Method to check whether(x – a), and (x + a)are factors of a polynomi

1.	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» 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

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»

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

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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

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