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.)
Factoring Quadratic Polynomials
We will now work in
the opposite direction—factoring. First we will factor quadratic polynomials,
expressions of the form ax2 + bx + c (where a is not 0). For example
x2 + 5x + 6 is factored as (x + 2) (x + 3). Quadratic polynomials whose
first factors are x2 are the easiest to factor. Their factorization always
begins as (x ± _)(x ± _ ). This forces the first factor to be x2 when
the FOIL method is used All you need to do is fill in the two blanks and decide
when to use plus and minus signs. All quadratic polynomials factor though some
do not factor ‘‘nicely.’’ We will only concern ourselves with ‘‘nicely’’
factorable polynomials in this chapter.
Alfi Blog
Februari 16, 2026
Admin
Bandung Indonesia
Factoring Quadratic Polynomials
We will now work in
the opposite direction—factoring. First we will factor quadratic polynomials,
expressions of the form ax2 + bx + c (where a is not 0). For example
x2 + 5x + 6 is factored as (x + 2) (x + 3). Quadratic polynomials whose
first factors are x2 are the easiest to factor. Their factorization always
begins as (x ± _)(x ± _ ). This forces the first factor to be x2 when
the FOIL method is used All you need to do is fill in the two blanks and decide
when to use plus and minus signs. All quadratic polynomials factor though some
do not factor ‘‘nicely.’’ We will only concern ourselves with ‘‘nicely’’
factorable polynomials in this chapter.
More on the Distribution Property—the FOIL Method
The FOIL method
helps us to use the distribution property to help expand expressions like (x + 4)(2x
– 1). The letters in ‘‘FOIL’’ describe the sums and products.
Alfi Blog
Februari 15, 2026
Admin
Bandung Indonesia
More on the Distribution Property—the FOIL Method
The FOIL method
helps us to use the distribution property to help expand expressions like (x + 4)(2x
– 1). The letters in ‘‘FOIL’’ describe the sums and products.
Reducing a fraction
or adding two fractions sometimes only requires that –1 be factored from one or
more denominators. For instance in 
the numerator and denominator are
only off by a factor of –1. To reduce this fraction, factor –1 from the
numerator or denominator:
Alfi Blog
Februari 14, 2026
Admin
Bandung Indonesia
Reducing a fraction
or adding two fractions sometimes only requires that –1 be factored from one or
more denominators. For instance in the numerator and denominator are
only off by a factor of –1. To reduce this fraction, factor –1 from the
numerator or denominator:
Factoring to Reduce Fractions
Among factoring’s
many uses is in reducing fractions. If the numerator’s terms and the
denominator’s terms have common factors, factor them then cancel. It might not
be necessary to factor the numerator and denominator completely.
Alfi Blog
Februari 13, 2026
Admin
Bandung Indonesia
Factoring to Reduce Fractions
Among factoring’s
many uses is in reducing fractions. If the numerator’s terms and the
denominator’s terms have common factors, factor them then cancel. It might not
be necessary to factor the numerator and denominator completely.
