Answer:
The solutions to your three problem question are:
1.
a. 10x^2 −2x -12
b. 14x^2 + 7x -41
2. 30x^3 + 9x^2 + 32x - 7
3.
n1 = 8
n2 = -2
Explanation:
1. First problem
We need to Add or subtract the expressions to find the equivalent terms
a) (−2x^2 −4x + 13)+ (12x^2 + 2x −25)
We add together the terms with the same exponent
= (−2x^2 + 12x^2 ) + (−4x + 2x) + (13 - 25)
= (10x^2 ) + (−2x) + (-12)
= 10x^2 −2x -12
b) (7x^2 + 4x − 26)− (−7x^2 − 3x + 15)
= (7x^2 + 4x − 26) + (7x^2 + 3x - 15)
We add together the terms with the same exponent
= (7x^2 + 7x^2 ) + (4x + 3x) + (- 26 -15)
= (14x^2 ) + (7x) + (-41)
= 14x^2 + 7x -41
2. Second problem
(5x − 1)(6x^2 + 3x + 7)
We need to multiply to find the equivalent expression\
(5x − 1)(6x^2 + 3x + 7) = (5x)*(6x^2 + 3x + 7) + (-1)*(6x^2 + 3x + 7)
= [(5x)*(6x^2 + 3x + 7)] + [-6x^2 - 3x - 7]
= [(5x*6x^2) + (5x*3x) + (5x*7)] + [-6x^2 - 3x - 7]
= [(30x^3) + (15x^2) + (35x)] + [-6x^2 - 3x - 7]
We add together the remaining terms
= [(30x^3) + (15x^2 - 6x^2) + (35x - 3x) - 7]
= (30x^3) + (9x^2) + (32x) - 7
= 30x^3 + 9x^2 + 32x - 7
3. Third problem
f(n) = n^2 − 6n − 16
We need to find the roots for the polynomial f(n)
That is, the values of n for which f(n) = 0
We can find an analysis of the function in the images below.
Lets use the quadratic formula
Let y = ax2 + bx + c
a = 1
b = -6
c = -16
x = -b/(2*a) ± sqrt(b^2 -4ac)/(2*a)
x = 3 ± 10/2 = 3 ± 5
roots
n1 = 8
n2 = -2