Question

With out division prove that x^4+2x^3-2x^2+2x-3 is exactly divisible by x^2+2x-3

Answer 1

Answer: H.P

Step-by-step explanation:

Hence by converse of factor theorem, (x + 3) is a factor of p(x). Hence by converse of factor theorem, (x - 1) is a factor of p(x). ⇒ p(x) is exactly divisible by (x2 + 2x - 3).

Let p(x) = [latex]x^{4} + 2x^{3} – 2x^{2} – 3[/latex]

=[latex] p(-3) = (-3)^{4} + 2(-3)^{3} – 2(-3)^{2} – 3[/latex]

= 81 – 54 – 18 – 6 – 3

= 0

Therefore, by the converse of factor theorem, (x+3)is a factor pf p(x)

Let p(1) =[latex] (1)^{4} + 2(1)^{3} – 2(1)^{2} + 2(1) – 3[/latex]

= 1 + 8 – 4 + 2 – 3

= 9 – 6 – 3=0

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