Answer: The greatest common factor is 2.
Step-by-step explanation: We are given to find the greatest common factor of the following expressions:
<u>Greatest Common Factor:</u> The GCF of two or more numbers (expressions) is the greatest factor that divides all the numbers or expressions.
We have
Therefore, the greatest common factor will be
Thus, the required greatest common factor is 2.
Answer:
According to tangents secant segments theorem,
11) x(16+x) = (x + 6)^2
x (16+x) = (x + 6)^2
16x + x^2 = x^2 + 2(6)(x) + 6^2
16x + x^2 = x^2 + 12x + 36
16x - 12x + x^2 - x^2 = 36
4x = 36
x = 36/4
x = 4
13) x(x + 5) = (x + 2)^2
x^2 + 5x = x^2 + 2x 2(2)(x) + 2^2
x^2 + 5x = x^2 + 4x + 4
x^2 -x^2 + 5x - 4x = 4
x = 4
14) x + 8( x + 8 + 32) = (3x) ^2
x + 8(x + 40) = 9x^2
x(x + 8) + 40(x + 8) = 9x^2
x^2 + 8x + 40x + 320 = 9x^2
x^2 + 48x + 320 =9x^2
48x + 320 = 9x^2 - x^2
48x + 320 = 8x^2
Dividing the whole eq. by 8,
6x = 40 = x^2
0 = x^2 - 6x - 40
0 = x^2 - 10x + 4x - 40
0 = x(x - 10) + 4(x - 10)
x - 10 = 0 OR x + 4 = 0
x = 10 OR x = - 4
length cannot be negative, so,
x = 10
15) (x + 3) ( x + 3 + 15) = (2x) ^2
(x + 3) (x + 18) = 4x^2
x(x + 18) + 3(x + 18) = 4x^2
x^2 + 18x + 3x + 54 = 4x^2
x^2 + 21x + 54 = 4x^2
0 = 4x^2 - x^2 - 21x - 54
0 = 3x^2 - 21x - 54
Dividing the whole eq. by 3,
x^2 - 7x - 18 = 0
x^2 - 7x - 18 = 0
x^2 - 9x + 2x - 18 = 0
x(x - 9) + 2 (x - 9)
x + 2 = 0 Or x - 9 = 0
x = -2 or x = 9
length cannot be negative,so,
x = 9
