when is partial factoring used?
When no other method helps you break up a complex polynomial?
We are learning about parabolas and the question was using partial facotring to find 2 points that lie on the parabola. How would I do that?
Ex. y=x^2-12x+23
x^2 + 12x + ? what is the ? to make a perfect square. Answer, half of 12, squared, or six squared, or ...
x^2+12x+36 makes a perfect square.
y= x^2+12x + 36 +23 -36 Notice we added 36 and subtracted 36 to keep it equal to y.
y= (x+6)^2 - 13
In mrs.Quimby's Class, everyone plays on a team. There are five more soccer players than baseball players. There are three more students on the track team than on the baseball team.There are two more football players than hockey players. There are three more students on the track team than the football team. Then number of baseball and football players equals 8. How many players are on each team? how many students are there in the class?
Partial factoring is a method used in algebra to simplify expressions or solve equations involving polynomials. It is particularly useful when dealing with quadratic or higher degree expressions.
Partial factoring is typically used in a few situations:
1. Simplifying expressions: When faced with a polynomial expression, partial factoring can be used to rewrite it in a factored form. This can help to reveal common factors or simplify the expression.
2. Solving equations: In some cases, partial factoring can be employed to solve equations involving polynomials. By factoring out common terms or using factoring techniques, you can transform the equation into an easier form to solve.
3. Finding roots: Partial factoring can be useful when you are trying to find the roots or zeros of a polynomial function. By factoring out known factors or using factoring techniques, you can often determine the values for which the polynomial equals zero.
To effectively use partial factoring, follow these general steps:
1. Identify common factors: Look for any common factors that can be factored out from the expression. This involves finding common terms or using factoring techniques like the distributive property.
2. Apply factoring techniques: Utilize specific methods like difference of squares, grouping, or perfect square trinomial to factor the expression as much as possible.
3. Simplify the expression: After partial factoring, simplify the factored expression by combining like terms or rearranging it to a more compact and manageable form.
Overall, partial factoring is a versatile tool that can be used in various scenarios to simplify expressions, solve equations, or find the roots of polynomial functions.