Question

When a polynomial p(x) is divided by x+3 the quotient is x^2-x+5 and the remainder is 2. find p(x)?

Answer 1

p(x) ÷ (x +3) = (x² - x + 5) + 3/(x + 3)

p(x) = (x + 3)(x² - x + 5) + 3                      multiplied both sides by (x + 3)

p(x) = x(x² - x + 5) + 3(x² - x + 5) + 3        multiplied (x + 3) and (x² - x + 5)  

p(x) = (x³ - x² + 5x) + (3x² - 3x + 15) + 3    distributed (x) and (3)

p(x) = x³ + 2x² + 2x + 18                             added like terms

Answer:  p(x) = x³ + 2x² + 2x + 18

Answer 2

$p(x)=( x+3)(x^2-x+5)+2\\\\ p(x)=x^3-x^2+5x+3x^2-3x+15+2\\\\ p(x)=x^3+2x^2+2x+17$