Two forms of the Division Algorithm are shown below. Identify and label each term or function.
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- Describe the end behavior of each polynomial. (a) y=x38x2+2x15 End behavior: y as x y as x (b) y=2x4+12x+100 End behavior: y as x y as xarrow_forwardWhich of the following polynomial functions has a graph that crosses the x- axis at (-4,0)? A. f(x) = (x – 4) (x + 4) B. f(x) = x(x + 4)? C. f(x) = -(x – 4)* D. f(x) = (x - 4)3 Which of the following polynomial functions has a graph that touches the x-axis at (-4,0)? A. fAx) = (x- 4) (x + 4) B. f(x) = x(x + 4)? C. fAx) = -(x- 4)* D. f(x) = (x – 4)3arrow_forwardA country's census lists the population of the country as 245 million in 1990, 289 million in 2000, and 325 million in 2010. Fit a second-degree polynomial passing through these three points. (Let the year 2000 be x = 0, the year 2020 be x = 20, and let p(x) represent the population in millions.) p(x) = million Use this polynomial to predict the populations in 2020 and in 2030. 2020 million million 2030 Need Help? Watch It Read Itarrow_forward
- Use synthetic division to divide f(x) by x- k for the given value of k. Then express f(x) in the form f(x) = (x- k)q(x) +r for the given value of k. f(x) = - 6x + 2x² + 5x – 10; k= 2 O A. f(x) = (x - 2)(- 6x2 - 10x + 15) – 40 O B. f(x) = (x - 2)(- 6x2 + 10x + 25) - 40 O c. f(x) = (x -2)(- 6x2 - 10x – 15) – 40 O D. f(x) = (x+ 2)(- 6x2 + 10x + 25) – 40arrow_forwardA country's census lists the population of the country as 245 million in 1990, 289 million in 2000, and 325 million in 2010. Fit a second-degree polynomial passing through these three points. (Let the year 2000 be x = 0, the year 2020 be x = 20, and let p(x) represent the population in millions.) P(x) = million X Use this polynomial to predict the populations in 2020 and in 2030. 2020 353 million 2030 373 million Submit Answerarrow_forward(-5,0) (-2,0) (2,0) -6 -3 -2 3. (0,-4) -10arrow_forward
- Determine the end behavior of this functionarrow_forwardGraph the polynomial function using a calculator. f(x) = x(x - 4)(x + 4) y 6아 60 40 4아 20- 20 -8 -6 14 -2 2 6 8 -8 -6 -4 -2 2 4 -20- -40- 4아 -60- -60 y y 6아 60 4아 40 2아 2아 -8 -6 -4 -2 2 6 8 -8 -6 -4 2 4 8 20- -20- -4아 -4아 -60 -60- Determine the intercepts. x-intercept (x, y) = (smallest x-value) x-intercept (x, y) = x-intercept (x, y) = (largest x-value) y-intercept (x, y) = Determine the end behavior. As x- -0, f(x) - -00 As x- 0, f(x) →arrow_forwardGraph each polynomial functionarrow_forward
- A secret code has been embedded into a polynomial function f(x). The code has 5 digits that are arranged from least to greatest. The digits are the zeroes of f(x). A spy overheard that two of the digits are 1 and 8. If f(æ) = x7 – 18x6 + 118x5 – 414x4 + 1141æ³ – 2268x² + 1440x , factor f(x) to find the code. - Enter the 5 digit code. Type answer here. Be careful with spelling.arrow_forwardThe polynomial p(x)=(3−2x)(x2−5)p(x)=(3−2x)(x2−5) is graphed in the coordinate plane. Which statement about the graph is correct? Responses As x→∞x→∞, p(x)→∞p(x)→∞ and as x→−∞x→−∞, p(x)→∞p(x)→∞ As x rightarrow infinity, p times x rightarrow infinity and as x rightarrow negative infinity, p times x rightarrow infinity As x→∞x→∞, p(x)→∞p(x)→∞ and as x→−∞x→−∞, p(x)→−∞p(x)→−∞ , As x rightarrow infinity, p times x rightarrow infinity and as x rightarrow negative infinity, p times x rightarrow negative infinity As x→∞x→∞, p(x)→−∞p(x)→−∞ and as x→−∞x→−∞, p(x)→∞p(x)→∞ , As x rightarrow infinity, p times x rightarrow negative infinity and as x rightarrow negative infinity, p times x rightarrow infinity As x→∞x→∞, p(x)→−∞p(x)→−∞ and as x→−∞x→−∞, p(x)→−∞arrow_forwarda) Graph the following polynomial function using mapping notation. Show all wor 10 8 +2) + 3 g(x) = (-;* + %3D 4 2 10-8-6 8 10 -2 2. -2 -4 -4 -6 -8 -10 b) State the D+R: Domain: Range:arrow_forward
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