Question

1. If (x - 2) is a factor of 2x3 – x2 - px - 2
(a) find the value of p, and
(b) with the value of p, factorize the above expression completely.​

Answer 1

Answer:

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Step-by-step explanation:

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Answer 2

Answer:

• The value of p is 5.
• The Factors of 2x³ - x² - 5x - 2 are x - 2, x + 1 and 2x + 1.

Step-by-step explanation:

Given,

• (x - 2) is a factor of 2x³ - x² - px - 2.

To Find,

• The value of p.
• With the value of p, All Factors.

Solution,

g(x) = x - 2 is a factor of p(x) = 2x³ - x² - px - 2.

g(x) = x - 2

• So, x = 2

Putting this value of x in p(x),

• → p(x) = 2x³ - x² - px - 2
• → p(2) = 2(2)³ - (2)² - p(2) - 2
• → 0 = 2(8) - 4 - 2p - 2
• → 2p = 16 - 4 - 2
• → 2p = 10
• → p = 5

The value of p is 5.

Putting This value of p in p(x),

• → p(x) = 2x³ - x² - px - 2
• → p(x) = 2x³ - x² - 5x - 2

Factorisation of p(x),

• → 2x³ - x² - 5x - 2
• → 2x³ - 4x² + 3x² - 5x - 2
• → 2x²(x - 2) + 3x² - 6x + x - 2
• → 2x²(x - 2) + 3x² - 6x + x - 2
• → 2x²(x - 2) + 3x(x - 2) + 1(x - 2)
• → (x - 2)(2x² + 3x + 1)
• → (x - 2)(2x² + 2x + x + 1)
• → (x - 2)(2x(x + 1) + 1(x + 1)
• → (x - 2)(x + 1)(2x + 1)

The Factors of 2x³ - x² - 5x - 2 are x - 2, x + 1 and 2x + 1.

Required Answer,

• The value of p is 5.
• The Factors of 2x³ - x² - 5x - 2 are x - 2, x + 1 and 2x + 1.