Dividing Polynomials by Binomials

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What is a polynomial?

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A polynomial is a mathematical expression consisting of variables (also called indeterminates) and coefficients, combined using addition, subtraction, multiplication, and non-negative integer exponents.

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What is a binomial?

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A binomial is a polynomial that contains exactly two terms, which are typically separated by a plus or minus sign.

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What does it mean to divide polynomials?

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Dividing polynomials involves finding how many times a polynomial (the dividend) can be divided by another polynomial (the divisor), resulting in a quotient and possibly a remainder.

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What is synthetic division?

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Synthetic division is a simplified method of dividing a polynomial by a binomial of the form (x - c), which is faster than long division.

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What is the Remainder Theorem?

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The Remainder Theorem states that when a polynomial f(x) is divided by (x - c), the remainder of that division is equal to f(c).

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What is the Factor Theorem?

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The Factor Theorem states that (x - c) is a factor of the polynomial f(x) if and only if f(c) = 0.

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How do you factor a quadratic polynomial?

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To factor a quadratic polynomial of the form ax^2 + bx + c, find two numbers that multiply to ac and add to b, then rewrite the polynomial using these numbers.

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What is the first step in dividing polynomials using long division?

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The first step is to divide the leading term of the dividend by the leading term of the divisor to find the first term of the quotient.

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What is the significance of the leading coefficient in polynomial division?

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The leading coefficient is important because it determines the degree and the end behavior of the polynomial, influencing the division process.

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