Question

what substitution should be used to rewrite 16(x³ + 1)² − 22(x³ + 1) − 3 = 0 as a quadratic equation?
○ u = (x³)
○ u = (x³ + 1)
○ u = (x³ + 1)²
○ u = (x³ + 1)³

Explanation:

To rewrite the equation \(16(x^{3}+1)^{2}-22(x^{3}+1)-3 = 0\) as a quadratic equation, we need to identify a substitution \(u\) such that the equation is in the form \(au^{2}+bu + c=0\). Notice that \((x^{3}+1)\) appears squared and to the first power. If we let \(u=(x^{3}+1)\), then \((x^{3}+1)^{2}=u^{2}\) and the equation becomes \(16u^{2}-22u - 3=0\), which is a quadratic equation.

Answer:

B. \(u=(x^{3}+1)\)