a) The cubic polynomial f (x) is defined by f(x) = x² + ax² + 14x + a + 1 where a is a constant. It is given that x + 2 is a factor of f(x). (i) Use the factor theorem to find the value of a. (i) Hence, factorize f (x) completely.

Q: g(x) is a 4th degree polynomial function with real coefficients and zeros at х%3D 2, —3 and i. (a)…

A: a. If a polynomial has complex root a+ib then its other root must be a-ib. If we have zeros α,β,γ…

Q: 1) Sketch a cubic polynomial whose zeros are -1, 2, and 9

A:

Q: find the real polynomial f(x) which has zeros x=1 (multiplicity 2) and x=2+i (multiplicity 1). you…

A: We have given the zeros x = 1 with multiplicity 2 and x = 2+i with multiplicity 1.

Q: Consider the following higher degree polynomial function f(x) = -2x2 (5-2x) (x² + 1). f) Sketch the…

A: Hence the required answer is given belowExplanation:Step 1: Step 2: Step 3: Step 4:

Q: Find the coefficients a,b in the function f(x)=ax+b so that (f(x1)-y1)^2+(f(x2)-y2)^2+(f(x3)-y3)^2…

A: Given data: Function fx=ax+b so that fx1-y12+fx2-y22+fx3-y32 is as small as possible. Given table of…

Q: Write the the function f(x) = x² – 2x + 6 in the form f(x) = a(x – p)² + q by completing the square:…

A: Given function f(x)=x2-2x+6. The objective is to write the function in the form f(x)=a(x-p)2+q by…

Q: (b.) The function, f(x)= ax'-bx² +cx-12 , has a remainder 30 when divided by x - 3. If (x-2) and…

A: Given: fx=ax3-bx2+cx-12 which has a remainder 30 when divided by x-3 and,           x-2 and x+3 are…

Q: If f(x) is a polynomial function satisfying f(x) ·ƒ ( ² ) = f(x) + f ( ² ) a and f(4) = 65, then…

A:

Q: If f(x) is a polynomial of the first degree and a is not equal to B, show that f(x)= f(B)(x-a) -…

A:

Q: Which polynomial function in standard form has a root of multiplicity 1 at x= 3, and a root of…

A: A polynomial function has a root of multiplicity 1 at x=3, and a root of multiplicity 2 at x=4

Q: Let P(x) be a polynomial of degree 5 with roots 2, – 5 and (3 + i). Write P(x) as a product of…

A: It is given that the roots of 5 degree polynomial are 2,-5,3+i

Q: Find an 4th degree polynomial function with real coefficients whose zeros are 4,–1,2, v2i and a…

A: Here degree of polynomial is 4 so it has 4 roots.

Q: Consider the following higher degree polynomial function f(x) = -2x² (5-2x) (x² + 1). a) What is the…

A: (a) degree of the function=5(B) 4 distinct Zeroes = 0,25​,−i,i         In which two are real zeroes…

Q: Identify the following for the polynomial function: i) iv) g(x)=x (3x+4) (-2x+1)(x-5) the degree the…

A:

Q: The function f(x) = x³ + 5x²-√x + 1 is a polynomial of degree 3.

A:

Q: 3. Write the polynomial f(x) = x − 11x³ + 40x² − 55x + 25 in the form f(x) = (x−a)Q(x) + f(a) for…

A:

Q: "The factored form of a polynomial function is f(x)=(x−1−3)(x−2−3i)(x−1−3)(x−2+3i). What is the…

A: "The factored form of a polynomial function is f(x)=(x−1−3)(x−2−3i)(x−1−3)(x−2+3i). What is the…