Use the Remainder Theorem to find which of the following is a factor of 2x^3+3x^2-5x-6

Olszarv5h

Olszarv5h

Answered question

2023-02-02

Use the Remainder Theorem to find which of the following is a factor of 2 x 3 + 3 x 2 5 x 6
(1) x+1 (2) 2x-1 (3) x+2

Answer & Explanation

usifaneledv2

usifaneledv2

Beginner2023-02-03Added 10 answers

By remainder theorem we know that when a polynomial f (x) is divided by x - a, then the remainder is 0.
Let f ( x ) = 2 x 3 + 3 x 2 5 x 6
(1) f ( 1 ) = 2 ( 1 ) 3 + 3 ( 1 ) 2 5 ( 1 ) 6 = 2 + 3 + 5 6 = 0
Therefore, (x + 1) is a factor of the polynomial f(x).
(2) f ( 1 2 ) = 2 ( 1 2 ) 3 + 3 ( 1 2 ) 3 5 ( 1 2 ) 6
= 1 4 + 3 4 + 5 6 6
= 5 2 5 = 15 2 0
Therefore, (2x - 1) is not a factor of the polynomial f(x).
(3) f ( 2 ) = 2 ( 2 ) 3 + 3 ( 2 ) 2 5 ( 2 ) 6 = 16 + 12 + 10 6 = 0
Hence, (x + 2) is a factor of the polynomial f(x).

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