Question

2x^4-7x^3-13x^2+63x-45
find the factors step by step
please answer its urgent

Answer 1

Answer:

Step-by-step explanation:

p(x)=2x^4-7x^3-13x^2+63x-45

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)  

 (x - 1)(2x³ - 5x³ - 18x + 45)  

= (x - 1)[2x² (x - 3) + x(x - 3) - 15(x - 3)]

= (x - 1)(x - 3)(2x² + x - 15)

= (x - 1)(x - 3)(2x² + 6x - 5x - 15)  

= (x - 1)(x - 3)[2x(x + 3) - 5(x + 3)]  

⇒ p(x) = (x - 1)(x - 3)(x + 3)(2x - 5)