Hi

f(x)= x^3+2x^2-13x+10 

    x^3+2x^2-13x+10 =0   |Determined x = 1 a root, thus (x-1) a factor

f(x)= (x-1)(x^2+3x-10)   |divided (x^3+2x^2-13x+10) by (x-1)

f(x)= (x-1)(x+5)(x-2)    |factored (x^2+3x-10)

       Note:SUM of the inner product(5x) and the outer product(-2x) = 3x



f(x)= 2x^4+6x^3-2x^2-6x 

f(x)= 2x(x^3+3x^2-x-3)  |factoring out the 2x

(x^3+3x^2-x-3) = 0      |Determined x = -1 a root, thus (x+1) a factor

f(x)= 2x(x+1)(x^2+2x-3) |divided (x^3+3x^2-x-3)by (x+1)

f(x)= 2x(x+1)(x+3)(x-1) |factored (x^2+2x-3)

           Note:SUM of the inner product(3x) and the outer product(-x) = 2x



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





 

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