Question

57. Show that x + 1 and 2x – 3 are factors of 2x3 - 9x2 + x + 12.

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Answer 1

Let p(x) = 2x3 – 9x2 + x + 12 [Note: Here the polynomial should be 2x3 – 9x2 + x + 12, not 2x3 – 9x3 + x + 12]

Consider, (x + 1)

Put x + 1 = 0 ⇒ x = – 1

Now, consider p(– 1) = 2(– 1)3 – 9(– 1)2 + (– 1) + 12 = – 2 – 9 – 1 + 12 = 0

∴ (x + 1) is a factor of p(x)

Now, consider 2x – 3 = 0

∴ (2x – 3) is a factor of p(x).

Hence, (x + 1) and (2x – 1) and factor of 2x3 – 9x2 + x + 12