if f(x) = 3x^3 + x-3 and g(x)= -3+4x+5x^2. Find a and b

Question

a)     (f+g)(x) 

b)      (f-g)(x)

Answer 1

f(x) = 3x³ + x - 3

g(x) = 5x² + 4x - 3

 

(f+g)(x) = f(x) + g(x)

 

= (3x³ + x - 3) + (5x² + 4x - 3)

 

Combine like terms:

 

= 3x³ + 5x² + (x + 4x) + (-3 - 3)

 

(f+g)(x) = 3x³ + 5x² + 5x - 6

 

(f*g)(x) = f(x)*g(x)

 

= (3x³ + x - 3)*(5x² + 4x - 3)

 

= 3x³*5x²+ 3x³*4x+ 3x³*(-3)+ x*5x²+ 4*4x+ x*(-3)+ (-3)*5x²+ (-3)*4x+ (-3)*(-3)

 

= 15x⁵ + 12x⁴ - 9x³ + 5x³ + 4x² - 3x -15x² - 12x + 9

 

Combine like terms:

 

= 15x⁵ + 12x⁴ + (-9x³ + 5x³) + (4x² - 15x²) + (-3x - 12x) + 9

 

= 15x⁵ + 12x⁴ - 4x³ -11x² -15x + 9