+1418 Fill in the blanks with numbers to make a true equation
3x^2 + 12x + 4 - x^3 + 8x - 5x + 7x^2 + 11 = __ (x + __)^3 + __(x + __)^2 + __x + ___
+289 \(3x^2 + 12x + 4 - x^3 + 8x - 5x + 7x^2 + 11 \)
We can simplify this:
\(-x^3+10x^2+15x+15\)
We have:
\(-x^3+10x^2+15x+15= a(x+b)^3+c(x+d)^2+ex+f\)
a must equal -1 and b must equal 0 to get -x^3
c must equal 10 and d must equal 0 to get 10x^2
e must equal 15
f must equal 15
Answer, -1 , 0 , 10 , 0 , 15 , 15
I think that this is the only set of numbers that can fill in the blanks, although it is possible that there could be other values for b and d, which could also change e or f, but probably this is the only answer.
+289 \(3x^2 + 12x + 4 - x^3 + 8x - 5x + 7x^2 + 11 \)
We can simplify this:
\(-x^3+10x^2+15x+15\)
We have:
\(-x^3+10x^2+15x+15= a(x+b)^3+c(x+d)^2+ex+f\)
a must equal -1 and b must equal 0 to get -x^3
c must equal 10 and d must equal 0 to get 10x^2
e must equal 15
f must equal 15
Answer, -1 , 0 , 10 , 0 , 15 , 15
I think that this is the only set of numbers that can fill in the blanks, although it is possible that there could be other values for b and d, which could also change e or f, but probably this is the only answer.
