Miike012 said:Is this term factorable?
9a^2 - 6a + 1 -x^2 - 8dx - 16d^2
I don't see anything that I can group or any simple factors to factor out...
Miike012 said:9a^2 - 6a + 1 - (x^2 + 8dx + 16d^2)
= (3a - 1)^2 - (x + 4d)^2
= (3a - 1 + x + 4d)(3a - 1 - x - 4d)
How do you know what the roots are?
A factor in algebra is a number or expression that divides evenly into another number or expression. This means that when a factor is multiplied by another number or expression, the result is the original number or expression.
To find the factors of a number, you can start by listing all of the numbers that divide evenly into that number. Then, you can check each number to see if it is a factor by dividing the original number by that number. If the result is a whole number, then the number is a factor. The factors of a number are always in pairs, with one factor being smaller than or equal to the square root of the original number and the other factor being larger than or equal to the square root of the original number.
A factor tree is a diagram that is used to break down a number or expression into its prime factors. To use a factor tree to solve an algebra problem, you start by writing the number or expression at the top of the tree. Then, you divide the number or expression by its smallest prime factor and write the result below it. You continue this process until all of the numbers or expressions in the tree are prime factors. Then, you can multiply these prime factors together to find the final solution to the algebra problem.
To factor a polynomial expression, you start by looking for the greatest common factor (GCF) of all the terms in the expression. This is the largest number or expression that divides evenly into all of the terms. Then, you can use different factoring methods such as grouping, difference of squares, or perfect square trinomials to further factor the expression. The goal is to break down the expression into simpler factors that can be multiplied together to get the original expression.
Factoring and simplifying are both methods used to manipulate algebraic expressions, but they have different purposes. Factoring involves breaking down an expression into smaller factors, while simplifying involves reducing an expression to its simplest form by combining like terms and using the rules of exponents. Factoring is often used to solve equations, while simplifying is used to make calculations easier.