Home > Algebra > Monomial Factors of Polynomials

Is it possible to factor #y= 4x^2 -12x + 9 #? If so, what are the factors?

Answer 1

Yes. #y=(2x-3)^2#

If the general form of the factored quadratic is #y = (ax +b)(cx+d)# then #y = acx^2 + (bc+ad)x +bd)#

This means that we need factors #a# and #c# that multiply to give #4# and #b# and #d# that multiply to give #9#. #bc # and #ad# must add up to give # -12#

Because the sign of the middle term is negative and the sign of the last term is positive, both #b# and #d# must be negative. In this example #ac# and #bd# both give squares - #4# and #9# respectively. The answer is therefore #(2x - 3)(2x -3)# #=(2x-3)^2#

By signing up, you agree to our Terms of Service and Privacy Policy

Answer 2

Jameson Allen

Yes, it is possible to factor the quadratic equation ( y = 4x^2 - 12x + 9 ). The factors are ( (2x - 3)^2 ).

By signing up, you agree to our Terms of Service and Privacy Policy

Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.