Yuri thinks that [image 1] is a root of the following function.q(x) = 6x3 + 19x2 – 15x – 28Explain to Yuri why [image 2] cannot be a root.

Answer:

According to the rational root theorem, potential rational roots must be in theform where p is a factor of the constant term and q is a factor of the leading coefficient. 3 is not a factor of 28, and 4 is not a factor of 6. So, does not satisfy the rational root theorem. Substituting in for x does not result in 0. The remainder is not 0 when dividing by x –