There are several ways to factor a quadratic, I don't know which one you learned.
A popular one these days seems to be "decomposition"
step 1: multiply the coefficients of the first and last terms ...
(3)(-14) = -42
step 2: find the factors of -42 that add up to -1, the coefficient of the middle term ...... factor pairs of -42: -1,42 ; -2,21 ; -3,14 ; -6,7 ; -7,6 ;
1,-42 ; 2,-21 ; 3,-14 ; 6,-7 ;
looks like we need -7 + 6 = -1
step 3: replace the middle term of -x with -7x + 6x
3x^2 - 7x + 6x - 14
step 4: factor by grouping ....
x(3x - 7) + 2(3x - 7)
= (3x - 7)(x + 2)
Attempt to do the 2nd in the same way, use my list of factor of -42 I used for the first one.
What is your conclusion?
For most simple cases you should not have to list or even consider the majority of the factor pairs.
If you cannot find a pair of factors which does not add up to the middle term, it will NOT factor over the rationals.
Another quick way to decide if the quadratic factors is to evaluate the discriminant, that is, for ax^2 + bx + c evaluate b^2-4ac
If it is NOT a perfect square, your quadratic will NOT factor over the rationals.
for your case: b^2 - 4ac = (13)^2 -4(3)(-14) = 337
since 337 is NOT a perfect square, you will not be able to factor rational factors.
Factorise
1.3x^2 -x -14
2. 3x^2-13x- 14
1 answer
1 answer