Factor each polynomial completely. If the polynomial cannot be factored, say it is prime. x3+8x2−20x

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Factor each polynomial completely. If the polynomial cannot be factored, say it is prime.  x3+8x2−20x

Bernard Lacey · Accepted Answer

Step 1  Factorizing a polynomial is breaking a polynomial into product of small polynomials. If we multiply again those smaller polynomial with each other we will get the same polynomial.  There are many ways of factorizing, one such is taking GCF (greatest common factor) of the each term of the polynomial and taking GCF common and represent it in terms of GCF and another factor.   Important property is distributive property which is given by a(b+c)=ab+ac. It is taking common value from the function and representing it in terms of common factor and another function.  Step 2  Find GCF of each term in polynomial x3+8x2−20x  x3=x⋅x⋅x  8x3=2⋅2⋅2⋅x⋅x⋅x  20x=2*2*5*x  The GCF of x3+8x2−20x is x. take GCF out as common and represent it in terms of product of GCF and another function.  x3+8x2−20x=x(x2+8x−20)...(1)  Step 3  Factor the function x2+8x−20 from equation (1) by writing 8x as 10x-2x and taking common values out.  x2+8x−20=x2+10x−2x−20  =x(x+10)-2(x+10)  =(x-2)(x+10)   (using distributive property)...(2)  Put value of factor of x2+8x−20 from equation (2) in equation (1)  x3+8x2−20x=(x)(x−2)(x+10)  Therefore, factors of x2+8x−20 is (x)(x-2)(x+10)

Factor each polynomial completely. If the polynomial cannot be factored,

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