Class 9 Maths Polynomials Factor Theorem

Factor Theorem

 x – a is a factor of the polynomial p(x), if p(a) = 0. Also, if x – a is a factor of p(x), then p(a) = 0, where a is any real number. This is an extension to remainder theorem where remainder is 0, i.e. p(a) = 0.

Numerical: Examine whether x + 2 is a factor of p(x)= x3 + 3x2 + 5x + 6

Solution : The zero of x + 2 is –2.  As, per factor theorem, x+2 is factor of p(x) if p(-2) = 0.

 p(–2) = (–2)3 + 3(–2)2 + 5(–2) + 6 =  0.

Thus, x+2 is factor of p(x)= x3 + 3x2 + 5x + 6

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