- Discriminant Formula: b² - 4ac, with a = x^2 coefficient, b = x coefficient, and c = constant
So firstly, using our equation plug in the values into the discriminant formula and solve as such:
(-7)² - 4 × 3 × 4
49 - 48
1
So our discriminant is 1. <u>Since 1 is positive and a perfect square, this means that there are 2 real, rational solutions.</u>
Answer:
Evaluating Polynomials:
a. f(1) = -10
b. f(-3) = -239
c. f(2)² = 3125
Factoring Polynomials:
a. (x + 1)(x² - 5x + 6) = (x + 1)(x - 3)(x - 2)
b. (x² - x - 6)(x² + 6x + 9) = (x - 3)(x + 2)(x + 3)(x + 3)
c. x³ + 3x² - 4x - 12 = (x + 3)(x - 2)(x + 2)(x - 2)(x + 2)
Answer:
Step-by-step explanation:
2a. f(-3) = (-3)^2-4(-3)+6 = 9+12+6 = 27
2b. f(-2) = 3(-2)^2-(-2)^3 -2 +1 = 3(4) - (-8) -2 +1
= 12+8-1 = 19
The degree of a polynomial is the highest power of its terms.
The power of a term is the sum of the powers of all the variables in a term.
A polynomial is written starting with the greatest power in standard form.
In the first case, the power of the first term is 3, the power of the second is 3 (2 from x + 1 from y) but the power of x has decreased so it is the second term, and then so on.
In the second case, the power is starting form 2 and then increasing to 3. This is incorrect.
Therefore, Marcus' suggestion is correct.
