QuestionQuestion

Transcribed TextTranscribed Text

(1 point) Suppose f ( x) = x5 ( 5 - 2x3 ). (a) The roots of f ( x) are x = O, 1.35720880 Is repeated , enter lt only once .) (b) As X -+ 00 , f (x) -+ (b) As X -+ - 00, J (x) -+ help (numbers) (lf a root help (numbers) help (numbers) (1 point) For the tunction y = ( x - 3) (x + 2) ( 4x - 2), its y-i ntercept is y = its X-intercepts are X = Note: lf there is more than one answer enter them separated by commas . lf there are none , enter none . When X -+ 00, y -+ oo ( Input + or - for the answer ) When X -+ -00, y -+ oo ( Input + or - for the answer ) (1 point) Use synthetic division and the Remainder Theorem to evaluate P( e), where P (x) = x3 -3 x2 + 6x -14 , c = 2 The quot ient is [ l (1 point) Use synthetic division and the Remainder Theorem to evaluate P( e), where P( x) = x2 + 8x + 9, e = -1. °The quot ient is (1 point) Use synthetic division and the Remainder Theorem to evaluate P( e), where P(x) = x 4 + 7x3 + 3x 2 + 24x + 22, e= -7 th e quotient is (1 polnt) For the functlon y = l X - ti) l x + O), its y-i ntercept is -48 its X-intercepts are X = 8, -6 Note: lf there Is more than one X- lntercept wrlte the x-values separated by commmas. When X -+ 00, y -+ When X -+ -00, y -+ 00 (Input + or - for the answer) 00 (Input + or - for the answer) (1 polnt) What Is the degree of the followlng polynomlal? (x3a - l)( x3ª + 3) Degree: (1 point) The potynomiat f ( x) = ( 4 - 2x )(3x - 3)2 has degree= -3 ----- teadlng coeff lclent= --18- ---- constant coeff lclent= 1 (1 point) The potynomiat f ( x) = x5 ( 5 - 2x3 ) has degree= 8 teadlng coeff lclent= -2 constant coeff lclent= (1 point) Suppose f(x) = ( 4 - 2x)(3x - 3)2 . (a) The roots of f (X) are X = ¡ 2, 1 J help (numbers) (lf a root ~------~ is repeated , enter it only once .) (b) As X --+ 00, f(x) --+ help (numbers) (b) As X --+ -oo, f (X) --+ ~------~ help (numbers) (1 point) Suppose f(x) = - (3 - x)(x + 2)(5x + 2)2. (a)Therootso f f(x) are x = 3,-2,-215 is repeated , enter it only once.) (b) As X --+ 00, f (x) --+ (b) As X --+ -00, f (x) --+ help (numbers) (lf a root help (numbers) help (numbers) (1 point) Find the quotient and remainder using synthetic division for x5 - x4 + 8x3 - 8x2 + 2x - 10 x-1 The quotien t is (1 polnt) Flnd a degree 3 polynomla l having zeros -3, 4 and 8 and the coefflcle nt of x 3 equal 1. The polynomlal Is (1 point) Ust ali possible rational roots for the function f(x) = 7x4 + 5x3 + Ox2 - 9x + 91. Give your list in increasing order. Beside each poss ible rational root, type "yes· if it is a root and · no· if it is nota root. Leave any unnecessary answer blanks empty. Possible rational root: - Is it a root? 11 1 . Possible rational root: Is ita root? - Possible rational root: Is ita root? - Possible rational root: Is ita root? - Possible rational root: Is ita root? - Possible rational root: Is ita root? - Possible rational root: Is ita root? - Possible rational root: Is ita root? - Possible rational root: Is ita root? - Possible rational root: Is ita root? - Possible rational root: Is ita root? - Possible rational root: Is ita root? (1 point) Find all the real zeros of the polynomial P(x) = x3 - 2x2 - 9x + 4. Enter the real zeros as a comma -separated list: 14,-1 + sqrt(2), -1- sqrt(2) Note: Give exact answers; no decimals. lf needed, enter square root as sqrt, e.g. the square root of 2 should be enterad as sqrt(2). When x --> oo, P( x) --> 1 ---.------""--, When x --> -oo, P( x) --> Note: lf your answer is oo, enter infinity; if your answer is -oo, enter -infinity. (1 point) Find the quotient and remainder using synthetic division for x5 - x4 + 3x3 - 3x2 + 9x - 16 x - 1 The quotient is "'---------- ( 1 polnt) Glven that f ( x) Is a cublc functlon wlth zeros at - 6, 2, and 9, flnd an equatlon for f (x ) given that / (- 5) = 9. f( x) = (1 polnt) Flnd a degree 3 polynomlal whose coefflclent of x3 equal to 1. The zeros of thls polynomlal are 1, - 2i, and 2i. Slmplify your answer so that it has only real numbers as coeffic ients. Your answerIs (1 point) Find a degree 3 poly nomial that has zeros - 2, 3 and 8 and in which the coeffic ient of x 2 is -18. The polynomial is (1 point) For p(x) = 1.5 + x1 + 3x2 + 7x3 + 2x4 + 8x5 + 8x6 Degree of p = Leading term = Leading coefficien 6 8X"6 t = 8 Determine the coefficient and the degree of each term. Term Coefficient Degree 1.5 X 3x2 7x3 2x4 8x 5 8x6 l O A B l O ' ' e o 1. f(x) = (x - l)(x - 3)(x - 5) 2. f(x) = (x - l)(x - 3)(x + 5) 3. f(x) = (x - l)(x + 3)(x + 5) 4. f(x) = (x + l )(x + 3)(x + 5) . . 