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Polynomials in One Variable |
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Definition
A polynomial in one variable is any expression of the type anxn + an-1xn-1 + · · · + a2x2 + a1x + a0, where n is a nonnegative integer and an, . . . a0 are real numbers, called coefficients.
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The parts of a polynomial separated by plus signs. |
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In a polynomial in one variable of the type anxn + an-1xn-1 + · · · + a2x2 + a1x + a0, the leading coefficient is an. |
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In a polynomial in one variable of the type anxn + an-1xn-1 + · · · + a2x2 + a1x + a0, the constant term is a0. |
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In a polynomial in one variable of the type anxn + an-1xn-1 + · · · + a2x2 + a1x + a0, if an ≠ 0, the degree of the polynomial is n. |
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A polynomial in one variable of the type anxn + an-1xn-1 + · · · + a2x2 + a1x + a0 is said to be written in descending order because the exponents decrease from left to right. |
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The degree of a term is the sum of the exponents of the variables in that term. |
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The degree of a polynomial is the degree of the term of highest degree. |
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A polynomial with just one term e.g., -9y6 |
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A polynomial with two terms e.g., x2 + 4 |
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A polynomial with three terms e.g., 4x2 - 4xy + 1 |
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like terms or similar terms |
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Definition
If two terms of a n expression have the same variables raised to the same powers, they are called like terms or similar terms. We can combine, or collect, like terms using the distributive property. e.g., 3y2 + 5y2 = (3 + 5)y2 = 8y2 |
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Product of a Sum and a Difference |
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Definition
(A + B) (A - B) = A2 - B2 |
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(A + B) (C + D) = AC + AD + BC + BD |
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(A + B)3 = A3 + 3A2B + 3AB2 + B3 |
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