the following f(x) = x* + 6x³ +x² – 42x – 56 4: Factor the polynomial completely.

Q: Find all zeros of the polynomial. P(x) = x5 - 3x4 + 12x3 - 28x2 + 27x - 9

A: Zeroes of the polynomial are the values which return zero value for the polynomial. Highest power of…

Q: Find the condition which must be satisfied by the coefficients of the polynomial p(x) =x3 -px2…

A:

Q: What is the remainder when the polynomial f(x) = 4x* – 3x³ + x? + 10x – 1 is divided by (x- 2). %3D

A:

Q: Complete the term-coefficient-degree table for the polynomial  y4 -y3 + 12y2 +3y

A:

Q: What is the leading term of the polynomial (v2z – 3x

A: The given polynomial is:  2x2-3x+963x-1433

Q: Show that x−6 is a factor of the polynomial p(x)=(1/3)x^3 − (15/2)x^2 + 56x − 138. How many real…

A:

Q: Consider the polynomial function 1 f(x) = 6x° + 10æª 12 24x %3D -- - - 19

A: The given polynomial,f(x)=6x9+10x4-x312-24x-119

Q: H.W:- find the root of the polynomial below:- 5 x³+ 4x1-3x³+2x²+x+1=0

A: The roots of a polynomial are those values of the variable that cause the polynomial to evaluate to…

Q: 2.) Use factoring to find the real zeroes of the polynomial. a.) f(x)= 27x-64 b.) h(x) = 25x' +175x…

A: Given, f(x)=27x3-64 find the real zeroes of the function f(x)=027x3-64=027x3=64x3=433 x=43 function…

Q: Find the value ofc that makes x² +10x +c a perfect square polynomial

A:

Q: Find the condition which must be satisfied by the coefficients of the polynomial p(x)=x3-px2+qx-r,…

A: we know for cubic equation,  ax^3+bx^2+cx + d having roots α,β and γ  Sum of roots,α+β+γ=−b/a, Sum…

Q: Find all zeros of the polynomial. P(x) = 2x3 + 7x2 + 12x + 9

A: Find all zeros of the polynomial. P(x) = 2x3 + 7x2 + 12x + 9

Q: Find the roots of the polynomial: f(x) = x4 + 4x2 – 32.

A: We have to find the roots of polynomial: fx=x4+4x2-32 To find the roots of given polynomial we need…

Q: What is the largest multiplicity in the factored polynomial y = (x2 – 1)(x + 2)(x + 4)?

A: Here function is :  y = (x2 - 1) (x +2 ) (x+4)  It can be written as  y = ( x - 1)( x + 1 )( x + 2)(…

Q: Given p(x)=(x-4)^5 (x+1)(x-2)^3State the zeros and their multiplicities. What is the degreeof the…

A: Given:The function is, p(x) = (x−4)5(x+1)(x−2)3.

Q: Find the zeros of the polynomial p(x)=x4-16

A:

Q: Given that (x + 2) is a factor of the polynomial 2a – 5x2 + ax + a, the - value of the constant a is

A: If (x+2)  is factor of the polynomial 2x3-5x2+ax+a then remainder will be zero when we divide (x+2)…

Q: Find factor of polynomial of  p(x) = x^2 - 6x + 8

A:

Q: Find the degree of the polynomial. x2 + 6x° + 5x + 3x° – 4

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Q: Find the remainder if F(x)=6x^3+49x^2+90x+56 is divided by 3x-3

A: F(x)=6x3+49x2+90x+56 Since 3x-3 is linearwhere 3x-3=0⇒3x=3⇒x=1 Remainder of F(x) when divided by…

Q: How many zeros does the polynomial 3x2 + 2x + 1 have in Z6?  I thought it was three but that was…

A: Solution: Given Polynomial is  3x2+2x+1   over  ℤ6

Q: Find the roots of the polynomial: f (x) = x4 + 4x² – 32

A:

Q: 3. What is the kvalue for the polynomial x - 7x + 17x – 15 if a factor is x – 3? A. k= -3 B. k= 3 C.…

A: We can use factorisation in order to solve the given problem.

