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Question
When 3x2 – 5x + p is divided by (x – 2), the remainder is 3. Find the value of p. Also factorise the polynomial 3x2 – 5x + p – 3.
Solution
f(x) = 3x2 – 5x+ p
Let (x – 2) = 0, then x = 2
f(2) = 3 (2)2 – 5(2) + p
= 3 x 4 – 10 + p
= 12 – 10 + p
= 2 + p
∵ Remainder = 3
∴ 2 + p = 3
⇒ p = 3 – 2 = 1
Hence p = 1
Now f(x) = 3x2 – 5x + p – 3
= 3x2 – 5x + 1 – 3
= 3x2 – 5x – 2
Dividing by (x – 2), we get
`x - 2")"overline(3x^2 - 5x - 2)("3x + 1`
3x2 – 6x
– +
x – 2
x – 2
– +
x
3x2 – 5x – 2 = (x – 2)(3x + 1).
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