to be a divisor of -9 and q a divisor of 1 (-9 is the constant term and 1 is the coefficient of the highest power of m).
This means that all rational solutins must be divisors of 9.
So, you only have to try m = 1, m = -1, m= 3, m = -3, m = 9 and m = -9.
I besides m = 1, m = -3 is a solution. If you had found no other solution besides m = 1, then that would have menat that the other solutioins are not rational numbers. If we find one other, then that means that the remaining one must also be a rational number. But if only m = 1 and m = -3 are the possible rational solutions, this means that one of the roots is a double root.
In this case, you fiund that m = -3 is the double root, and the factorization is:
(m-1)(m+3)^2
To factor the expression m^3 + 5m^2 + 3m - 9, we can follow these steps:
Step 1: Look for common factors, if any.
In this case, there are no common factors among the terms.
Step 2: Group the terms.
Sometimes, grouping the terms can help us identify patterns or common factors. Let's pair the terms:
(m^3 + 5m^2) + (3m - 9)
Step 3: Factor out the greatest common factor (GCF) from each pair.
From the first pair of terms (m^3 + 5m^2), we can factor out an m^2 since it is the highest exponent common to both terms:
m^2(m + 5)
From the second pair of terms (3m - 9), we can factor out a 3:
3(m - 3)
Step 4: Combine the factored terms.
Now we have m^2(m + 5) + 3(m - 3)
And that's the factored form of the expression m^3 + 5m^2 + 3m - 9.