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# Factors

/Tag: Factors
21 08, 2016

By |2016-10-21T13:16:59+10:00August 21st, 2016|Tags: , , , |0 Comments

Solving Quadratic Equations with Factors worked examples Solve x2 + 8x + 7 = 0.  (x + 7)(x + 1) = 0 Consider what will multiply to 7 and add to 8 ⇒ 7, 1 x = -7, x = -1 if the question is positive, then the answer is negative so the [...]

21 08, 2016

## Quadratic Equations By Factoring – Harder Case

By |2016-10-21T13:16:59+10:00August 21st, 2016|Tags: , , , |0 Comments

Solving Quadratic Equations with Factors: Harder Case worked examples Solve 4x2 + 4x - 15 = 0.  4x2 + 4x - 15 = 0 4x2 + 10x - 6x - 15 = 0 Step 1: multiply the coefficient of x2 by the constant ie 4 × -15 = -60 Step 2: [...]

25 07, 2016

## Factor By Grouping

Factor By Grouping worked examples further examples harder examples Factorise: 7x - y + 49x2 - y2. = 7x - y  + (7x - y)(7x + y) =(7x - y)[1 + (7x + y)] = (7x - y)(1 [...]

25 06, 2016

## Algebra Fractions Adding And Subtracting

By |2016-12-20T19:13:50+10:00June 25th, 2016|Tags: , , , |0 Comments

Algebra Fractions: Adding And Subtracting worked examples Simplify $\frac{x-1}{x+3}+\frac{2x-5}{x+2}$. $=\frac{(x-1)(x+2)}{(x+3)(x+2)}+\frac{(2x-5)(x+3)}{x+3)(x+2)}$ find the LCD (lowest common denominator) this will be: (x + 3)(x + 2) the first term needs to be multiplied by (x + 2) and the second term by (x + 3)  $=\frac{x^2+2x-x-2}{(x+3)(x+2)}+\frac{2x^2+6x-5x-15}{x+3)(x+2)}$ expand the top binomials (do [...]

31 05, 2016

By |2016-11-26T11:29:51+10:00May 31st, 2016|Tags: , , , |0 Comments

Quadratic Factors worked examples Factorise x2 + 6x + 8.  x2 + bx + c = (x + 4)(x + 2) we need to consider the factors of 8 (c): 8 & 1, 4 & 2 which pair of this will add to 6 (b)? 8 + 1 [...]

31 05, 2016

Quadratic Factors - Harder Case worked examples Factorise 4x2 + 4x - 15.  Method 1 4x2 + 4x - 15 = 4x2 + 10x - 6x - 15 Step 1: multiply the coefficient of x2 by the constant ie 4 × -15 = -60 Step 2: Consider what will [...]

31 05, 2016

## Quadratic Factors – Harder Case

By |2017-04-15T10:35:52+10:00May 31st, 2016|Tags: , , , |0 Comments

Quadratic Factors: Non-Monic (Harder Case)    worked examples Factorise 4x2 + 4x - 15.  Method 1 4x2 + 4x - 15 = 4x2 + 10x - 6x - 15 Step 1: multiply the coefficient of x2 by the constant ie 4 × -15 = -60 Step 2: Consider what [...]

14 09, 2015

## Difference Of Two Squares

Difference Of Two Squares $a^2-b^2=(a-b)(a+b)$ worked examples Factorise x2 -100. = (x - 10)(x + 10) this is the difference of two squares where the first term is x2 and the second term is 100, which is 102 Factorise y2 -25. this is the difference of two squares [...]

25 08, 2015

## Prime Factors

By |2016-10-21T13:17:09+10:00August 25th, 2015||Comments Off on Prime Factors

Prime Factors Prime factors are factors of a number which are prime numbers only. worked examples Find the prime factors of 12.  12: 1, 2, 3, 4, 6, 12 Find the factors of 12 ∴ prime factors are:  2, 3 1, 4, 6 and 12 are not prime numbers. leaving us [...]

25 08, 2015

## Common Factors

By |2016-10-21T13:17:09+10:00August 25th, 2015||Comments Off on Common Factors

Common Factors Common factors are factors that fit into both of the numbers evenly, without any remainders. worked examples Find the common factors of 12 and 48.  12: 1, 2, 3, 4, 6, 12  Find the factors of 12 48: 1, 2, 3, 4, 6, 8, 12, 16, 24, 48 [...]