If x – 3 is a factor of x2 – 6x + 12, then find the value of k. Also, find the other factor of the – polynomial for this value of k
Solution: Here, x – 3 is a factor of x2 – kx + 12 ∴ By factor theorem, putting x = 3, we have remainder 0. ⇒ (3)2 – k(3) + 12 = 0 ⇒ 9 – 3k + 12 = 0 ⇒ 3k = 21 ⇒ k = 7 Now, x2 – 7x + 12 = x2 – 3x – 4x + 12 = x(x – 3) – 4(x – 3) = (x – 3) (x – 4) Hence, the value of k is 7 and other factor is x – 4.
