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प्रश्न
Show that (x + 2) is a factor of f(x) = x3 + 4x2 + x – 6.
बेरीज
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उत्तर
1. Identify the value of c:
Set the binomial equal to zero:
x + 2 = 0
⇒ x = –2
Therefore, c = –2.
2. Substitute x = –2 into the polynomial f(x):
f(–2) = (–2)3 + 4(–2)2 + (–2) – 6
3. Simplify the terms:
(–2)3 = – 8
4(–2)2 = 4(4) = 16
+(–2) = –2
4. Calculate the final result:
f(–2) = –8 + 16 – 2 – 6
f(–2) = 8 – 2 – 6
f(–2) = 0
Since f(–2) = 0, the remainder is zero. By the Factor Theorem, (x + 2) is ) verified as a factor of x3 + 4x2 + x – 6.
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