i. p(x) = x2 + 3x + 1 , q(x) = 2x – 4
p(x) × q(x) = (x2 + 3x + 1) (2x – 4)
The degree of p(x) x q(x) is 3.
ii. p(x) = x2 + 3x + 1 is a second degree polynomial.
If the degree of the polynomial p(x) × r(x) is 5, then p(x) × r(x) must have a term of x5 .
x2 × x3 = x5
So, r(x) is a third-degree polynomial.
iii. If p(x) is a third-degree polynomial, then p(x) must have a term of x3
q(x) is a fourth-degree polynomial, then q(x) must have a term of x4
Then in p(x) × q(x), must have a term of x3 × x4 = x7
So p(x) × q(x) is a seventh-degree polynomial. In general,
If p(x) is an mth degree polynomial and q(x) is an n,h degree polynomial then p(x) × q(x) is an (m + n),h degree polynomial.