Question

Method to check whether(x – a), and (x + a)are factors of a polynomial P(x). 

Check whether (x + 2) and (x – 5) are factors of the polynomial p(x) = x² + 7x + 10

Answer 1

When a polynomial p(x) is divided by (x – a), if p(a) = 0 then (x – a) is a factor of p(x). 

When a polynomial p(x) is divided by (x + a),

if p(–a) = 0 then (x + a) is a factor of p(x).

p(x) = x² + 7x + 10 p(–2) = 4 – 14 + 10 = 0 (1)

\(\therefore\) x + 2 is a factor (1)

Remainder p(5) = (5)² + 7(5) +10 (1) 

= 25 + 35 + 10 ≠ 0 (1) 

\(\therefore\) x – 5 is not a factor