how to divide two polynomials?
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['Divide the first term of the numerator by the first term of the denominator, and put that in the answer.', 'Multiply the denominator by that answer, put that below the numerator.', 'Subtract to create a new polynomial.']
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You add polynomials when there are plus signs. You subtract them when there is a minus sign. Remember to only add/subtract like terms within the polynomials.
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You can find the roots, or solutions, of the polynomial equation P(x) = 0 by setting each factor equal to 0 and solving for x. Solve the polynomial equation by factoring. Set each factor equal to 0. 2x4 = 0 or (x – 6) = 0 or (x + 1) = 0 Solve for x.
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['Isolate the radical on one side of the equation.', 'Square both sides of the equation.', 'Solve the new equation.', 'Check the answer.']
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Synthetic division is generally used, however, not for dividing out factors but for finding zeroes (or roots) of polynomials. More about this later. If you are given, say, the polynomial equation y = x2 + 5x + 6, you can factor the polynomial as y = (x + 3)(x + 2).
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To find the square root of a polynomial, arrange the terms with reference to the powers of some number; take the square root of the first term of the polynomial for the first term of the root, and subtract its square from the polynomial; divide the first term of the remainder by twice the root found for the next term ...
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['Go to EQN mode and scroll over to the Degree? section ( MODE MODE MODE 1 → ).', 'Enter the degree ( 2 or 3 ).', 'Enter the 3 or 4 (real) polynomial coefficients, from highest degree downward.', 'Scroll up and down through the solution set. Complex-valued solutions are included.']
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['Find the LCM [Least common multiple] of both the expressions.', 'Change each of the polynomial fractions to make their denominators equal to the LCD.', 'Subtract both the expressions.']
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['The bottom numbers are different. See how the slices are different sizes? ... ', 'To make the bottom numbers the same, multiply the top and bottom of the first fraction (1/2) by 3 like this:', 'Subtract the top numbers and put the answer over the same denominator:', 'Simplify the fraction:']
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To add or subtract or multiply polynomials, remove parentheses and combine like terms. For multiplying, this amounts to multiplying each term in one polynomial by each term in the other. To multiply terms, multiply the coefficients and add the exponents on each variable.
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['Add the ratio terms to get the whole. Use this as the denominator. 1 : 2 => 1 + 2 = 3.', 'Convert the ratio into fractions. Each ratio term becomes a numerator in a fraction. 1 : 2 => 1/3, 2/3.', 'Therefore, in the part-to-part ratio 1 : 2, 1 is 1/3 of the whole and 2 is 2/3 of the whole.']
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['Step 1: Set up a product of two ( ) where each will hold two terms.', 'Step 2: Find the factors that go in the first positions.', 'Step 3: Find the factors that go in the last positions.']
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Divide two integers to obtain a remainder. For an example, dividing 4 into 6, or 6 ÷ 4, results in quotient of 1 and a remainder of 2. Write the remainder as the numerator in a fraction with the divisor as the denominator. In this example, writing the remainder over the divisor results in 2/4.
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['Cross-multiply the two fractions and subtract the second number from the first to get the numerator of the answer. ... ', 'Multiply the two denominators together to get the denominator of the answer. ... ', 'Putting the numerator over the denominator gives you your answer.']
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['Find the GCF of all the terms in the polynomial.', 'Express each term as a product of the GCF and another factor.', 'Use the distributive property to factor out the GCF.']
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A polynomial equation with two terms usually joined by a plus or minus sign is called a binomial. Binomials are used in algebra. Polynomials with one term will be called a monomial and could look like 7x. A polynomial with two terms is called a binomial; it could look like 3x + 9.
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['Step 1: Set up the synthetic division. ... ', 'Step 2: Bring down the leading coefficient to the bottom row.', 'Step 3: Multiply c by the value just written on the bottom row. ... ', 'Step 4: Add the column created in step 3.']