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# Algebra

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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 + ___

Jan 12, 2024

#1
+289
+1

\(3x^2 + 12x + 4 - x^3 + 8x - 5x + 7x^2 + 11 \)

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.

Jan 12, 2024

#1
+289
+1

\(3x^2 + 12x + 4 - x^3 + 8x - 5x + 7x^2 + 11 \)

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.

DS2011 Jan 12, 2024