Question

Examine whether x-1 ix a factor of the following polynomials
1)2x-5x²+x+2
2)4x + 5x2-3x+6​

Answer 1

Answer:

Let f(x) = x - 1

=> 0 = x - 1

=> x = 1

By reaminder theorem,

By substituting x in (1),

$2x - 5 {x}^{2} + x + 2 \\ = 2(1) - 5( {1})^{2} + 1 + 2 \\ = 2 - 5 + 1 + 2 \\ = 0$

Therefore, x - 1 is a factor of (1) as reaminder is 0.

By substituting x in (2),

$4x + 5 {x}^{2} - 3x + 6 \\ = 4(1) + 5( {1})^{2} - 3(1) + 6 \\ = 4 + 5 - 3 + 6 \\ = 12$

Therefore, x - 1 is not a factor of (2) as remainder is 12.

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