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Using the Reminder Theorem, Factorise of the Following Completely. 2x3 + X2 – 13x + 6 - Mathematics

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Question

Using the Reminder Theorem, factorise of the following completely.

2x3 + x2 – 13x + 6

Solution

Let f (x) = 2x3 + x2 − 13x + 6
For x = 2,
f(x) = f(2) = 2(2)3 + (2)2 − 13(2) + 6 = 16 + 4 − 26 + 6 = 0
Hence, (x − 2) is a factor of f(x).

∴ 2x^3 + x^2 - 13x + 6 = (x-2) (2x^2 + 5x -3)

= (x-2)(2x^2 + 6x -x -3)

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

= (x - 2)(x + 3) (2x - 1)

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APPEARS IN

Selina Solution for Concise Mathematics for Class 10 ICSE (2020 (Latest))
Chapter 8: Remainder and Factor Theorems
Exercise 8(B) | Q: 2.2 | Page no. 112
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Using the Reminder Theorem, Factorise of the Following Completely. 2x3 + X2 – 13x + 6 Concept: Factorising a Polynomial Completely After Obtaining One Factor by Factor Theorem.
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