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If p(x) = x3 + 2x2 – 3x + 1 and q(x) = x3 – 2x2 + 3x + 5

(a) Find p(x) + q(x). What is its degree?

(b) Find p(x) – q(x). What is its degree?

1 Answer

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(a) p(x) = x3 + 2x2 – 3x + 1,

q(x) = x3 – 2x2 + 3x + 5

p(x) + q(x)

= x3 + 2x2 – 3x + 1 + x3 – 2x2 + 3x + 5

= 2x3 + 6

Degree = 3

(b) p(x) – q(x)

= x3 + 2x2 – 3x + 1 – (x3 – 2x2 + 3x + 5)

= x3 + 2x2 – 3x + 1 -x3 + 2x2 – 3x – 5

= 4x2 – 6x – 4

Degree = 2

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