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This algebra 1 math tutorial from NutshelMath offers help in factoring polynomials. Polynomials are algebraic expressions assembled out of multiple terms using only addition, subtraction, multiplication and whole-number exponents. Higher-order polynomials, such as trinomials will have factors that are other polynomials of a lower order, such as binomials. Learning how to factor polynomials is a powerful skill to be used in simplifying and solving algebraic equations.
This tutorial presents examples and tips which will help in factoring trinomials of one variable, which are polynomials with three terms and a single variable. It is best to start with trinomials with terms written in descending order of power. When factoring trinomials with a leading coefficient of one and a power of two, first draw two sets of parentheses for the two binomials factors. The leading term, of power two, will factor into two terms of power one. These terms, will be the leading terms of the two binomials, and can be written as the first terms in each set of parentheses. Since the leading coefficient of the trinomial was one, the coefficients of both of these factors will be one. Looking at the signs of the second and third terms of the trinomial will indicate the signs of the second terms of each binomial factor. If both signs are positive, then the signs of the second terms in the binomials will be positive. If the linear term in the trinomial is negative and the constant is positive, then the signs of the second terms in the binomial factors will be negative. If the sign of the constant term in the trinomial is negative, then the signs of the second terms of the binomial factors will be different from one another. To complete the factoring of the trinomial, find the factors of the constant term in the trinomial which add up to the coefficient of the linear term in the trinomial. These two factors will be the second terms of the binomial factors. If there are no factors of the constant that add to the coefficient of the linear term, then the trinomial cannot be easily factored.
Mastering the factoring of polynomials is a very important skill in algebra for solving and simplifying polynomial equations.
This algebra 1 math tutorial from NutshelMath offers help in factoring polynomials. Polynomials are algebraic expressions assembled out of multiple terms using only addition, subtraction, multiplication and whole-number exponents. Higher-order polynomials, such as trinomials will have factors that are other polynomials of a lower order, such as binomials. Learning how to factor polynomials is a powerful skill to be used in simplifying and solving algebraic equations.
This tutorial presents examples and tips which will help in factoring trinomials of one variable, which are polynomials with three terms and a single variable. It is best to start with trinomials with terms written in descending order of power. When factoring trinomials with a leading coefficient of one and a power of two, first draw two sets of parentheses for the two binomials factors. The leading term, of power two, will factor into two terms of power one. These terms, will be the leading terms of the two binomials, and can be written as the first terms in each set of parentheses. Since the leading coefficient of the trinomial was one, the coefficients of both of these factors will be one. Looking at the signs of the second and third terms of the trinomial will indicate the signs of the second terms of each binomial factor. If both signs are positive, then the signs of the second terms in the binomials will be positive. If the linear term in the trinomial is negative and the constant is positive, then the signs of the second terms in the binomial factors will be negative. If the sign of the constant term in the trinomial is negative, then the signs of the second terms of the binomial factors will be different from one another. To complete the factoring of the trinomial, find the factors of the constant term in the trinomial which add up to the coefficient of the linear term in the trinomial. These two factors will be the second terms of the binomial factors. If there are no factors of the constant that add to the coefficient of the linear term, then the trinomial cannot be easily factored.
Mastering the factoring of polynomials is a very important skill in algebra for solving and simplifying polynomial equations.