Multiply by 5

Learning Objectives Multiply a polynomial expression by 5 using the distributive property. Multiply a radical expression by 5 and correctly simplify the result. Define the function g(x) = 5f(x) given a function f(x) in quadratic or linear form. Describe the graphical transformation that occurs when a function f(x) is multiplied by 5. Apply the concept of multiplying by 5 to solve algebraic equations involving parentheses. Differentiate between multiplying a function by 5 and evaluating a function at 5x. How can a simple operation like multiplying by 5 completely change the shape of a parabola or the outcome of a physics equation? 🚀 In this lesson, we'll elevate the basic concept of 'multiplying by 5' to a Grade 9 algebraic level. You will learn how this oper...

TermDefinitionExample Scalar MultiplicationThe process of multiplying a mathematical object (like a polynomial, vector, or function) by a single number (a scalar). In this lesson, our scalar is 5.Multiplying the polynomial (x + 2) by the scalar 5 results in 5(x + 2) = 5x + 10. Distributive PropertyA fundamental property of algebra which states that multiplying a sum by a number is the same as multiplying each addend by the number and then adding the products.5(a + b) = 5a + 5b. For the polynomial (x^2 - 3x), 5(x^2 - 3x) = 5x^2 - 15x. CoefficientA numerical or constant quantity placed before and multiplying the variable in an algebraic expression.In the term 7x^2, the coefficient is 7. When we multiply this term by 5, we get 35x^2, and the new coefficient is 35. Vertical StretchA transform...

Multiplication over Polynomials 5 \cdot (ax^n + bx^{n-1} + \dots + c) = 5ax^n + 5bx^{n-1} + \dots + 5c Use the distributive property to multiply the scalar 5 by the coefficient of every single term inside the polynomial. Multiplication of Functions Given a function f(x), the new function g(x) = 5f(x) is a vertical stretch of f(x) by a factor of 5. To find the expression for the new function, enclose the entire expression for f(x) in parentheses and multiply it by 5. Multiplication of Radical Expressions 5 \cdot (a\sqrt{b} + c\sqrt{d}) = 5a\sqrt{b} + 5c\sqrt{d} The scalar 5 multiplies only the coefficients outside the radical signs. The radicands (the numbers inside the square roots) remain unchanged.