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.
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 This topic has 1 reply, 1 voice, and was last updated 1 year, 7 months ago by ProtonsTalk.

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April 14, 2022 at 10:56 am #20422
One root of f(x) = 2×3 + 9×2 + 7x – 6 is –3. explain how to find the factors of the polynomial.
 This topic was modified 1 year, 7 months ago by ProtonsTalk.
 This topic was modified 1 year, 7 months ago by ProtonsTalk.
 This topic was modified 1 year, 7 months ago by ProtonsTalk.
 This topic was modified 1 year, 6 months ago by ProtonsTalk.
April 14, 2022 at 11:06 am #20424::One root of f(x) = 2x^{3} + 9x^{2} + 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) = 2x^{3} + 9x^{2} + 7x – 6Splitting the x^{2} and x term and getting x+3 common
=> 2x^{3} + 6 x^{2} + 3 x^{2} + 9x – 2x – 6=> 2x^{2} .( x + 3) + 3x .(x + 3) 2 .(x +3)
=> ( x+3) .( 2x^2 + 3x 2 )
Now factorizing the quadratic equation as usual.
=> (x +3) ( 2 x^{2} + 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.
 This reply was modified 1 year, 6 months ago by ProtonsTalk.
 This reply was modified 1 year, 6 months ago by ProtonsTalk.

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