Answer :
The factor theorem, factorize: p(x) = 2x^4- 7x^3-13x² +63x-45 is p(x) = (x - 1)(x-3)(x + 3)(2x-5). Therefore, option B. p(x) = (x - 1)(x-3)(x + 3)(2x - 5) is correct.
45±1, ±3, ±5, ±9, ±15, ±45
If we put x = 1 in p(x)
p(1) = [tex]2(1)^4-7(1)^3-13(1)^2 +63(1)-45[/tex]
p(1)=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) =[tex]2(3)^4-7(3)^3-13(3)^3 +63(3) -45[/tex]
p(3) = 162-189-117+189-45=162-162 = 0
Hence, x = 3 or (x - 3) = 0 is the factor of p(x).
p(x) =[tex]2x^4-7x^3-13x^2 +63x-45[/tex]
: p(x) = [tex]2x^3(x-1)-5x^2(x-1) - 18x(x-1) + 45(x-1)[/tex]
⇒ p(x) =[tex](x - 1)(2x^3-5x^2-18x + 45)[/tex]
⇒ p(x) = [tex](x - 1)(2x^3-5x^2-18x + 45)[/tex]
⇒ p(x) = (x-1)[2x²(x-3) + x(x-3)-15(x-3)]
⇒ 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).
Question
Using factor theorem, factorize: p(x) = 2x^4- 7x^3-13x² +63x-45
A. p(x) = (x - 1)(x + 3)(2x-5) -
B. p(x) = (x - 1)(x-3)(x + 3)(2x - 5)
C. p(x) = (x + 1)(x-3)(x+3)(2x + 5)
D. p(x) = (x - 1)(x-3)(2x-5)
