factorise 2x4 - 7x3 - 13x2 +63x - 45
Answers
Answer:
p(x) = 2x4 - 7x3 - 13x2 + 63x - 45
Step-by-step explanation:
45 ⇒ ±1,±3,±5,±9,±15,±45
if we put x = 1 in p(x)
p(1) = 2(1)4 - 7(1)3 - 13(1)2 + 63(1) - 45
2 - 7 - 13 + 63 - 45 = 65 - 65 = 0
∴ x = 1 or x - 1 is a factor of p(x).
Similarly, if we put x = 3 in p(x)
p(3) = 2(3)4 - 7(3)3 - 13(3)2 + 63(3) - 45
162 - 189 - 117 + 189 - 45 = 162 - 162 = 0
Hence, x = 3 or x - 3 = 0 is the factor of p(x).
p(x) = 2x4 - 7x3 - 13x2 + 63x - 45
∴ p(x) = 2x3 (x - 1) -5x2 (x - 1) - 18(x - 1) + 45(x - 1)
2x4 - 2x3 (x - 1) - 5x2 - 18x2 + 18x + 45x - 54
⇒ p(x) = (x - 1)(2x3 - 5x2 - 18x + 45)
⇒ p(x) = (x - 1)(2x3 - 5x2 - 18x + 45)
⇒ p(x) = (x - 1)[2x2 (x - 3) + x(x - 3) - 15(x - 3)]
⇒ p(x) = (x - 1)[2x3 - 6x2 + x2 - 3x - 15x + 45]
⇒ p(x) = (x - 1)(x - 3)(2x2 + x - 15)
⇒ p(x) = (x - 1)(x - 3)(2x2 + 6x - 5x - 15)
⇒ p(x) = (x - 1)(x - 3)[2x(x + 3) - 5(x + 3)]
⇒ p(x) = (x - 1)(x - 3)(x + 3)(2x - 5)