Answer:
Step-by-step explanation:
21
i)
[tex]x^2 + 9x + 18\\x^2 + 6x + 3x + 18\\x(x+6) + 3(x+6)\\(x+3)(x+6)\\[/tex]
ii)
[tex]6x^2 + 7x -3\\6x^2 + 9x - 2x -3\\3x(2x+3)-1(2x+3)\\(3x-1)(2x+3)[/tex]
iii)
[tex]2x^2 -7x - 15\\2x^2 -10x +3x - 15\\2x(x-5) + 3(x-5)\\(2x +3)(x-5)[/tex]
iv)
[tex]84 -2r - 2r^2\\-2r^2 - 2r + 84\\-2(r^2 + r - 42)\\-2(r^2 +7r- 6r - 42)\\-2((r(r+7) - 6(r+7))\\-2(r-6)(r+7)[/tex]
22
Given that the polynomial is divisible by x + 2.
That means x + 2 is a factor.
=> x = -2 is a root
Therefore,
[tex]f(x) = x^3 - 2mx^2 + 16\\f(-2) = 0\\(-2)^3 - 2m(-2)^2 + 16 = 0\\-8 -8m +16=0\\-8m + 8 = 0\\-8m = -8\\m= \frac{-8}{-8} = 1[/tex]
23
Given x + 1 is a factor.
That means x = -1 is a root
Therefore,
[tex]g(x) = ax^3 + x^2 -2x +4a -9\\g( -1) = 0\\a(-1)^3 + (-1)^2 -2(-1) + 4a - 9 = 0\\-a + 1 + 2 + 4a - 9 = 0\\3a + 3 - 9 = 0\\3a -6=0\\3a = 6\\a = 2[/tex]
