Question

What substitution should be used to rewrite 16(x^3 + 1)^2 - 22(x^3 + 1) -3=0 as a quadratic equation?

1) u=(x^3)
2) u=(x^3+1)
3) u=(x^3+1)^2
4) u=(x^3+1)^3

Answer 1

"2"

Explanation:

The quadratic equation has the form:

`ay^2 + by + c`

Looking at the expression given, if we can replace "(x^3 + 1)" with another variable, such as u, then it will create a quadratic equation in the form shown above.

Let's replace "(x^3 + 1)" with u and check if it creates a quadratic:

`16(x^3 + 1)^2 - 22(x^3 + 1) -3=0\\16u^2 -22u-3=0`

yes, this works because the equation we got in u falls in the quadratic category.

Answer choice 2 is right.