How do you factor #3x^2-11x-20#?

Question

Hazel Anglin · Accepted Answer

Find a factor multiplying to -60 (3*-20) and adds to -11

basically youll want to start by looking at the factors of -60 to see which will add to -11: 1 * 60 230 320 415 512 6*10 etc As you can see, if you use the 4*15 factor, a negative 15 and a positive 4 will give you -11 if they're added and -60 when multiplied. So you then replace the -11x with -15x + 4x to give you this: #3x^2-15x+4x-20# Then group them with parenthesis: #(3x^2-15x)+(4x-20)# Now find the GCFs of the things in the parenthesis: You can factor a 3 and an x out of the first, and a 4 out of the second. #3x(x-5) + 4(x-5)# (you'll know if you did it right because the things still in parenthesis will be the same (the x-5)) Then the things on the outside of the parenthesis are put together as one factor and the ones inside are the other factor: #(3x+4) and (x-5)# are the factors (you can continue to solve it to find the values of x by setting the equations equal to 0) #3x+4=0# minus 4 on both sides #3x=4# divide both sides by 3 #x=4/3# and #x-5=0# add 5 to both sides #x=5#

Isaiah Anthony · Answer

undefined To factor the quadratic expression 3x^2 - 11x - 20, you need to find two numbers that multiply to -60 (the product of 3 and -20) and add up to -11 (the coefficient of the middle term). The two numbers are -15 and 4. Therefore, the factored form of the expression is (3x + 4)(x - 5).