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Find each product and write the result in standard form. (7 - 5i)(- 2 - 3i)
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Ch. 1 - Equations and Inequalities
Blitzer8th EditionCollege AlgebraISBN: 9780136970514
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TOC.tableOfContents
- Ch. P - Fundamental Concepts of Algebra311
- Ch. 1 - Equations and Inequalities398
- Ch. 2 - Functions and Graphs407
- Ch. 3 - Polynomial and Rational Functions306
- Ch. 4 - Exponential and Logarithmic Functions247
- Ch. 5 - Systems of Equations and Inequalities173
- Ch. 6 - Matrices and Determinants143
- Ch. 7 - Conic Sections124
- Ch. 8 - Sequences, Induction, and Probability251
Capitolo 2, Problema 13
Solve each equation in Exercises 1 - 14 by factoring. 7 - 7x = (3x + 2)(x - 1)
Guida verificata passo dopo passo1
Start by expanding the right-hand side of the equation \(7 - 7x = (3x + 2)(x - 1)\) using the distributive property (FOIL method): multiply each term in the first binomial by each term in the second binomial.
After expanding, rewrite the equation so that all terms are on one side, setting the equation equal to zero. This means subtracting the entire right-hand side expression from the left-hand side.
Combine like terms to simplify the equation into a standard quadratic form: $ax^2 + bx + c = 0$.
Factor the quadratic expression obtained. Look for two numbers that multiply to \(a \times c\) and add to \(b\), or use other factoring techniques such as grouping or special products.
Set each factor equal to zero and solve for \(x\) to find the solutions to the original equation.
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Factoring Quadratic Equations
Factoring involves rewriting a quadratic expression as a product of two binomials or other polynomials. This method is used to simplify equations and find their roots by setting each factor equal to zero.
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Solving Quadratic Equations by Factoring
Setting Equations to Zero
To solve polynomial equations by factoring, the equation must be rearranged so that one side equals zero. This allows the use of the zero-product property, which states that if a product equals zero, at least one factor must be zero.
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03:42Finding Zeros & Their Multiplicity
Zero-Product Property
The zero-product property states that if the product of two expressions is zero, then at least one of the expressions must be zero. This principle is essential for solving equations after factoring, as it leads to finding the solutions.
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3:49Product, Quotient, and Power Rules of Logs
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