1.

Find the H.C.F. of p(x) = 2x3 – 3x2 – 2x + 3 and q(x) = 3x2 + 8x + 5.1. (x + 1)2. (x – 1)3. (2x – 3)4. (2x + 1)

Answer» Correct Answer - Option 1 : (x + 1)

Given:

p(x) = 2x3 – 3x2 – 2x + 3 and q(x) = 3x2 + 8x + 5

Concept:

H.C.F. of two or more equations is the greatest factor that divides each of them exactly.

Calculation:

The factors of p(x) = 2x3 – 3x2 – 2x + 3

⇒ x2 × (2x – 3) – 1 × (2x – 3)

⇒ (x2 – 1) × (2x – 3)

⇒ (x – 1) × (x + 1) × (2x – 3)

And, the factors of q(x) = 3x2 + 8x + 5

⇒ 3x2 + 5x + 3x + 5

⇒ x × (3x + 5) + 1 × (3x + 5)

⇒ (3x + 5) × (x + 1)

∴ The required H.C.F. is (x + 1).


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