Question

Determine whether (x – 3) is a factor of polynomial x³ – 19x + 30.

Let P(x) = x³ – 19x + 30

By remainder theorem, `square` will be a factor of P(x), if P(3) = 0

Now, P(3) = `square` – 19 `square` + 30

= `square  –  square` + 30

= `square  –  square`

= 0

∵ P(3) = 0

Hence, `square` is a factor of polynomial x³ – 19x + 30.

Answer 1

Let P(x) = x³ – 19x + 30

By remainder theorem, x – 3 will be a factor of P(x), if P(3) = 0

Now, P(3) = (3)³ – 19 (3)  + 30

= 27 –  57 + 30

= 57 – 57

= 0

∵ P(3) = 0

Hence, x – 3 is a factor of polynomial x³ – 19x + 30.