Question

If P(x) = 3x² + x² - 1 and Q(x) = 2x³ + x² + 1, find an expression for

1) P(x) + Q(x)
2) 3P(x) +Q(x)
3) P(x) - 2Q (x)
4) P(x)Q(x)

Answer 1

Explanation:

arithmetic operations on functions are done with their expressions, and all just normally. nothing special.

and I am sure you made a typo :

P(x) = 3x³ + x² - 1

right ?

1.

P(x) + Q(x) = (3x³ + x² - 1) + (2x³ + x² + 1) =

= 3x³ + x² - 1 + 2x³ + x² + 1 =

= 5x³ + 2x²

2.

3P(x) + Q(x) = 3(3x³ + x² - 1) + (2x³ + x² + 1) =

= 9x³ + 3x² - 3 + 2x³ + x² + 1 =

= 11x³ + 4x² - 2

3.

P(x) - 2Q(x) = (3x³ + x² - 1) - 2(2x³ + x² + 1) =

= 3x³ + x² - 1 - 4x³ - 2x² - 2 =

= -x³ - x² - 3

4.

P(x)Q(x) = (3x³ + x² - 1) × (2x³ + x² + 1) =

= 6x⁶ + 3x⁵ + 3x³ + 2x⁵ + x⁴ + x² - 2x³ - x² - 1 =

= 6x⁶ + 5x⁵ + x⁴ + x³ - 1