Can someone explain this to me plese:
to factor a number you....
and then can you explain to me
To factor an algebraic expression into prime factors means.....
thanks
This is how I would complete these two sentences.
To factor a number, you break it down into smaller parts.
To factor an algebraic expression into prime factors means to rewrite the expression in simplest form.
I hope this helps and is what you were asking.
Yes, that is a good explanation, but let me provide a more detailed explanation for both scenarios:
To factor a number, you break it down into smaller parts. In other words, you find the factors of the given number that are smaller than the number itself. For example, to factor the number 12, you would look for two numbers that multiply together to give you 12. In this case, the factors of 12 are 1, 2, 3, 4, 6, and 12. So, to factor 12, you could write it as 2 × 2 × 3, which reflects the factors of the number.
To factor an algebraic expression into prime factors means to rewrite the expression in simplest form using prime numbers. An algebraic expression is a mathematical expression that contains variables, constants, and mathematical operations. Prime factors are the prime numbers that divide into the given expression. To factor an algebraic expression into prime factors, you look for common factors (numbers that divide evenly into the expression) and separate the expression into its prime factors. For example, let's say you have the algebraic expression 12x^2 + 4x. To factor it into prime factors, you would first look for common factors:
12x^2 + 4x = 4x(3x + 1)
In this case, the common factor is 4x. Then, you can further simplify the expression by factoring out the prime factors of the expression within the parentheses. In this example, we cannot factor the expression 3x + 1 any further since it is already in its simplest form. Therefore, the fully factored form of the algebraic expression 12x^2 + 4x is simply 4x(3x + 1).
I hope this provides a clearer understanding of the concepts. Let me know if you have any further questions!