devyy Understanding the Difference of Squares The difference of squares is a common algebraic factorization technique that takes the form of a² – b² = (a – b)(a + b). We’ll analyze the expression provided and identify notable patterns that may indicate a difference of squares. Breaking Down the Expression The given expression can be stated … Read more
To find the remainder when the polynomial x4 + 36 is divided by x2 + 8, we can use polynomial long division or synthetic division. However, for many polynomial operations, a more straightforward approach is to express the dividend in a suitable form. 1. **Expressing the Dividend:** Start with: x4 + 36 2. **Dividing Terms**: … Read more
The original price of the pants is $3500. To calculate the discount amount, you need to first find 20% of the original price. Here’s how you can do it step by step: Convert the percentage to a decimal by dividing by 100: 20% = 20/100 = 0.20. Multiply the original price by the decimal: $3500 … Read more
To find the value of the discriminant for the quadratic equation 3x² + 2x, we first need to identify the coefficients in the standard form of a quadratic equation, which is generally expressed as ax² + bx + c = 0. Here, we can rewrite the equation: 3x² + 2x = 0 can be interpreted … Read more
To understand how many cubic feet are in one unit of sand, we first need to clarify what ‘unit of sand’ means, as this terminology can vary based on context and location. Often, one unit of sand can refer to a cubic yard, especially in construction and landscaping. If we take a cubic yard as … Read more
The least common multiple (LCM) of two numbers is the smallest multiple that is evenly divisible by both numbers. To find the LCM of the denominators 16 and 58, we can use the following steps: Prime Factorization: First, we will find the prime factorization of both numbers. For 16: 16 = 2 × 2 × … Read more
Understanding Set Equality To say that two sets are equal, we must verify that they contain exactly the same elements. In mathematical terms, if A and B are two sets, they are considered equal, written as A = B, if every element of A is also an element of B, and vice versa. Key Points … Read more
To rewrite the expression 4×12 + 5×6 + 14 = 0 as a quadratic equation, we need to use a substitution that simplifies the terms. Let’s introduce a new variable, say y, where we define it as: y = x6 With this substitution, we can express: x12 = (x6)2 = y2 x6 = y Now … Read more
Understanding the Equation The equation given is 0x² + 6 = 0. Let’s break it down: In this equation, 0x² signifies that the coefficient of x² is zero. This means that the term involving x does not contribute to the equation. Thus, the equation simplifies to 6 = 0, which is clearly incorrect. Analyzing the … Read more
Solving the Equation √(2x + 1) = 3 To solve the equation √(2x + 1) = 3, follow these steps: Square both sides: Squaring both sides of the equation removes the square root: (√(2x + 1))² = 3² This simplifies to: 2x + 1 = 9 Solve for x: Next, isolate x by first subtracting … Read more