Question

Examine whether x-1 is a factor of 2x 3 -5x 2 +x+2.

Answer 1

Step-by-step explanation:

your answer is p(x) = 0 is the answer

Answer 2

( x - 1 ) is a factor of 2x³ - 5x² + x + 2.

Given: The expression 2x³ - 5x² + x + 2 and the expression ( x - 1 ).

To Find: Whether ( x - 1 ) is a factor of 2x³ - 5x² + x + 2.

Solution:

• Whenever we are required whether a given expression or value is a factor of a given expression, we need to implement the remainder theorem.

• The remainder theorem states that, if we divide a polynomial P(x) by a factor ( x – a); that isn’t essentially an element of the polynomial; and if we get the result of the function to be zero, then we can conclude that the expression is a factor of P(x).

• This can be shown as;

          P(x) = ax² + bx + c

      ⇒ P (a) = 0  

So, ( x - a ) is a factor of P(x).

Coming to the numerical, we are given;

The expression = 2x³ - 5x² + x + 2

So, P(x) = 2x³ - 5x² + x + 2

And, x - 1 = 0,

So, putting x = 1 in the function P(x), we shall apply Remainder's theorem.

            P (x) = 2x³ - 5x² + x + 2

        ⇒ P (1) = 2 × (1)³ - 5 × (1)² + 1 + 2\

        ⇒ P (1) = 2 - 5 + 1 + 2

        ⇒ P (1) = 5 - 5

        ⇒ P (1) =  0

Since, the result of the expression comes out to be zero, we can say that (x-1) is a factor of 2x³ - 5x² + x + 2.

Hence, ( x - 1 ) is a factor of 2x³ - 5x² + x + 2.

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