Quadratic Trinomial where a = 1
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This document provides instructions for factoring quadratic trinomials where the leading term is equal to 1. It defines a quadratic trinomial as an expression in the form of ax^2 + bx + c, where b and c are constants and a ≠ 0. It consists of three terms. The document then presents two examples of factoring trinomials where a = 1 by listing all pairs of numbers with a product equal to c and a sum equal to b, and writing the factors. It concludes by emphasizing that to factor where a = 1, get the factors of the last term where the sum is the middle term coefficient.
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Linear equations inequalities and applications
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3.3 Zeros of Polynomial Functions
This document discusses key concepts related to finding zeros of polynomial functions including:
1) The factor theorem, which states that a polynomial x - k is a factor of a function f(x) if and only if f(k) = 0.
2) The rational zeros theorem, which gives possible rational zeros based on the factors of the leading coefficient and constant term.
3) The fundamental theorem of algebra, which states that every polynomial of degree n has n complex zeros and examples of finding functions based on given zeros.
4) The conjugate zeros theorem, which states that if z = a + bi is a zero, then z = a - bi is also a zero for polynomials with real coefficients.
5
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This document provides information about several advanced algebra topics:
1. The Remainder Theorem states that when dividing a polynomial f(x) by x-c, the remainder is equal to f(c).
2. The Factor Theorem states that if f(c) = 0, then x-c is a factor of the polynomial.
3. Synthetic division is a method for dividing polynomials without subtracting, by multiplying the coefficients.
4. The Rational Zeros Theorem can be used to find all possible rational zeros of a polynomial by considering factors of the leading coefficient and constant term.
Factoring Polynomials in Modular Approach
The document provides lessons on factoring polynomials with common monomial factors and the difference of two squares. It explains that to factor polynomials with common monomial factors, one must find the greatest common factor (GCF) and divide each term by the GCF. It also explains that to factor the difference of two squares, one must get the square root of each term and use those roots to form the sum and difference as factors. Examples are provided to demonstrate these factoring techniques step-by-step. The document aims to teach learners how to completely factor different types of polynomials.
6.3 presentation
This document provides examples of solving systems of linear equations by elimination. It explains the steps:
1) Write the system so that like terms are aligned.
2) Eliminate one variable by adding or subtracting the equations.
3) Substitute the value into one equation to solve for the other variable.
4) Write the solution as an ordered pair and check.
It shows how to multiply equations by a number to produce opposite coefficients for elimination. Examples demonstrate solving systems by addition, subtraction, and multiplication.
Math 116 pres. 1
CHAPTER 2 Whole Numbers: Introducing a Mathematical System
2.3 Algebraic Extensions of Order of Operations to Polynomials
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- 1. Factoring : Quadratic Trinomial where a = 1 Lorie Jane L. Letada Module 1
- 2. Objectives At the end of this lesson, you are expected to: identify a quadratic trinomial with leading term equal to one; factor the quadratic trinomial completely.
- 3. Review REVIEW ON THE LAWS OF MULTIPLYING AND ADDING INTEGERS.
- 4. What’s New
- 5. What is it The expression above is called quadratic trinomial. A quadratic trinomial is an expression in the form of 𝑎𝑥2 + 𝑏𝑥 + 𝑐 where b and c are constants and a ≠ 0. It consists of three terms. Now, let us learn how to factor trinomial in general form where a = 1.
- 6. Example 1 Factor 𝑥2 + 7𝑥 + 12 Step 1. Step 2. List all pairs of numbers with a product equal to c (last term) and find the sum of each pair. Find the factor of the first term. 𝑥2 = 𝑥 • x Step 3. Choose the pair that adds up to b or the middle coefficient of the given expression. In this case, the shaded row of the table is the pair.
- 7. Step 4. Write the factors. 𝑥2 + 7𝑥 + 12 = 𝑥 + 4 (𝑥 + 3) To check, follow the FOIL method or the distributive property of multiplication.
- 8. Example 2 Factor 𝑥2 − 7𝑥 + 12 Step 1. Step 2. List all pairs of numbers with a product equal to c (last term) and find the sum of each pair. Find the factor of the first term. 𝑥2 = 𝑥 • x Step 3. Choose the pair that adds up to b or the middle coefficient of the given expression. In this case, the shaded row of the table is the pair.
- 9. Step 4. Write the factors. 𝑥2 − 7𝑥 + 12 = 𝑥 − 4 (𝑥 − 3) To check, follow the FOIL method or the distributive property of multiplication.
- 10. Activity 1.5
- 11. What I need to remember A quadratic trinomial is an expression in the form of 𝑎𝑥2 + 𝑏𝑥 + 𝑐 where b and c are constants and a ≠ 0. It consists of three terms. To factor quadratic trinomial where a = 1, get the factor of the last term and the sum should be the middle term coefficient.
- 12. "The way to get started is to quit talking and begin doing." -- Walt Disney