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If p(x) = x2 + 3x + 1 and q(x) = 2x – 4, then

i. Find the degree of the polynomial p(x) q(x).

ii. If the degree of p(x) × r(x) is 5, then find the degree of the polynomial r(x) .

iii. If p(x) is a third degree polynomial and q(x) is a fourth degree polynomial then find the degree of p(x) × q(x).

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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.

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