7 Factor completely Show work following the methods discusse

7) Factor completely. Show work following the methods discussed in Sections 6.1 - 6.4 of our text, and show the check by re-multiplication of the factors. If the polynomial is not factorable, write “prime.” 3x² + 9x + 6

Solution

3x²+9x+6 =3(x²+3x+2)
=>3x²+9x+6 =3(x²+x+2x+2)
=>3x²+9x+6 =3(x(x+1)+2(x+1))
=>3x²+9x+6 =3((x+1)(x+2))
=>3x²+9x+6 =3(x+2)(x+1)

check:
3(x+2)(x+1)
=3(x(x+1)+2(x+1))
=3(x²+x +2x+2)
=3(x²+3x+2)
=3x²+(3*3x)+(3*2)
=3x²+9x+6

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