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Graph the polynonmial function P(x)=x^4 + x^3 - 3x^2 -5x -2 and use the zeros (x-intercepts) to find a factorization of P(x).
give different values for x ,find P(x) and make a table as follows
say x=0,we get P(x)=x^4 + x^3 - 3x^2 -5x -2=0+0-0-0-2=-2
for x=-1,we get P(x)=(-1)^4+(-1)^3-3(-1)^2-5(-1)-2=1-1-3+5-2=0..etc..
when you plot the graph it looks as follows
see where all the curve cuts X axis ..there Y=P(x)=0..those values of x coordinates are the roots of the polynomial.we saw P(x)=0 at x=-1..so x+1 is a factor..proced on this basis to find other factors from the graph.for ex at x=2 the curve cuts x axis and so x=2 is a root and x-2 is a factor