Question

in the polynomial $(ax^6 bx^8 cx^3 d)(x^5 ex^4 f)(x^2 gx h)$, letters $a$ through $h$ are all nonzero constants. what is the degree of the polynomial?

Answer 1

I assume you mean the polynomial

`(ax^6 + bx^8 + cx^3 + d) (x^5 + ex^4 + f) (x^2 + gx + h)`

The degree of this polynomial is the exponent of the largest power of
`x` in the expansion of the product.

This term is the product of the largest power terms in each factor. These are

`ax^6 + bx^8 + cx^3 + d \implies bx^8`

`x^5 + ex^4 + f \implies x^5`

`x^2 + gx + h \implies x^2`

So, the largest power term in the polynomial is

`bx^8 \cdot x^5 \cdot x^2 = bx^(15)`

and the degree is 15.