Question

One root of f(x) = 2x3 + 9x2 + 7x – 6 is –3. Explain how to find the factors of the polynomial.

Answer 1

Answer:

The other two factors are : ( 2 x - 1 ) and ( x + 2 )

Step-by-step explanation:

If ( - 3 ) is one of the values of x then [ x - ( - 3 ) ] should be a factor of f(x). Let’s factorize f(x) . We get —

=> f(x) = 2x³ + 9x² + 7x – 6 = ( x + 3 ) ( 2 x² + 3 x - 2 )

Hence ( x + 3 ) is one factor.

Again : 2 x² + 3 x - 2 = 2 x² + 4 x - x - 2 = 2 x ( x + 2 ) - ( x + 2 )

=> ( 2 x - 1 ) * ( x + 2 )

Hence 2x³ + 9x² + 7x – 6 = ( x + 3 ) ( 2 x - 1 ) ( x + 2 )

Hence the other two factors are : ( 2 x - 1 ) and ( x + 2 )

Answer 2

Answer:

(x+3) is a factor of polynomial.

∴ f(x) = 2x^3 + 9x^2 + 7x – 6

= 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 )

= (x +3) ( 2 x^2 + 4x - x - 2)

= ( x +3) [ 2x (x + 2) - ( x+ 2)]

= ( x + 3 )( x + 2) ( 2x - 1 )

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