Divide by 4

Learning Objectives Apply division by 4 to factor polynomials with a common factor. Use division by 4 as the first step in solving quadratic equations by completing the square. Simplify radical expressions by identifying and factoring out perfect squares, specifically 4 and its multiples. Analyze and describe horizontal transformations of functions involving a factor of 4. Efficiently find the vertex of a parabola when the 'a' coefficient is 4. Manipulate polynomial expressions and equations by dividing every term by 4 to simplify the problem. Ever feel like a complex algebra problem is just a simple one in disguise? What if the secret to solving `4x² + 24x - 16 = 0` was as easy as dividing by 4? 🤔 This tutorial goes beyond basic arithmetic. We will explore how t...

TermDefinitionExample Greatest Common Factor (GCF)The largest number and/or variable that divides into each term of a polynomial expression without a remainder.In the polynomial `4x² + 8x - 12`, the GCF is 4. Dividing the polynomial by 4 gives `4(x² + 2x - 3)`. Quadratic Equation in Standard FormAn equation of the form `ax² + bx + c = 0`, where 'a', 'b', and 'c' are constants and 'a' is not equal to 0.`4x² + 16x + 8 = 0` is a quadratic equation where a=4, b=16, and c=8. Dividing by 4 simplifies it to `x² + 4x + 2 = 0`. RadicandThe number or expression inside a radical symbol (√).In the expression `√48`, the radicand is 48. To simplify, we can factor it as `√(16 * 3)`. Since 16 is `4²`, we can see the connection to 4. Perfect Square TrinomialA trinom...

The Division Property of Equality If `A = B` and `C ≠ 0`, then `A/C = B/C`. This fundamental rule allows you to divide both sides of an equation by the same non-zero number. We use this to simplify entire quadratic or polynomial equations by dividing every single term by 4. Factoring out the GCF `4ax + 4b = 4(ax + b)` When every term in an expression shares a common factor of 4, you can 'factor it out'. This is equivalent to dividing each term by 4 and placing the result in parentheses with the 4 outside. Simplifying Radicals `√(4a) = √4 * √a = 2√a` If the radicand has a factor that is a perfect square (like 4), you can split the radical into two and simplify the perfect square part. This is a key step in simplifying radical expressions.