Question

Find the H.C.F. of the following by division method,
x³ + 3x² – 16x+ 12,
x³ + x² - 10x + 8



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Answer 1

Answer:

x² - 3x + 2

Step-by-step explanation:

f(x) = x³ + 3x² – 16x + 12

Check 1 and (- 1) for zeros of polynomial function.

f(1) = 1³ + 3 × 1² - 16 × 1 + 12 = 0 (Bingo) ⇒ (x - 1) is the factor of f(x).

(x³ + 3x² – 16x + 12) ÷ (x - 1) = x² + 4x - 12 = (x + 6)(x - 2)

x³ + 3x² – 16x + 12 = (x - 2)(x - 1)(x + 6)

g(x) = x³ + x² - 10x + 8

g(1) = 1³ + 1² - 10 × 1 + 8 = 0

(x³ + x² - 10x + 8) ÷ (x - 1) = x² + 2x - 8 = (x + 4)(x - 2)

x³ + x² - 10x + 8 = (x - 2)(x - 1)(x + 4)

GCF(f(x), g(x)) = (x - 2)(x - 1) = x² - 3x + 2