Show that (x- 3) is a factor of 2.x3 - 2x2 - 17x + 15. Hence express 2x³ – 2.x² – 17x + 15 in the form (x- 3)(Ax² + Bx + C), where the values A, B and Care to be found.

Q: Find the value of k such that x − 4 is a factor of x3 − kx2 + 2kx − 8.

A: Here we have to find the value of k,  It is given that,  x − 4 is a factor of f(x)= x3 − kx2 + 2kx −…

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

A:

Q: Show that x² − 4 is a factor of x⁴ − 5x³ + 2x² + 20x − 24

A:

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

A:

Q: The polynomial 2x^3 + ax^2 - 10x + b has a factor of ( x-1 ) and has a remainder of 15 when divided…

A:

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

A:

Q: 4. The polynomial equation whose roots are {-1, - ½ and 3} is А. 2х3- Зx2 - 8х-3%3D0 В. х3 - 6х2 - х…

A:

Q: Find m so that x + 5 is a factor of - 3x - 10x + 20x - 22x + m.

A: Given: x+5 is a factor of   -3x4-10x3+20x2-22x+m. To find: The value of m.

Q: Show that x² − 4 is a factor of x4 − 5x³+ 2x² + 20x − 24

A:

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

A:

Q: 4. x-2x+1= 3

A:

Q: xpress the polynomial in factored form p(x)=x^3-x^2-8x+12

A:

Q: 4x

A: Zeros of f(x) must satisfy f(x),i.e., f(x) will reduce to zero at the zeros of f(x).

Q: 9) Is x-2 a factor of x3 - 13x + 12?

A: To determine whether x-2 is a factor of x3-13x+12.

Q: Test the polynomial x – 2x3 + 6x – 3 for irreducibility over Q.

A: We have to check whether the polynomial x4-2x3+6x-3 is irreducible over the set of rational numbers…

Q: 4.  Show that X2? −4 is a factor of x4− 5x3 +2x?2+20x−24.

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 the value of k so that x-2 is a factor of P(x) = 2x3 – x2 + kx + 2

A:

Q: Determine the value of 7A+7M if 2x4 + 3x3 + + 8x2 + 9x + 3 A За + М + (1+x²)² х — 3 x(1+x²)² 1+x² ||

A: Given: 2x4+3x3+8x2+9x+3x1+x22=Ax-x-31+x2+3x+M1+x22

Q: 9) Is x-2 a factor of x3 – 13x + 12?

A:

Q: What is the equation whose roots are reciprocal of the roots of the equation of 2x2 + 5x + 2 = 0?

A:

Q: Why is x-3 a factor of m(x) x^3-x^2-5x-3

A: It is  polynomial equation.

Q: Prove that (x+2) is a factor of 3x'+8x+x-6 and find the other factor.

A: we have to find factor of the polinomial

Q: For the remainder of the division of x-2x²+3kx+18 by x-6 to be equal to zero, k must be equal to?

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 m so that x+5 is a factor of 5x3+29x2+mx+20

A: Let f(x)=5x^3 + 29x^2 +mx+20 , if (x+5) is a factor of f(x) then by factor theorem f(-5)=0

Q: Find the coefficient of x11 in (x2 - 3x) / (1 - x )4

A: Solution:

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

A:

Q: By what polynomial of lowest degree must (x2 – 64)(x² + 5x – 24) be multiplied to make it a perfect…

A: Givem polynomial is (x2-64)(x2+5x-24)To find lowest degree multiplier to make it perfect square.

Q: Find m so that x– 5 is a factor of f (x)= 4x² – 21x² +mx–15.

A: Consider the given polynomial fx=4x3-21x2+mx-15

Q: Gives that f(x) 5x^3-54x^2+170x-104. And that 5+i is a zero, factor f(x) completely.

A: If 5+i is a zero then (5-i) is also a zero.

Q: Solve the polynomials 3y-{[-4(x-y)+(2x - y)]-3x -[(5y-3(x-2y)]-2(-6x + y)}

A: Given polynomial,  3y-{[-4(x-y)+(2x - y)]-3x -[(5y-3(x-2y)]-2(-6x + y)}

Q: Calculate the real values of x and y such that (x + y)° is bigger than 8. hinh ai is a solution of…

A: Since you have asked multiple questions, we will solve the first question for you. If you want any…

Q: Find m so that x+4 is a factor of 5x^3 +18x^2+mx+16

A:

Q: Q3//A/By using co- factor 1 -2- if AD find A1 =? %3D 3. 2-

A:

Q: 1. Is (x – 3) a factor of the polynomial p(x) = x' – 11x + 6? Why or why not? 2. What is the…

A:

Q: (d) Show that x^2 − 4 is a factor of x^4 − 5x^3 + 2x^2 + 20x − 24.

A:

Q: This problem requires that you show all work. Factor the GCF out of each term: 24z – 4x² + 16x Hint:…

A:

Q: (d) Show that x² – 4 is a factor of x* – 5x³ + 2x? + 20x – 24.

A:

Q: Show that x2− 4 is a factor of x4 − 5x3 + 2x2 + 20x − 24.

A:

Q: Find m so that x + 4 is a factor of 5x3 + 18x2 + mx+ 16

A:

Q: If we divide the polynomial P by the factor x - c and we obtain the equation P(x) = (x – c)Q(x) +…

A: we know that if we divide the polynomial px by the factor x-c and we obtain the equation…

Q: what is the factored form of ax^2+bx+c where the roots are x1 and x2?

A:

Q: (x - 2) is a factor for x2 - 5x + 6. صواب (خطأ

A: For   x-a to be a factor of a quadretic equation then x=a is a solution of the quadretic equation.

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 (x+3) a factor of 2x2 + 7x + 3

A:

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

A:

Q: Use Gramer Rale to Find ,2 -2x + 33-Z-1 X+23-2-4 -2x -y+7=-3

A: