Question

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Let m = x^2+3
Which equation is equivalent to (x^2+3)^2+7x^2+21=-10 in terms of m?
A. m^2+7m+10=0
B. m^2-7m+10=0
C. m^2+7m+31=0
D. m^2-7m+31=0

Answer 1

A. m^2+7m+10=0

Explanation:

This is a problem in pattern matching, and in substituting a variable for a pattern.

(x^2+3)^2 +7x^2 +21 = -10 . . . . . . given

(x^2 +3)^2 +7(x^2 +3) = -10 . . . . . factor the last two terms

m^2 +7m = -10 . . . . . . . . . . . . subsitute m for x^2 +3

m^2 +7m +10 = 0 . . . . . . . . add 10 to both sides; matches A