2 The function f(x) = ax³ + 4x² + bx-2, where a and b are constants, is such that 2x - 1 is a factor. Given that the remainder when f(x) is divided by x-2 is twice the remainder when f(x) is divided by x + 1, find the value of a and of b.

Q: Let a > 12 be a constant. Evaluate 4x2 + 32x + 40 + 2a dx (4x + a)(x² + 6x + 10)

A:

Q: If two of the factors for the function f (x) = x4 - 5x3 - 3x2 + 13x + 10 are (x - 5) and (x - 2),…

A:

Q: If f (x) = 2x2 - 7 and g(x) = x2 + x - 1, find f (-2), f (3), g(-4), and g(5).

A: A function is a relation between a set of two variables, one dependent variable and an independent…

Q: Given the function ƒ(x) = 5x¹ + 75x³ + 315x² + 405x, and one of its factors is (x + 9), write f(x)…

A: Giv     fx=5x4+75x3+315x2+405x    One of its factors is x+9 Factor out common terms:…

Q: Find all the factors of f (x) = x³ – 4x² + x + 6.

A: GIVEN: f(x) = x3 - 4x2 + x + 6

Q: If f(x) = 4x 2 – 3x + 6, find f(-2).

A: We  have  given function  f(x) =  4x2-3x+6 To Find : The value of f(-2) Concept If we have a…

Q: coming year. Total profit from planting xj acres at farm j is expressed by the function P(x,, X2,…

A: profit = 235x1 + 540x2 + 252x3 - 525000 we are given that x1 = 300 x2 = 600 x3 = 450

Q: If f(x) = - 3x + 3, g(x) = - 2x² - 4x – 5, and h(x) = - 4x + 8, find h( - 3). h( - 3) =D

A: According to the problem, we have

Q: If f(x) = 2x² – 3.x +5 , find f(4).

A: Given f(x)= 2x2-3x+5 Now we have to find f(4)  by substituting 4 in place of X and evaluate as shown…

Q: If f(x) = 2x – 6 and g(x) = x – 2x2, find each value. f(2)

A: Given functions are: fx=2x-6 and, gx=x-2x2 We have to find the value of f2.

Q: If h(x) = -2x2 - x + 4, find h(-2), h(-3), h(4), and h(5).

A: We have to find the value of the function at certain points . In general for a function fx we can…

Q: Find f(-7) if (x)=2x+8

A: Given  f(x)= 2x+8  we use substitution method to find value of f(x) at x= -7

Q: If Q(x) = 4x2 - 1, find Q(-10). Q(- 10) =

A: Here use simple algebraic formulation.