Question

Factor the following expression.
198q^3r^2 – 184q^2r^2 + 18qr^2

Answer 1

2qr^2(9q-1)(11q-9)

Answer 2

Factor out the 2qr^(2) from each term in the polynomial.
2qr^(2)(99q^(2))+2qr^(2)(-92q)+2qr^(2)(9)

Factor
2qr^(2)(99q^(2)-92q+9)

For a polynomial of the form ax^(2)+bx+c, find two factors of a*c (891) that add up to b (-92).In this problem -(1)/(9)*-(9)/(11)=(9)/(99) (which is (c)/(a)) and -(1)/(9)-(9)/(11)=-(92)/(99) (which is ((b)/(a)) ,

so
2qr^(2)(q-(1)/(9))(q-(9)/(11))

remove the fraction by multiplying the first term of the factor by the denominator of the second term.
2qr^(2)(9q-1)(11q-9)