Q&A for How to Solve Polynomials

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  • Question
    How did you get -2 in the second binomial?
    Donagan
    Top Answerer
    The original equation was 5x + 2 = 0. Then 2 was subtracted from both sides of the equation in order to begin the process of solving for x. This resulted in 5x = -2.
  • Question
    What do I get if I add x - 2 and 1/x?
    Donagan
    Top Answerer
    You get x - 2 + 1/x.
  • Question
    For trinomials, would I turn them into a quadratic polynomials and then binomials?
    Community Answer
    Yes. To factor a trinomial, you must split it into a quadratic polynomial.
  • Question
    How do I solve x4 - x2 = 0
    Donagan
    Top Answerer
    x^4 - x² = x²(x² - 1) = 0. Therefore, x² = 0, or x² - 1 = 0. If x² = 0, then x = 0. If x² - 1 = 0, then x = +/-1.
  • Question
    How do I solve the polynomial x - 2 = 0?
    Donagan
    Top Answerer
    Add 2 to both sides of the equation.
  • Question
    How can I solve the equation (x^3+6) (x^3-7)?
    Donagan
    Top Answerer
    It's not an equation, so it can't be "solved." In other words, no value for x can be found. However, if you just want to perform the multiplication, you'll get the product x^6 - x³ - 42.
  • Question
    Ax * 4 - 4x * 3 + bx * 2 - 100x + 24. When x=4, how do I solve this?
    Community Answer
    Because x = 4, the remainder theorem states that P(4) = 0. So sub P(4) = 0, essentially then solve for A.
  • Question
    How do I solve y^3 - 2y^2 - 9j + 18 = 0?
    Donagan
    Top Answerer
    Because the equation has two unknown variables (y and j), it can't be solved. When you have two unknowns, you need two independent equations in those unknowns in order to solve for them.
  • Question
    How do I solve 25x^3 = 64x?
    Donagan
    Top Answerer
    Divide both sides of the equation by x: 25x² = 64. Then find the square root of both sides: +/- 5x = +/- 8. So x = +/- 8/5.
  • Question
    How do you solve this equation: P of X equal to 6 X square + X - 1 equal to zero?
    Iris8989
    Community Answer
    The sentence means, 6x^2 + x - 1 = 0. To factor a trinomial, figure out what two numbers for the coefficients multiply to get 6. 3 and 2 (as well as 1 and 6) work. Next, find out what two numbers for the constants multiply to equal -1. Only 1 and -1 work. Use FOIL to test the numbers, and you will see that (3x-1)(2x+1) is the factored form. Set 3x - 1 and 2x + 1 equal to zero. x can equal 1/3 or -1/2.
  • Question
    How do you divide (x^3 + x^2 - x + 1) by (x -2)?
    Community Answer
  • Question
    How do you solve a two-term polynomial with an exponent of two, such as x^2-64?
    Community Answer
    You can't solve it unless it's an equation. If you were to set that expression equal to 0, then x² - 64 = 0. Add 64 to both sides: x² = 64, and x = +/- 8.
  • Question
    How do you find the value of a, b and c in: ax(x+3)+bx(x-1)+c(x-1)(x+3)=5x+3?
    Community Answer
    That's an equation in three unknowns (four if you count x as an unknown). To solve for three unknowns, you would need three independent equations. With just one equation in three unknowns, you could solve for just one unknown, and the solution would be in terms of the other two unknowns.
  • Question
    How to solve 4^n=2^2×4^2?
    Donagan
    Top Answerer
    4^n = (2²)(4 ²) = (4)(16) = 64. By inspection, 4³ = 64, so n = 3.
  • Question
    How do I solve (-6²)³?
    Donagan
    Top Answerer
    (-6²)³ = (-6)^6 = +46,656.
  • Question
    How do I factorize. 8a + 125ax³?
    Donagan
    Top Answerer
    First, factor out the a. What remains is the sum of two cubes: 8a + 125ax³ = a(8 + 125x³) = a[(2)³ + (5x)³]. Factoring the sum of two cubes yields this: a(2 + 5x)(2² - 10x + 25x²) = a(2 + 5x)(4 - 10x + 25x²).
  • Question
    How do I solve m-d+2=0?
    Donagan
    Top Answerer
    That appears to be an equation in two unknowns (m and d). In order to solve such an equation, you would need two separate equations, each containing both unknowns. The only alternative is to solve for one of the unknowns in terms of the other. In this case, m = d - 2, or d = m + 2.
  • Question
    How do I solve x^4-9x^2+18=0?
    Donagan
    Top Answerer
    This equation is solved similarly to x² - 9x +18 = 0 = (x - 6)(x - 3). x^4 - 9x² + 18 = 0 = (x² - 6)(x² - 3).
  • Question
    If x-1,and x-2 are factors of the polynomial equation X³ +ax² -7x+b,where a and b are constant what is the third factor and constant a and b?
    Community Answer
    Calculating (x3+ax2-7x+b)/(x-1) gives condition b=6-a. Calculating (x3+ax2-7x+b)/(x-2) gives condition b=6-4a. Solving both conditions give a=0 and b=6, we find polynomial x3-7x+6=(x-1)(x-2)(x+3)=0 results in solution x=-3,x=1 and x=2. Or, using property of roots in cubic equation: Since we know two roots of the polynomial and we know the minus times coefficient of x is equal to product of roots: r1*r2+r2*r3+r1*r3=-(-7) using r1=1 and r2=2 we have 1*2+2*r3+r3=-7 and we get r3=-3 coefficient of x2 is sum of roots r1+r2+r3=a this gives a= 1+2-3 so a=0 coefficient of constant is minus times product of roots -(r1*r2*r3)=b=-(1*2*-3) so b=6.
  • Question
    How do I solve If ( x – 2) is a factor of f(x) = 4x3 – 19x2 + ax – 14, and need to find, (a) the value of the constant a and (b) factorise and solve the polynomial?
    Community Answer
    (a) Calculate (4x3-19x2+ax-14)/(x-2)=4x2-11x+a-22. We get a condition for a : -14=-2(a-22) and then solve for a=29. (b) f(x)=4x3-19x2+29x-14=(x-2)(4x2-11x+7), solving quadratic part of f(x): g(x)=4x2-11x+7 x=(4x-7)(x-1) and find x=7/4 and x=1 (also possible with a,b,c formula), solving for f(x) we find x=1, x=7/4 and x=2.
  • Question
    What is standard form of a polynomial equation?
    Donagan
    Top Answerer
    There is no standard form, because a polynomial can have any number of terms.
  • Question
    How do I know if my polynomial is correct?
    Community Answer
    Use the answer that you got in the original equation to see if it still holds up. If you had the equation 3x + 2 = 5 and got x = 1, you can apply 3(1) + 2 = 5 to confirm your answer.
  • Question
    How do I solve y = -(x + 5) (2x + 3)(x - 2)(x - 4)?
    Donagan
    Top Answerer
    It's not possible to solve an equation expressed in two unknowns (x and y in this case).
  • Question
    How do I solve the equation 4x^3 + 3x = 0?
    Donagan
    Top Answerer
    4x³ + 3x = x(4x² + 3) = 0. Then x = 0, or (4x² + 3) = 0. In the latter case, 4x² = -3, x² = -¾, and x is the square root of a negative number, which is an "imaginary" number. If we restrict our answer to "real" numbers, x = 0.
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