40º
7) In this problem, we can see that both tangent lines to that circle come from the same point O.
So, we can write out the following considering that there is one secant line DO and one tangent line to the circle AO
The left term is (5x)³.
The right term is 10³.
So, you can use the formula for the factorization of the difference of cubes.
... a³ - b³ = (a-b)(a² +ab +b²)
Here, you have a=5x, b=10, so the factorization is
... 125x³ -1000 = (5x-10)(25x² +50x +100)
The zeros for this function are -2, -1 and a double root of 0.
You can find this by first factoring the polynomial on the inside of the parenthesis. Polynomials like this can be factored by looking for two numbers that multiply to the constant (2) and add up to the second coefficient (3). The numbers 2 and 1 satisfy both of those needs and thus can be used as the numbers in a factoring.
x^2(x^2 + 3x + 2)
x^2(x + 2)(x + 1)
Now to find the zeros, we set each part equal to 0. You may want to split the x^2 into two separate x's for this purpose.
(x)(x)(x + 2)(x + 1)
x = 0
x = 0
x + 2 = 0
x = -2
x + 1 = 0
x = -1
