Q. 1 D5.0( 1 Vote )
Let us calculate and write, which of the following polynomials will have a factor (x + 1)?
3 + 3x – 5x3 – 5x4
Answer :
Formula used.
If f(x) is a polynomial with degree n
Then (x – a) is a factor of f(x) if f(a) = 0
1st we find out zero of polynomial x + 1
x + 1 = 0
x = – 1
if f(x) is 3 + 3x – 5x3 – 5x4
then putting x = – 1;
f( – 1) = 3 + 3( – 1) – 5( – 1)3 – 5( – 1)4
= 3 + 3 × ( – 1) – 5 × ( – 1) – 5 × 1
= 3 – 3 + 5 – 5
= 0
Conclusion.
∴ (x + 1) is a factor of 3 + 3x – 5x3 – 5x4
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