Q. 1 C4.0( 4 Votes )

# Let us calculate and write, which of the following polynomials will have a factor (x + 1)?

7x^{3} + x^{2} + 7x + 1

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

1^{st} we find out zero of polynomial x + 1

x + 1 = 0

x = – 1

if f(x) is 7x^{3} + x^{2} + 7x + 1

then putting x = – 1;

f( – 1) = 7( – 1)^{3} + ( – 1)^{2} + 7( – 1) + 1

= 7 × ( – 1) + 1 + 7 × ( – 1) + 1

= – 7 + 1 – 7 + 1

= – 12

Conclusion.

∴ (x + 1) is not a factor of 7x^{3} + x^{2} + 7x + 1

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