The coefficient of the x2 term will not always factor away. In
order to factor quadratics such as 4x2 + 8x + 3 you will need to try
all combinations of factors of 4 and of 3: 
. The blanks will be filled in with the factors of 3. You will need to
check all of th possibilities: 
:
Alfi Blog
Februari 21, 2026
Admin
Bandung Indonesia
The coefficient of the x2 term will not always factor away. In
order to factor quadratics such as 4x2 + 8x + 3 you will need to try
all combinations of factors of 4 and of 3: . The blanks will be filled in with the factors of 3. You will need to
check all of th possibilities: :
The difference of
two squares can come in the form xn – cn where n is any even
number. The factorization is xn – cn = (xn/2 –
cn/2)(xn/2 + xn/2). [When n is odd, xn
– cn can be factored also but this factorization will not be covered
here.]
Alfi Blog
Februari 20, 2026
Admin
Bandung Indonesia
The difference of
two squares can come in the form xn – cn where n is any even
number. The factorization is xn – cn = (xn/2 –
cn/2)(xn/2 + xn/2). [When n is odd, xn
– cn can be factored also but this factorization will not be covered
here.]
This shortcut can help you identify quadratic polynomials that do not
factor ‘‘nicely’’ without spending too much time on them. The next three
examples are quadratic polynomials that do not factor ‘‘nicely.
Alfi Blog
Februari 19, 2026
Admin
Bandung Indonesia
This shortcut can help you identify quadratic polynomials that do not
factor ‘‘nicely’’ without spending too much time on them. The next three
examples are quadratic polynomials that do not factor ‘‘nicely.
There is a factoring shortcut when the first term is x2. If
the second sign is plus, choose the factors whose sum is the coefficient of the
second term. For example the factors of 6 we need for x2 – 7x + 6
need to sum to 7: x2 – 7x + 6 = (x – 1)(x – 6). The factors of 6 we
need for x2 + 5x + 6 need to sum to 5: x2 + 5x + 6 = (x + 2)(x + 3).
Alfi Blog
Februari 18, 2026
Admin
Bandung Indonesia
There is a factoring shortcut when the first term is x2. If
the second sign is plus, choose the factors whose sum is the coefficient of the
second term. For example the factors of 6 we need for x2 – 7x + 6
need to sum to 7: x2 – 7x + 6 = (x – 1)(x – 6). The factors of 6 we
need for x2 + 5x + 6 need to sum to 5: x2 + 5x + 6 = (x + 2)(x + 3).
Once the signs are
determined all that remains is to fill in the two blanks. Look at all of the
pairs of factors of the constant term. These pairs will be the candidates for
the blanks. For example, if the constant term is 12, you will need to consider
1 and 12, 2 and 6, and 3 and 4. If both signs in the factors are the same,
these will be the only ones you need to try. If the signs are different, you
will need to reverse the order: 1 and 12 as well as 12 and 1; 2 and 6 as well
as 6 and 2; 3 and 4 as well as 4 and 3. Try the FOIL method on these pairs.
(Not every trinomial can be factored in this way.)
Alfi Blog
Februari 17, 2026
Admin
Bandung Indonesia
Once the signs are
determined all that remains is to fill in the two blanks. Look at all of the
pairs of factors of the constant term. These pairs will be the candidates for
the blanks. For example, if the constant term is 12, you will need to consider
1 and 12, 2 and 6, and 3 and 4. If both signs in the factors are the same,
these will be the only ones you need to try. If the signs are different, you
will need to reverse the order: 1 and 12 as well as 12 and 1; 2 and 6 as well
as 6 and 2; 3 and 4 as well as 4 and 3. Try the FOIL method on these pairs.
(Not every trinomial can be factored in this way.)
. The blanks will be filled in with the factors of 3. You will need to
check all of th possibilities: 
:
