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# Factoring Trinomials

❶The first term is s 2 , after dividing its exponent by two, we place s on the left of each set of parentheses. This video includes sample exercises and step-by-step explanations of polynomial factoring and multiplication for the California Standards Test.

## Handling Coefficients

Math - Algebra II. Factoring Polynomials Sort by: A helpful scientific calculator that runs in your web browser window. Completing the square with Sal Khan. In this video, Salman Khan of Khan Academy explains completing the square. Polynomial Factoring and Multiplication. This video includes sample exercises and step-by-step explanations of polynomial factoring and multiplication for the California Standards Test.

Excellent site showing examples of algebra, trig, calculus, differential equations, and linear algebra. Some worked example problems that point out many common errors students make when solving them.

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Once you have checked the greatest common factor and factored it out, then you can factor the trinomial. Now on the left of each set of parentheses, write all of the variables from the first term with half the exponent.

The first term is s 2 , after dividing its exponent by two, we place s on the left of each set of parentheses. The last term in the trinomial does not have any variables, so we do not need to carry any variables into the parentheses as a result. The coefficients are 1 and 6. Now write all pairs of factors of 1 in a vertical column and write all pairs of factors of 6 in another vertical column.

For the number 1, there is only one pair of factors, eliminating any choice. Thus the 1s can be inserted on the left side of each set of parentheses. Now a pair of factors of 6 must be chosen. To make sure all pairs are considered, check each pair of factors starting with the pair on the top of the list and working toward the bottom of the list.

The problem below is similar to the last problem, but it has two negative signs in the expression. Write all of the variables from the first term with half the exponent in the front of each set of parentheses.

Again, since there are no variables in the last term, nothing is written on the right side of each set of parentheses. Write out the factors of the coefficients of the first and last terms.

The expression p 2 - 20p - 21 is equivalent to the original expression. There is a small variation in this problem however -- the first term has a coefficient that is not 1.

Write each variable of the first and last terms in their respective positions, but with only half the exponent. The first term has the variable c 2 , with half its exponent it becomes c which is written on the left of each set of parentheses. The last term does not have any variables to write. Because the last term is negative, write a plus sign in the middle of the first set of parentheses and a - sign in the middle of the second.

To find the right combination of factors, we will use Trial and Error as in the last two lessons, but we must try different factors for both the first and last terms. Each pair of factors must be tried in two arrangements. The work below will explain this a little better. After you write out a possible combination, FOIL the factored polynomial.

## Main Topics

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Factoring Perfect Square Trinomials Factoring x 2 x + 49 follows those rules. First, find the square root of the outside terms, so that the square root of x 2 is x, and the square root of 49 is 7. Because it is a perfect square, the sign between the terms is the same as the sign of the middle term.