Table of Contents
- 1 Can there be more than one answer when factoring?
- 2 What is the number one rule when factoring?
- 3 What are some examples of quadratic equation in 2 variables?
- 4 What are the 4 methods of factoring?
- 5 How do you know when to factor out a negative?
- 6 How do you find the first term in each factor?
- 7 How do you factor a polynomial by factoring?
Can there be more than one answer when factoring?
Usually, you can get to the correct answer regardless of which factoring method — and whatever order — you choose. If you have to factor an expression more than once, however, the first step should always be an attempt to factor out the greatest common factor.
What is the number one rule when factoring?
RULE # 1: The First Rule of Factoring: Always see if you can factor something out of ALL the terms. This often occurs along with another type of factoring.
What method should you use to check whether your factors of a polynomial are correct?
for example, follow these steps:
- Break down every term into prime factors.
- Look for factors that appear in every single term to determine the GCF.
- Factor the GCF out from every term in front of parentheses, and leave the remnants inside the parentheses.
- Multiply out to simplify each term.
How can you determine if you have found the correct factors of a quadratic expression?
If both the roots satisfy the quadratic equation, then you have factorised it correctly.
What are some examples of quadratic equation in 2 variables?
A quadratic equation in two variables is an equation that’s equivalent to an equation of the form p(x, y)=0 where p(x, y) is a quadratic polynomial. Examples. 4×2 – 3xy – 2y2 + x – y + 6 = 0 is a quadratic equation, as are x2 – y2 = 0 and x2 + y2 = 0 and x2 – 1 = 0. y = x2 is a quadratic equation.
What are the 4 methods of factoring?
The four main types of factoring are the Greatest common factor (GCF), the Grouping method, the difference in two squares, and the sum or difference in cubes.
How do you do the factorization method?
A Method For Simple Cases
- Step 1: Find two numbers that multiply to give ac (in other words a times c), and add to give b.
- Step 2: Rewrite the middle with those numbers:
- Step 3: Factor the first two and last two terms separately:
What are the factoring rules?
- x2 – (r + s)x + rs = (x – r)(x – s)
- x2 + 2ax + a2 = (x + a)2 and x2 – 2ax + a2 = (x – a)2
- Difference of squares: a2 – b2 = (a – b)(a + b)
- Difference of cubes: a3 – b3 = (a – b)(a2 + ab + b2)
- a4 – b4 = (a – b)(a3 + a2b + ab2 + b3) = (a – b) [ a2(a + b) + b2(a + b) ] = (a – b)(a + b)(a2 + b2)
How do you know when to factor out a negative?
The laws of multiplication state that when a negative number is multiplied by a positive number, the product will be negative. So, if considering a factor pair of a negative product, one of these factors must be negative and the other factor must be positive.
How do you find the first term in each factor?
Okay since the first term is x 2 x 2 we know that the factoring must take the form. We know that it will take this form because when we multiply the two linear terms the first term must be x 2 x 2 and the only way to get that to show up is to multiply x x by x x. Therefore, the first term in each factor must be an x x.
What is factoring and how does it work?
Let’s start out by talking a little bit about just what factoring is. Factoring is the process by which we go about determining what we multiplied to get the given quantity. We do this all the time with numbers. For instance, here are a variety of ways to factor 12.
What is a good example of a factor problem?
Example Problem Factor x2 + 7x +10. Factor x2 + 7x +10. x2 + 5x + 2x +10 Rewrite the middle term 7x as 5x + 2x. x(x + 5) + 2 (x + 5) Group the pairs and factor out the commo (x + 5) (x + 2) Factor out the common factor (x + 5). Answer (x + 5) (x + 2)
How do you factor a polynomial by factoring?
When factoring in general this will also be the first thing that we should try as it will often simplify the problem. To use this method all that we do is look at all the terms and determine if there is a factor that is in common to all the terms. If there is, we will factor it out of the polynomial.