Q. 11 C5.0( 5 Votes )

# Which of the followings is a linear polynomial?A. x + x2B. x + 1C. 5x2 – x + 3D.

For option (a),

We have x + x2

In this expression, we have 2 terms.

The degree of this expression is 2 (largest exponent of x).

But linear polynomial has a degree of 1, so that it can give exactly one root.

x + x2 is not a linear polynomial.

For option (b),

We have x + 1

In this expression, we have 2 terms.

And the degree of this expression is 1 (largest exponent of x).

This compliments the definition of a polynomial.

x + 1 is a linear polynomial.

For option (c),

We have 5x2 – x + 3.

In this expression, we have 3 terms.

And the degree of this expression is 2 (largest exponent of x).

This violates the definition of linear polynomial, as the degree of linear polynomial is always 1.

5x2 – x + 3 is not a linear polynomial.

For option (d),

We have

Let us simplify the expression.

x2 = 1

x2 – 1 = 0

This now is an algebraic expression, having 2 terms.

The degree of this expression is 2 (largest exponent of x).

This again doesn’t satisfy the criteria of linear polynomial, which says that degree should be 1.

is not a linear polynomial.

Thus, option (b) is correct.

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