SOLUTION: hi the type of homework i have is called " factoring complex quadratics" the equation is m^2+18m+77. my teacher had us do this square with four boxes that you work with (im sorry i

Question 756174: hi the type of homework i have is called " factoring complex quadratics" the equation is m^2+18m+77. my teacher had us do this square with four boxes that you work with (im sorry i forgot with its called) so i put m^2 into the top left side and the 77 in the bottom right corner. then im supposed to make an X chart and i put 77m^2 on the top and the 18m on the bottom leaving the two sides blank, im supposed to find out two numbers that make 77 and 18 but i cant figure it out and its taking forever, i hope you get what i am talking about. please help.
Answer by josgarithmetic(39617) (Show Source): You can put this solution on YOUR website!
The description you give of the process is like an attempt to factorize the given quadratic expression. By just looking at the polynomial , we might not know if it uses complex roots or complex binomial factors; maybe it does.

So you want two numbers, like u and v so that uv=77 and u+v=18. The idea is that . We will still get another quadratic equation in trying to find u and v.

Try first, all the factorizations for 77. What are they?
and . The second one does not promise much help. Let's try seeing what the first one will do for us:

Will the product be 77 and the sum be 18?
as we expect.
which is what we also wanted.
The numbers for u and v then are and .

The factorization for your given quadratic expression is .

---------------------------------------------------------

::: You WERE trying to put entries into a grid arrangment, so let's look at that.

_________m___________(___)________
-
-
m_______m^2__________(___)____
-
-
(__)____(___)_________77______

And maybe you are trying to fill in like this?....

_________m___________(u_)________
-
-
m_______m^2__________(u*m_)____
-
-
(v)____(v*m_)_________77______

That might help you to see how the terms occur in the multiplication process but you would still need to show combining the terms of m so as to say um+vm=18m which is how you knew that you want u+v=18.

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