Question

2X-5 IS A FACTOR OF 2X3-3X2-17+30 FIND THE OTHER FACTORS

Answer 1

Answer:

f(x) = 2x3 − 3x2 − 17x + 30If (x − 2) is a factor of f(x) then f(2) must be zeroNow, f(2) = 2 (2)3 − 3 (2)2 − 17 × 2 + 30 ⇒ f(2) = 2× 8 − 3 × 4 − 34 + 30 ⇒ f(2) = 16 − 12 − 34 + 30 ⇒ f(2) = 0Since f(2) = 0Hence, (x − 2) is a factor of f(x)Now, f(x) = 2x3 − 3x2 − 17x + 30 = 2x3 − 4x2 + x2 − 2x − 15x + 30 = 2x2 (x − 2) + x (x − 2) − 15 (x − 2) =(x − 2) (2x2 + x − 15) = (x − 2) {2x2 + 6x − 5x − 15} = (x − 2) {2x (x + 3) −5 (x + 3)} = (x − 2) {(x + 3) (2x − 5)} = (x − 2) (x + 3) (2x − 5)

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