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Questions and Answers
What is the result of the subtraction problem $(3x^2 - 2x + 1) - (x^2 + x - 2)$?
$2x^2 - 3x + 3$
Factor the polynomial $x^2 + 7x + 12$. Explain your steps.
$(x + 3)(x + 4)$
Multiply the polynomials $(x + 2)(x - 3)$. Simplify your result.
$x^2 - x - 6$
Add the polynomials $(2x^2 + 3x - 1) + (x^2 - 2x - 3)$. Simplify your result.
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Factor the polynomial $x^2 - 4x - 5$. Explain your steps.
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Multiply the polynomials $(x - 1)(x + 4)$. Simplify your result.
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When multiplying two polynomials, what is the degree of the product in terms of the degrees of the two polynomials?
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What is the purpose of combining like terms when multiplying two polynomials?
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What is the main difference between GCF factoring and difference of squares factoring?
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What is the advantage of factoring a polynomial?
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When factoring a polynomial using the sum and difference method, what are the two formulas that are used?
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What is the process of factoring by grouping, and when is it used?
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When multiplying two polynomials, why is it necessary to multiply each term in the first polynomial by each term in the second polynomial?
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What is the role of the greatest common factor in GCF factoring?
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Study Notes
Polynomials
Addition and Subtraction of Polynomials
- To add or subtract polynomials, combine like terms:
- Combine terms with the same variable(s) and exponent(s)
- Add or subtract coefficients
- Simplify the result
- Example:
(3x^2 + 2x - 1) + (2x^2 - 4x - 3) = ?
- Combine like terms:
5x^2 - 2x - 4
- Combine like terms:
- Important to note:
- You can only add or subtract polynomials with the same variables and exponents
Factoring Polynomials
- Factoring is the process of expressing a polynomial as a product of simpler expressions
- Types of factoring:
- Greatest Common Factor (GCF):
ax + ay = a(x + y)
- Difference of Squares:
a^2 - b^2 = (a + b)(a - b)
- Sum and Difference:
a^2 + 2ab + b^2 = (a + b)^2
anda^2 - 2ab + b^2 = (a - b)^2
- Greatest Common Factor (GCF):
- Example: Factor
x^2 + 5x + 6
- Look for two numbers whose product is 6 and sum is 5:
2
and3
- Factor:
(x + 2)(x + 3)
- Look for two numbers whose product is 6 and sum is 5:
Multiplication of Polynomials
- To multiply polynomials, use the distributive property:
- Multiply each term in one polynomial by each term in the other polynomial
- Combine like terms
- Simplify the result
- Example:
(2x + 3)(x + 4) = ?
- Multiply each term:
2x^2 + 8x + 3x + 12
- Combine like terms:
2x^2 + 11x + 12
- Multiply each term:
- Important to note:
- Be careful when multiplying polynomials with multiple terms and variables
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Description
Test your understanding of polynomial operations, including addition, subtraction, factoring, and multiplication. Practice combining like terms, finding greatest common factors, and using the distributive property to multiply polynomials.