Home Forums Math One root of f(x) = 2x^3 + 9x^2 + 7x – 6 is –3. explain how to find the factors of the polynomial. Reply To: One root of f(x) = 2x^3 + 9x^2 + 7x – 6 is –3. explain how to find the factors of the polynomial.

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    One root of f(x) = 2x3 + 9x2 + 7x – 6 is –3 this means
    (x+3) is a factor of polynomial.

    So, to find we will try to reduce this cubic into a quadratic equation by using this given factor.

    To do that we have to take out x+3 common out from the equation
    f(x) = 2x3 + 9x2 + 7x – 6

    Splitting the x2 and x term and getting x+3 common
    => 2x3 + 6 x2 + 3 x2 + 9x – 2x – 6

    => 2x2 .( x + 3) + 3x .(x + 3) -2 .(x +3)

    => ( x+3) .( 2x^2 + 3x -2 )

    Now factorizing the quadratic equation as usual.
    => (x +3) ( 2 x2 + 4x – x – 2)

    => ( x +3) [ 2x (x + 2) – ( x+ 2)]

    => ( x + 3 )( x + 2) ( 2x – 1 ) = 0

    x + 2 = 0 or 2x – 1 = 0

    So, the other factors are -2 and 1/2

    Note: If you are not able to take the given factor common as shown above, you can also use polynomial division to get the quadratic.

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