Page 156 - Algebra

Exercise:
1. If (x – 3) is a factor of f(x) = b(x4 – 3x2) + c(x3 – 9), which of the given statements holds true?
a) 3b + c = 0 b) b – 3c = 0 c) b+ 3c = 0 d) 3b – c = 0 e) b + 6c = 0
2. For what real value of x, does the following equation holds true? x4 –7x3 +4x–28=0
a) x = 2 b) x = –2 c) x = 7 d) x = – 7 e) Cannot be determined
3. Find the remainder of the polynomial when 3x3 – 8x2 + 5x – 18 is divided by x – 3.
a) 2 b) 4 c) 6 d) – 6 e) – 7
4. It’s given that a f(x) is a polynomial function and f(–6) = 0. Which of the following statements is true?
a) The remainder of the function is –6 b) The remainder of the function is 6 c) x – 6 is a factor of f(x) d) x + 6 is a factor of f(x)
e) None of these
5. Find the value of m, which is a nonzero constant in the following equation.
f(x) =x4 – mx2 – 10x + 24
In the Cartesian plane, the function intersects the x-axis at (4, 0) (-3, 0) (1, 0) and (b, 0).
a)m = –6 b) m = 6 c) m = 12 d) m = 15 e) Cannot be determined
6. At how many different points does the factor of the equation intersect the x-axis?
f(x) = 9x4
a) 0 c) 2 e) 4
– 12x3 – 6x + 8
b) 1 d) 3
Page 155 of 177
Algebra I & II