+1729 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 + ___
+291 3x2+12x+4−x3+8x−5x+7x2+11
We can simplify this:
−x3+10x2+15x+15
We have:
−x3+10x2+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.
+291 3x2+12x+4−x3+8x−5x+7x2+11
We can simplify this:
−x3+10x2+15x+15
We have:
−x3+10x2+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.
