Question

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Answer 1

Answer:

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Answer 2

Qᴜᴇsᴛɪᴏɴ :-

show That, (2x + 7) is a factor of 2x³ + 5x² - 11x - 14. Hence Factorize the given Expression completely using the Factor Theorem. ?

Sᴏʟᴜᴛɪᴏɴ :-

→ f(x) = 2x³ + 5x² - 11x - 14

→ (2x + 7) = 0

→ 2x = (-7)

→ x = (-7)/2

So, By Remainder Theorem the Factor will give Remainder as 0.

f(-7/2) = 2x³ + 5x² - 11x - 14 = 0

→ 2(-7/2)³ + 5(-7/2)² - 11(-7/2) - 14 = 0

→ (-343/4) + 245/4 + (77/2) - 14 = 0

→ (-343/4 - 14) + (245/4) + (154/4) = 0

→ (-399/4) + (245/4) + (154/4) = 0

→ (-399/4) + 399/4 = 0

→ 0 = 0

Hence, we can conclude That, (2x + 7) ie a Factor of given Polynomial.

Now, Factorisation :-

→ 2x³ + 5x² - 11x - 14

→ x²(2x + 7) - x(2x + 7) - 2(2x + 7)

→ (2x + 7)(x² - x - 2)

→ (2x + 7)(x² + x - 2x - 2)

→ (2x + 7)[ x(x + 1) - 2(x + 1) ]

→ (2x + 7)(x - 2)(x + 1) (Ans.)