Please help with multiplying binomials! Show your work! (3n+2)(n+3)
1 answer:
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The quotient of a trinomial and monomial can be 9x² +2x + 1 while the product of the polynomials x² + 2x + 1 and 3x² - 1 is 3x⁴ + 6x³ + 2x² - 2x - 1
<h3>The quotient of a trinomial and monomial</h3>Let the variable be x.
Trinomial are polynomials that have three terms, while monomials have a single term.
Using the above definition, we have:
Trinomial = 9x³ + 2x² + x
Monomial = x
The quotient of the above is represented as:
Evaluate the quotient
9x² +2x + 1
<h3>The product or quotient of polynomials</h3>To do this, we make use of the following polynomials:
x² + 2x + 1 and 3x² - 1
The product is represented as:
(x² + 2x + 1) * (3x² - 1)
Expand
3x⁴ - x² + 6x³ - 2x + 3x² - 1
Evaluate the like terms
3x⁴ + 6x³ + 2x² - 2x - 1
Hence, the product of the polynomials x² + 2x + 1 and 3x² - 1 is 3x⁴ + 6x³ + 2x² - 2x - 1
Read more about polynomials at:
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Answer:
- zeros are {-2, 3, 7} as verified by graphing
- end behavior: f(x) tends toward infinity with the same sign as x
Step-by-step explanation:
A graphing calculator makes finding or verifying the zeros of a polynomial function as simple as typing the function into the input box.
<h3>Zeros</h3>The attachment shows the function zeros to be x ∈ {-2, 3, 7}, as required.
<h3>End behavior</h3>The leading coefficient of this odd-degree polynomial is positive, so the value of f(x) tends toward infinity of the same sign as x when the magnitude of x tends toward infinity.
- x → -∞; f(x) → -∞
- x → ∞; f(x) → ∞
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<em>Additional comment</em>
The function is entered in the graphing calculator input box in "Horner form," which is also a convenient form for hand-evaluation of the function.
We know the x^2 coefficient is the opposite of the sum of the zeros:
-(7 +(-2) +3) = -8 . . . . x^2 coefficient
And we know the constant is the opposite of the product of the zeros:
-(7)(-2)(3) = 42 . . . . . constant
These checks lend further confidence that the zeros are those given.
(The constant is the opposite of the product of zeros only for odd-degree polynomials. For even-degree polynomials. the constant is the product of zeros.)
