Alan

Like so:

Tackle these sort of problems like this:

As follows:

The cosine rule here can be written as:

12^2 = a^2 + 10^2 - 2*a*10*cos(60deg)

or  a^2 - 20*cos(60deg)*a - 44 = 0

solve the quadratic equation to find a.

To find the value of a that makes the curve continuous at the upper intersection, set x = 2 in the upper two expressions and equate them:

i.e.   a*(2) + 3 = (2) + 5

or   2a+3 = 7

      a = 2

Similarly to find the value of b that makes the curve continuous at -2, set

 (-2) + 5 = 8*(-2) + b

I'll let you finish.

"Let f(x) be a polynomial such that f(0) = 4,f(1) = -5, and f(2) = 11. Find the remainder when f(x) is divided by x(x - 1)(x - 2)."

Note:  The equation for r(1) should be:   a + b + c = -5.

This should help:

2010a + 2014b = 2018         (1)

2012a + 2016b = 2020         (2)

Subtract:  (2) - (1)

2a + 2b = 2  or

a + b = 1                             (3)

so b = 1-a, put this into (1)

2010a +2014(1 - a) = 2018    Simplify:

-4a = 4

a = -1

put this back into (3) to find b, then find a - b.

Alternatively, you could just add them all up to get

10a + 10b + 10c + 10d = 0

so:    a + b + c + d = 0

See answer at https://web2.0calc.com/questions/this-problem-hurts#r2