f(x) = x3 + 10x2 + ax + b
(x-1) is a factor so f(1) = 0 ie 1 + 10 + a + b = 0
(x-2) is a factor so f(2) = 0 ie 8 + 40 + 2a + b = 0
Solve these two simultaneous equations:
Sutracting the first from the second:
37 + a = 0 so that a = -37
and then b = 26
Find values of the variable for which the value of the polynomial is zero.
How many numbers from 11 to 50 are there which are exactly divisible by 7 but not by 3? Five Four Six Two * * * * * Good strategy! List all possible values and one of them must be correct! The correct answer is 4.
zero
-2 and -6
The values of the variables which make the polynomial equal to zero
Substitute that value of the variable and evaluate the polynomial.
false
Find values of the variable for which the value of the polynomial is zero.
The graph of a polynomial in X crosses the X-axis at x-intercepts known as the roots of the polynomial, the values of x that solve the equation.(polynomial in X) = 0 or otherwise y=0
A local minimum.
extreme
2 or 5
How many numbers from 11 to 50 are there which are exactly divisible by 7 but not by 3? Five Four Six Two * * * * * Good strategy! List all possible values and one of them must be correct! The correct answer is 4.
zero
4 and 5 -4 and -8
-2 and -6
The values of the variables which make the polynomial equal to zero