Question

What should be added to the quadratic polynomial x²-5x+4 so that 3 is a zero of the resulting polynomial ?

Answer 1

P(x) = x² - 5x + 4

P(3) = 3² - 5*3 + 4

P(3) = 9- 15 + 4

P(3) = -2

Since, -2 is the remainder,

Therefore, 2 must be added to P(x) So that 3 will be a zero of the polynomial.

Verification:

P(x) = x² - 5x + 4

Adding 2,

P(x) = x²- 5x + 6

P(3) = 3² - 5*3 + 6

P(3) = 9 - 15 + 6

P(3) = 15-15

P(3) = 0

Hence, 2 is supposed to be added to the polynomial, for 3 to become a zero of the polynomial.