Polynomials

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Step 1: The highest power of x is 1. Step 2: So the degree is 1. Step 3: A degree-1 polynomial is a linear polynomial. Answer: 3x + 5 is a linear polynomial of degree 1.

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Step 1: Look at the highest power of x. Step 2: The highest power is 2. Step 3: So the degree is 2. Answer: The polynomial is quadratic and its degree is 2.

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Step 1: The highest power of x is 3. Step 2: So the degree is 3. Step 3: A degree-3 polynomial is cubic. Answer: 5x^3 - 4x^2 + x - 1 is a cubic polynomial of degree 3.

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Step 1: In a polynomial, the power of the variable must be a whole number. Step 2: Here the power is 1/2, which is not a whole number. Answer: It is not a polynomial.

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Step 1: Rewrite 1/x as x^-1. Step 2: A polynomial cannot have negative powers of the variable. Answer: It is not a polynomial.

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Step 1: Substitute x = 2. Step 2: p(2) = (2)^2 - 2(2) - 3 Step 3: p(2) = 4 - 4 - 3 Step 4: p(2) = -3 Answer: p(2) = -3, so 2 is not a zero of the polynomial.

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Step 1: Set p(x) = 0. Step 2: x^2 - 2x - 3 = 0 Step 3: Factorise: (x - 3)(x + 1) = 0 Step 4: So x = 3 or x = -1 Answer: The zeroes are 3 and -1.

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Step 1: Substitute x = 2. Step 2: p(2) = (2)^2 - 2(2) - 3 Step 3: p(2) = 4 - 4 - 3 = -3 Step 4: Since p(2) is not 0, 2 is not a zero. Answer: 2 is not a zero of p(x).