Illustrative Math - Algebra 2 - Unit 2 - Lesson 9

State the degree and end behavior of f(x)=-x^{3}+5x^{2}+6x+1. Explain or show your reasoning.

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The graph of a polynomial function f is shown. Select all the true statements about the polynomial.

• The degree of the polynomial is even.
• The degree of the polynomial is odd.
• The leading coefficient is positive.
• The leading coefficient is negative.
• The constant term of the polynomial is positive.

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Write the sum of 5x^{2}+2x-10 and 2x^{2}+6 as a polynomial in standard form.

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F.BF.3

State the degree and end behavior of f(x)=4x^{3}+3x^{5}-x^{2}-2. Explain or show your reasoning.

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Select all the polynomial functions whose graphs have BIx-intercepts at x=4,-\frac{1}{4},-2.

• {"blocks":[{"key":"0","text":"(x+4)(4x-1)(x-2)","type":"unstyled","depth":0,"inlineStyleRanges":[],"entityRanges":[{"offset":0,"length":16,"key":0}],"data":{}}],"entityMap":{"0":{"type":"MATH","mutability":"MUTABLE","data":{}}}}
• {"blocks":[{"key":"0","text":"(x-4)(4x+1)(x+2)","type":"unstyled","depth":0,"inlineStyleRanges":[],"entityRanges":[{"offset":0,"length":16,"key":0}],"data":{}}],"entityMap":{"0":{"type":"MATH","mutability":"MUTABLE","data":{}}}}
• {"blocks":[{"key":"0","text":"(x-4)(4x-1)(x-2)","type":"unstyled","depth":0,"inlineStyleRanges":[],"entityRanges":[{"offset":0,"length":16,"key":0}],"data":{}}],"entityMap":{"0":{"type":"MATH","mutability":"MUTABLE","data":{}}}}
• {"blocks":[{"key":"0","text":"(x+4)(4x+1)(x+2)","type":"unstyled","depth":0,"inlineStyleRanges":[],"entityRanges":[{"offset":0,"length":16,"key":0}],"data":{}}],"entityMap":{"0":{"type":"MATH","mutability":"MUTABLE","data":{}}}}
• {"blocks":[{"key":"0","text":"(2x+4)(4x-1)(x-2)","type":"unstyled","depth":0,"inlineStyleRanges":[],"entityRanges":[{"offset":0,"length":17,"key":0}],"data":{}}],"entityMap":{"0":{"type":"MATH","mutability":"MUTABLE","data":{}}}}

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F.BF.3