Question

Factor -16t^2 +128t+50? I got this far: 2(-8t^2+64t+25) This is where I'm stuck. Please help and give me tips on how to solve similar problems. Thank you

Answer 1

Do you know how to solve quadratic equations?

Answer 2

Yes, but I am supposed to solve this by factoring. I wish I could used the quadratic eqauation

Answer 3

Good, you can use this skill to solve these type of problems. What you want to do is to find the roots of the polynomial. Then you can write the polynomial on the form
\[(x−a)(x−b)\]
Where a and b are the roots. For example if we have
\[x^2+x−2\]

It has the roots 1 and -2. So it is the same as (x-1)(x+2) or
\[x^2+x−2=(x−1)(x+2)\]

So we have factored it!

Answer 4

This can be done using one of the following methods:

First:
Let f(t)=-16t^2 +128t+50 (function)
Replace t by a number until you obtain zero

Example: f(2)=0 then (t-2) is a factor of f(t)
Then the following factor is easy to obtain.

Second:
Use this formula:
\[t=(-b \pm \sqrt{b ^{2}-4ac})\div2a\]
a=-16, b=128 and c=50

Answer 5

Thanks. I'm still rather lost. My professor said something about taking the sum of a and c and making that the product and making c the sum to factor and I'm still lost

Answer 6

Try to solve the equation
\[ -16t^2 +128t+50=0 \]
That is, find the polynomial's roots. When you have got the roots you can use the formula I gave you above to find it's factors.

Answer 7

Take x^2-5x+6 for example

Answer 8

6=-2 x -3
-5= -2 + -3

Thus x^2-5x+6=(x-2)(x-3)

Answer 9

Ok Thanks