Q: The polynomial p(x) has the rest (x+2) when dividing it by (x^2+2x-3) and the rest 1 when dividing…

A: We have given that  p(x) leaves the remainder (x+2) when divided by x2+2x-3 and  p(x) leaves the…

Q: Find all the zeros of the polynomial function. (Se fx) =x - 6r³ + 7x² + 6x- 8 1 g(x) = x-9x2- 4x +…

A: Given; 1) f(x)=x4-6x3+7x2+6x-8 2) g(x)=x4-9x2-4x+12

Q: The leading coefficient of the polynomial + 4x^12 + 4x^6 + x^4 – x is * 10 12 4

A: 1. Given polynomial is 5x10 + 4x12 + 4x6 + x4 - x As the leading coefficient of the polynomial is…

Q: The problem involve the Remainder Theorem.

A: Given, P(x)=x500+6x101-x2-2x+4 We know by remainder theorem ,if a Polynomial function P(x) is…

Q: Find the zeros of the polynomials f(x) =x2-5x2-16x +80 ,if it's two zeros are equal in magnitude but…

A: Consider the polynomial  fx=x3−5x2−16x +80

Q: Find the remainder when f(x) = 2x5 – 8x3 +3 is divided by 3x + 2. -

A: Long Division of Polynomials: A long division polynomial is an algorithm for dividing polynomial by…

Q: Is −4 a zero of the polynomial f(x) = 3x4− 6x3+ 5x − 12?

A: For x=4 to be the zero of the given polynomial it must fulfil the necessary condition given as.

Q: Q1. Perform factorization of zero: Gy - 5) (3x³ – 81)(4x + 13)(v3x – 1)(12x + 12) = 0

A: (78y-5)(3x3-81)(4x+13)(3x-1)(12x+12)=0⇒(78y-5)=0 ⇒78y=5 ⇒y=8x57⇒y=407.Or 3x3-81=0⇒ 3x3=81…

Q: Is f(X) = -9X8 + 15x3-8X2 + 2X + 37 a polynomial? %3D

A: To be a polynomial, exponents should not be radicals, rational numbers.

Q: Find all zeros of the polynomial. P(x) = x3 - 7x2 + 17x - 15

A:

Q: The polynomial f (x) = x + 16x + k is a perfect square trinomial. What is the value of k?

A: Given data: The given expression for the trinomial is f(x)=x2+16x+k. The standard expression for the…

Q: What is the degree of the polynomial 9 - 3x + 4y - x2? O 1 O 2 3. O 4

A: Degree is heightest power of polynomial.

Q: Express the second order polynomial p(x) = x^2 + 4x + 13 in the sum of square form

A:

Q: By what polynomial must x3-4 x2y+5xy2-2y3 be divided to obtain a quotient of x-y?

A:

Q: Complete the term-coefficient-degree table for the polynomial. y4 − y3 + 10y2 + 7y

A: The degree of polynomial is equal to the degree of the highest degree term.

Q: Find the condition which must be satisfied by the coefficients of the polynomial p(x)…

A: The solution is given below in the next step:

Q: 5. If the remainder dividing the polynomial P(x) = 2x³ + kx? + 7x +6 by x- 4 is 114, find the…

A: Quotient Remainder theorem  The answer after we divide one number by another. dividend ÷ divisor =…

Q: Evaluate the polynomial for x= 3 f(x) = 4x3 -10x +23

A: For evaluating any polynomial f(x) = ax3+bx+c. at x=x0 . replace the value of x with x0 Therefore at…

Q: Use the Factor Theorem to show that the statement in the exercise is true.

A:

Q: Show that is a zero of the polynomial 2 P(x) = 2x* + æ – 5a2 +10x - 4

A:

Q: Consider the polynomial p (x) = 2 (x + 1) (x – 3)² (A) As х — —о y →? (B) As y →? (C) Find the zeros…

A:

Q: Find the remainder when the polynomial 2x* – 5x² + 12x – 7 is divided by (x – 1).

A:

Q: Factor out the GCF from the given polynomial y(x+1)+3(x+1)

A: The given expression is y(x+1)+3(x+1)   Known fact: The greatest common factor or GCF is the largest…

Q: find the degree of the polynomial. 5x3y + 4x4y2 - 3x3y2

A: Given, 5x3y+4x4y2-3x3y2