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When x3 + 2x2 + 4x + b is divided by (x + 1), the quotient is x2 + ax + 3 and the remainder

(a) 1, 0 

(b) –1, 0 

(c) 1, 1 

(d) –1, –1

1 Answer

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Best answer

(a) 1, 0

Let f (x) = x3 + 2x2 + 4x + b. 

When divided by (x + 1), the remainder = f (–1) 

Given, remainder = – 3 + 2b 

∴ –3 + 2b = f (–1) = (–1)3 + 2 (–1)2 + 4 (–1) + b 

⇒ –3 + 2b = –1 + 2 – 4 + b 

⇒ –3 + 2b = –3 + b. 

This is only possible when b = 0. 

∴ f (x) = x3 + 2x2 + 4x. 

Now dividing f (x) by (x + 1), we see that

∴ Quotient = x2 + ax + 3 = x2 + x + 3 ⇒ a = 1.

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