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Use the Remainder Theorem to Find Which of the Following is a Factor of 2x3 + 3x2 – 5x – 6. 2x – 1 - ICSE Class 10 - Mathematics

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Question

Use the Remainder Theorem to find which of the following is a factor of 2x3 + 3x2 – 5x – 6. 

2x – 1 

Solution

By remainder theorem we know that when a polynomial f (x) is divided by x – a, then the remainder is f(a).  

Let f(x) = 2x3 + 3x2 – 5x – 6 

`f(1/2)=2(1/2)^3+3(1/2)^2-5(1/2)-6` 

`1/4+3/4-5/2-6`  

`-5/2-5=-15/2`≠0 

Thus, (2x – 1) is not a factor of the polynomial f(x)

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Solution Use the Remainder Theorem to Find Which of the Following is a Factor of 2x3 + 3x2 – 5x – 6. 2x – 1 Concept: Remainder Theorem.
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