Factoring polynomials is a fundamental skill in algebra, often used to simplify and solve equations. The basic rule of factoring involves a few straightforward steps that can be applied to various polynomials.

Firstly, the process begins by grouping the first two terms of the polynomial together and then grouping the last two terms together. This grouping helps identify any common factors within these sets. In the example of a polynomial like ( ax^2 + bx + cx + d ), we would group ( ax^2 + bx ) together and ( cx + d ) together.

Secondly, we proceed to factor out the Greatest Common Factor (GCF) from each separate binomial. This step involves finding the largest expression that can be divided evenly into each term of the binomial. By factoring out this common factor, we are left with simpler expressions inside parentheses.

Lastly, we factor out the common binomial. After factoring out the GCF from each binomial, we should look for any common factors that remain in both binomials. This common binomial can then be factored out, leaving us with the fully factored form of the polynomial. It’s important to note that when we multiply our factored form back together, we should get the original polynomial.

In summary, the basic rule of factoring involves grouping terms, factoring out the GCF from each binomial, and then factoring out the common binomial. This systematic approach helps simplify polynomials and is crucial for solving equations in algebra. When done correctly, factoring should yield a result that, when multiplied back, reproduces the original polynomial.

(Response: The basic rule of factoring involves grouping terms, factoring out the GCF, and factoring out the common binomial to simplify polynomials.)

Factoring polynomials is a fundamental skill in algebra, often used to simplify and solve equations. The basic rule of factoring involves a few straightforward steps that can be applied to various polynomials.

Firstly, the process begins by grouping the first two terms of the polynomial together and then grouping the last two terms together. This grouping helps identify any common factors within these sets. In the example of a polynomial like ( ax^2 + bx + cx + d ), we would group ( ax^2 + bx ) together and ( cx + d ) together.

Secondly, we proceed to factor out the Greatest Common Factor (GCF) from each separate binomial. This step involves finding the largest expression that can be divided evenly into each term of the binomial. By factoring out this common factor, we are left with simpler expressions inside parentheses.

Lastly, we factor out the common binomial. After factoring out the GCF from each binomial, we should look for any common factors that remain in both binomials. This common binomial can then be factored out, leaving us with the fully factored form of the polynomial. It’s important to note that when we multiply our factored form back together, we should get the original polynomial.

In summary, the basic rule of factoring involves grouping terms, factoring out the GCF from each binomial, and then factoring out the common binomial. This systematic approach helps simplify polynomials and is crucial for solving equations in algebra. When done correctly, factoring should yield a result that, when multiplied back, reproduces the original polynomial.

(Response: The basic rule of factoring involves grouping terms, factoring out the GCF, and factoring out the common binomial to simplify polynomials.)