Question

HCF of 3x cube + x + 4 and 2x cube - x square + 3 is

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Answer 1

Answer:

x + 1

Step-by-step explanation:

Given polynomials are:

(i) 3x³ + x + 4

= 3x³ + 3x² - 3x² -3x + 4x + 4

= 3x²(x + 1) - 3x(x + 1) + 4(x + 1)

= (x + 1)(3x² - 3x + 4)

(ii) 2x³ - x² + 3

= 2x³ + 2x² - 3x² - 3x + 3x + 3

= 2x²(x + 1) - 3x(x + 1) + 3(x + 1)

= (x + 1)(2x² - 3x + 3)

∴ HCF(3x³ + x + 4, 2x³ - x² + 3) = (x + 1).

Hope it helps!