Answer:
Explanation:
16. Here are the steps for factoring linear expressions:
Identify the terms in the expression. For example, if the expression is 3x + 6, the terms are 3x and 6.
Determine if there is a common factor in the terms. A common factor is a number or variable that divides into each term evenly. For example, in the expression 3x + 6, the common factor is 3.
Factor out the common factor by dividing each term by the common factor. For example, in the expression 3x + 6, we can factor out 3: 3x + 6 = 3(x + 2).
Check if there are any other common factors in the remaining terms. For example, in the expression 2x^2 + 4x, we can factor out 2x: 2x^2 + 4x = 2x(x + 2).
If the expression is a trinomial (three terms), check if it can be factored using the FOIL method. For example, in the expression x^2 + 5x + 6, we can factor it as (x + 2)(x + 3) by finding two numbers that multiply to 6 and add up to 5.
If the expression has more than three terms, try grouping the terms into pairs and factoring out a common factor from each pair. For example, in the expression 2x^3 + 4x^2 + 3x + 6, we can group the terms as (2x^3 + 4x^2) + (3x + 6) and factor out 2x^2 from the first group and 3 from the second group to get 2x^2( x + 2) + 3(x + 2), which can be factored further as (2x^2 + 3)(x + 2).
Check your factoring by multiplying the factors back together using the distributive property to make sure they equal the original expression.
17. To factor out the GCF (Greatest Common Factor) of 18x and 12, we first need to find the highest factor that both terms have in common. In this case, the GCF is 6:
18x = 6 * 3 * x
12 = 6 * 2
So, we can rewrite 18x + 12 as:
18x + 12 = 6 * 3 * x + 6 * 2
Now we can factor out the GCF of 6:
18x + 12 = 6(3x + 2)
Therefore, the factored form of 18x + 12 is 6(3x + 2).