Factor f(x)=x^4-x^3-7x^2+x+6 into linear factors given that 1 is a zero of f(x)

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# 1 Answer

You can use synthetic division.

1 | 1 -1 -7 1 6

........1..0 -7 -6

---------------------

....1 0..-7 -6|0

By oberving, -1 is another root.

-1 | 1 0 -7 -6

.......-1 1..6

-----------------

.....1 -1 -6|0

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

f(x) = (x-1)(x+1)(x-3)(x+2) <==Answer