how to factorise quartic equations?
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If the quartic equation is also a difference of squares; then it can be factored just like a difference of squares can be factored. A difference of squares comes in the form of a2-b2 and factors like (a+b)(a-b). For example x4-81=0 would factor like (x2+9)(x2-9)=0. The (x2-9) will factor again to (x-3)(x+3).
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['Remove Common Factors if possible.', 'If the coefficient of the x2 term is 1, then. x2 + bx + c = (x + n)(x + m), where n and m. · Multiply to give c. · Add to give b.', 'If the coefficient of the x2 term is not 1, then use either. Guess-and Check. List the factors of the coefficient of the x2 term.']
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Step 2: Use a factoring strategies to factor the problem. Step 3: Use the Zero Product Property and set each factor containing a variable equal to zero. Step 4: Solve each factor that was set equal to zero by getting the x on one side and the answer on the other side. Step 1: Write the equation in the correct form.
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While factoring may not always be successful, the Quadratic Formula can always find the solution. The Quadratic Formula uses the "a", "b", and "c" from "ax2 + bx + c", where "a", "b", and "c" are just numbers; they are the "numerical coefficients" of the quadratic equation they've given you to solve.
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Begin by multiplying both sides by the LCD, x(x+1) x ( x + 1 ) . After distributing and dividing out the common factors, a quadratic equation remains. To solve it, rewrite it in standard form, factor, and then set each factor equal to 0. Check to see if these values solve the original equation.
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Set up your equation so that a2 + b2 = c2. This is the Pythagorean Theorem used for solving for the unknown side.
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Now we can solve a Quadratic Equation in 5 steps: Step 1 Divide all terms by a (the coefficient of x2). Step 2 Move the number term (c/a) to the right side of the equation. Step 3 Complete the square on the left side of the equation and balance this by adding the same value to the right side of the equation.
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You know by now how to solve a quadratic equation using factoring. Another way of solving a quadratic equation is to solve it graphically. The roots of a quadratic equation are the x-intercepts of the graph.
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['Factor each coefficient into primes. Write all variables with exponents in expanded form.', 'List all factors—matching common factors in a column. ... ', 'Bring down the common factors that all expressions share.', 'Multiply the factors as in (Figure).']
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['Factoring.', 'Completing the Square.', 'Quadratic Formula.', 'Graphing.']
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The correct answer is m = −8 or 3. You can find the solutions, or roots, of quadratic equations by setting one side equal to zero, factoring the polynomial, and then applying the Zero Product Property. The Principle of Zero Products states that if ab = 0, then either a = 0 or b = 0, or both a and b are 0.
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The equation y = ax2 + bx + c is in factored form when it is written as. y = a(x - r.
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['a2 – b2 = (a – b)(a + b)', '(a+b)2 = a2 + 2ab + b2', 'a2 + b2 = (a + b)2 – 2ab.', '(a – b)2 = a2 – 2ab + b2', '(a + b + c)2 = a2 + b2 + c2 + 2ab + 2bc + 2ca.', '(a – b – c)2 = a2 + b2 + c2 – 2ab + 2bc – 2ca.', '(a + b)3 = a3 + 3a2b + 3ab2 + b3 ; (a + b)3 = a3 + b3 + 3ab(a + b)']
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['The prime factorization of 6 is: 2 x 3.', 'The prime factorization of 30 is: 2 x 3 x 5.', 'The prime factors and multiplicities 6 and 30 have in common are: 2 x 3.', '2 x 3 is the gcf of 6 and 30.', 'gcf(6,30) = 6.']
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['Check the Equation.', 'Press Mode, then 1.', 'Select the Quadratic Equation.', 'Input Your Values.']
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['1 × 40 = 40.', '2 × 20 = 40.', '4 × 10 = 40.', '5 × 8 = 40. Therefore, the factors in pairs are (1, 40), (2, 20), (4, 10) and (5, 8).']
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Biquadratic equations. A biquadratic equation is a 4-degree equation without the terms of degree 1 and 3. To solve a biquadratic equation you have to do a change of variable: z = x2. Then you have to solve the quadratic equation and finally undo the change.