Factor the trinomial. If the trinomial cannot be found, say so.
11m^2 + 14m - 16
I just want to make sure...would the answer be (11m-8)(m+2) ?
Solve quadratic equation:
11 m ^2 + 14m - 16 = 0
The solutions are:
m1 = -2
m2= 8/11
Use formula for factoring quadratic equation:
a m ^ 2 + b m + c = a(m - m1)(m - m2)
Where m1 and m2 are solutions of quadratic equation
In our case we have:
11 m^ 2 + 14 m - 16 = 11(m - (-2)) (m - 8/11) that is
11 m^ 2 + 14 m - 16 = 11(m + 2)(m - 8/11)
We can simplify this expression by multiply the second bracket by 11.
After multiplying we have:
11 m^ 2 + 14 m - 16 = ( m + 2 )( 11 m - 8 )
To factor the trinomial 11m^2 + 14m - 16, we will use the factoring method called "ac method" or "splitting the middle term." Here's how you can do it:
1. Write down the trinomial in the form "am^2 + bm + c" with the coefficients a, b, and c.
In this case, a = 11, b = 14, and c = -16.
2. Multiply the coefficient of the squared term (a) by the constant term (c).
In this case, a * c = 11 * -16 = -176.
3. Find two numbers that multiply to give the result from step 2 (-176) and add up to the coefficient of the middle term (b), which is 14.
In this case, the numbers are -4 and 44, which multiply to -176 and add up to 14.
4. Rewrite the middle term (14m) using the numbers found in step 3 (-4 and 44), splitting it into two terms:
Rewrite 14m as -4m + 44m.
The trinomial becomes 11m^2 - 4m + 44m - 16.
5. Group the terms in pairs:
Rearrange the trinomial by grouping the first two terms together and the last two terms together:
(11m^2 - 4m) + (44m - 16).
6. Factor out the greatest common factor from each group:
Factor out m from the first group and 4 from the second group:
m(11m - 4) + 4(11m - 4).
7. Check if the terms in the parentheses are the same. If they are, you have successfully factored the trinomial.
In this case, both terms are 11m - 4.
The factored form of the trinomial 11m^2 + 14m - 16 is:
(11m - 4)(m + 4).
So, the answer would be (11m - 4)(m + 4), not (11m - 8)(m + 2).