Let h be a polynomial of degree 5, and suppose that h(x) = (x^2-7x+10)*g(x) where g(x) is a polynomial of degree b. Find b.

Guest Jul 15, 2023

#2**0 **

\(h(x)=(x^2-7x+10)*g(x) \\ \text{If h is a polynomial of degree 5, and it can be written as the product of two other polynomials} \\ \text{Then the sum of their highest powers must be 5.} \\ \text{Notice, the first term, namely, } \space\space x^2-7x+10 \space \text{has the highest power of "2"} \\ \text{Therefore, g(x) must be cubic polynomial. I.e. the highest power is "3"}. \\ \text{So,} \space\space 2+b=5 \iff b=3 \\ \text{I hope this helps, and do not hesitate to ask further questions.}\)

.Guest Jul 16, 2023