#factoring expressions

[er-cryptid]

Factoring Expressions Ex. 4

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[er-cryptid]

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[kerlonultra]

Factoring expressions

If the sign of the last term is positive, (1) find two numbers (both will be positive or both will be negative) whose product is the last term and whose sum is the coefficient of the middle term and (2) give both factors the sign of the middle term.įirst check to see whether you can monomial factor (factor out common terms). If the sign of the last term is negative, (1) find two numbers (one will be a positive number and the other a negative number) whose product is the last term and whose difference is the coefficient (number in front) of the middle term and (2) give the larger of these two numbers the sign of the middle term and the opposite sign to the other factor. To decide on the signs of the numbers, do the following. (2) Factor the last term and place the factors in the right sides of the parentheses. Place these factors in the left sides of the parentheses. Then if a = 1 (that is, the first term is simply x 2), use double parentheses and factor the first term. To factor polynomials having three terms of the form ax 2 + bx + c, (1) check to see whether you can monomial factor (factor out common terms). To factor the difference between two squares, (1) find the square root of the first term and the square root of the second term and (2) express your answer as the product of the sum of the quantities from Step 1 times the difference of those quantities.įactoring polynomials having three terms of the form ax 2 + bx + c When the common monomial factor is the last term, 1 is used as a place holder in the second factor.įactoring the difference between two squares To factor out a common factor, (1) find the largest common monomial factor of each term and (2) divide the original polynomial by this factor to obtain the second factor. To factor means to find two or more quantities whose product equals the original quantity. Quiz: Linear Inequalities and Half-Planes.Solving Equations Containing Absolute Value.Inequalities Graphing and Absolute Value.Quiz: Operations with Algebraic Fractions.Solving Systems of Equations (Simultaneous Equations).Quiz: Solving Systems of Equations (Simultaneous Equations).Quiz: Variables and Algebraic Expressions.Signed Numbers (Positive Numbers and Negative Numbers).Quiz: Simplifying Fractions and Complex Fractions.Simplifying Fractions and Complex Fractions.Quiz: Signed Numbers (Positive Numbers and Negative Numbers).Quiz: Multiplying and Dividing Using Zero.Quiz: Properties of Basic Mathematical Operations.Properties of Basic Mathematical Operations.

[maths-help]

Factorise these expression by completing the square: xpowerof2+2x-8 and another one xpowerof2-x+4 and if you don't mind can you please show me the steps thank you heaps

Hey,

we have a wonderful step-by-step tutorial written here! I hope that helps.

x²+2x-8 = (x+1)² - 9

x²-x+4 = (x-0.5)² + 3.75

-sorrel

[maths-help]

may I please have a step by step method to factor hard quadratic equations when the coefficient of x2 isn't 1..? I have a mock on wed😭

Hey Anon! We have a great step-by-step masterpost about quadratic expressions here, and it also covers factoring. There is also a great tutorial here which also covers factorising by solving first.

In short: Look for common factors/coefficents, and if this turns out to be too difficult, take the save road and use the quadratic formula.

Good luck for your mock!

-sorrel

[maths-help]

Previous Answer

"Hi. I need to factorise this. Y(squared)-6y-5=0"

you could also complete the square for this equation

 So you would have (y-3)^2-5-9 = 0

(y-3)^2-14 = 0 (y-3)^2 = 14 y-3 = +/- 3.74 (square root of 14)

y = +/- 3.74+3

 This means y either equals 6.74 or -0.74

-------

Yes, you can either use the quadratic formula here or the vertex form!

[maths-help]

please can you try to explain factorising to me? i dont know how to do this question: factorise 7xy - xy squared

(I suppose you mean 7xy - xy² since everything else doesn’t maky any sense)

First, we’ve got a really good explanation on factorising here.

By Factorising an equation, you drag out numbers or variables that can be found in both summands (in this case).

So let’s get the x out of there first:

x (7y-y²)

We’ve also got the y let in both summands in the bracket, so:

xy (7-y)

You could have also dragged out both of them (xy) first as an alternative. Now you can check if you’ve done everything right by multiplying the factors and your result is exactly what you started with.

-sorrel

[maths-help]

jumpingdandelionsasked:

(x+y)^3+(x-y)^3 and (a+b)^4-(a-b)^4

For the addition terms we've got a great post that explains why using Pascal's triangle is a lot easier than doing this by hand here.

However, for the terms with a negative algebraic sign, you can also use Pascal's triangle but you've got to substract every factor where y (or b in the second case) has an odd exponent.

The fact that the second one is a difference is why thus it looks like 8a³b+8ab³ in the end, having erased all factors where b's got an even exponent, while in the first case all factors where y's got an odd exponent get erased: 2x³+6xy².

-sorrel