SOLUTION: If 40x^2 + 102x + c = (4x + 13)( ax + b) , what is the value of c?

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Question 1089863: If 40x^2 + 102x + c = (4x + 13)( ax + b) , what is the value of c?
Answer by EMStelley(208) About Me  (Show Source):
You can put this solution on YOUR website!
40x%5E2+%2B+102x+%2B+c+=+%284x+%2B+13%29%28ax+%2B+b%29
Simplifying the right hand side, we have
40x%5E2+%2B+102x+%2B+c+=+4ax%5E2+%2B+4bx+%2B+13ax+%2B+13b
40x%5E2+%2B+102x+%2B+c+=+4ax%5E2+%2B+%284b+%2B+13a%29x+%2B+13b
Now, notice that we have an x^2 term on each side, an x term on each side, and a constant term on each side. Because the two sides are equal to each other, each of the individual terms must be equal. So, for the x^2 term, we have that:
40x%5E2+=+4ax%5E2
a+=+10
For the x term, we have:
102x+=+%284b+%2B+13a%29x
102+=+4b+%2B+13
102%2F13+=+4b
b+=+102%2F52+=+51%2F26
And lastly, for the constant term, we have:
c+=+13b
And we have a value for b, so
c+=+13%2A%2851%2F26%29+=+51%2F2