1 /1 (\ • . • • .. • ... J . . . . \ A B I , . • ' ' J• V . e D e 1.f( x) = - x3 + x2 + 6x a 2. f( x) = - x3 - x2 + 6x d 3 . f ( x) = x3 - x2 - 6x b 4 . f ( x) = x 3 + x 2 - Gx [ ••• A B •• • •• e D d 1. J(x) = x4 + 5x2 + 4 a 2.f(x) = x4 - 5x2 +4 b 3. J(x) = -x 4 + 5x2 - 4 e 4.f(x) = -x 4 -5x 2 - 4 (1 point) For the tunction y = ( x - 2) (x + 2) (6x - 2), its y-i ntercept is y = its X-intercepts are X = Note: lf there is more than one answer enter them separated by commas. lf there are none, enter nona . When X -+ 00, y -+ oo ( Input + or - for the answer ) When X -+ -00, y -+ oo ( Input + or - for the answer ) (1 point) For the tunction y = x4 - 5x 3 - 14x2, its y-i ntercept is y = .._ _______ ___, its X-intercepts are X = Note: lf there is more than one answer enter them separated by commas. lf there are none, enter nona . When :t -+ oo, y -+ oo (Input + or - tor the answer) When :t -+ -oo, y -+ oo (Input + or - tor the answer) (1 point) Let f(x) = x2 + 2x + 3 and g(x) = 4x3 - 5x2 + 4x + 1 For brevity let's write deg(p) for the degree of a polynomial p. So in the above example, deg(f) = 2 and deg(g) = 3. You can answer the follow ing questions without actually computing the indicated functions . deg(f + g) deg(f - g) deg(f g) deg(f o g) deg(g o f) (1 point) For the function y = ( x - 1 )2( x - 6), its y-intercept is y = its X-i ntercepts are X = Note: lf there is more than one answer enter them separated by commas. lf there are nona, enter nona . When X --> 00, y --> oo ( Input + or - for the answer ) When X --> -00, y --> oo ( Input + or - for the answer ) (1 point) For the tunction y = x 3 - x 2 - 12x, its y-i ntercept is y = its X-i ntercepts are X = Note: lf there is more than one answer enter them separated by commas. lf there are none, enter nona . When X -+ 00, y -+ oo ( Input + or - for the answer ) When X -+ -00, y -+ oo ( Input + or - for the answer ) (1 point) For the tunction y = x 4 - 5x3 - 24x2, its y-i ntercept is y = its X-i ntercepts are X = Note: lf there is more than one answer enter them separated by commas. lf there are none, enter nona . When X -+ 00, y -+ oo (Input + or - tor the answer) When X -+ -oo, y -+ oo (Input+ or - tor the answer) (1 point) For the tunction y = x3 - x 2 - 12x, its y-i ntercept is y = its X-i ntercepts are X = Note: lf there is more than one answer enter them separated by commas. lf there are none, enter nona . When X -+ 00, y -+ oo ( Input + or - for the answer ) Whenx -+ -oo, y-+ oo ( Input + or - for the answer ) (1 point) For the function y = x( X - 7) (X+ 6), its y-intercept is y = its X-i ntercepts are X = Note: lf there is more than one answer enter them separated by commas. lf there are none, enter none . When X -+ 00, y -+ oo ( Input + or - for the answer ) When X -+ -00, y -+ oo ( Input + or - for the answer ) (1 polnt) The polynom lal of degree 4, P( x) has a root of multlpllcity 2 at :i; = 4 and roots of multip licity 1 at X = O and X = -4. lt goes through the point ( 5, 4.5} Find a formula for P( X). P(x) = (1 point) Find the quotient and remainder using long dlvision for 2x3 - 8x2 + 7 x - 13 2x2 + 5 The quotlent Is

Solution PreviewSolution Preview

This material may consist of step-by-step explanations on how to solve a problem or examples of proper writing, including the use of citations, references, bibliographies, and formatting. This material is made available for the sole purpose of studying and learning - misuse is strictly forbidden.

    $90.00 for this solution

    PayPal, G Pay, ApplePay, Amazon Pay, and all major credit cards accepted.

    Find A Tutor

    View available Mathematics - Other Tutors

    Get College Homework Help.

    Are you sure you don't want to upload any files?

    Fast tutor response requires as much info as possible.

    Decision:
    Upload a file
    Continue without uploading

    SUBMIT YOUR HOMEWORK
    We couldn't find that subject.
    Please select the best match from the list below.

    We'll send you an email right away. If it's not in your inbox, check your spam folder.

    • 1
    • 2
    • 3
    Live Chats