1. f(x) = 9x² + 6x - 8
f(x) = (3x - 2)(3x + 4)
When (3x - 2) = 0, then x = 2/3
When (3x + 4) = 0, then x = -4/3
Answer: The zeros are two divided by three and negative four divided by three.
2. f(x) = 9x³ - 45x² + 36x
f(x) = 9x(x² - 5x + 4)
= 9x(x - 1)(x - 4)
When 9x = 0, then x = 0
When (x-1) = 0, then x = 1
When (x-4) = 0, then x = 4
Answer: 0, 1 and 4
3. f(x) = 4(x+7)²(x-7)³
When (x+7)² = 0, then x = -7 (twice)
When (x-7)³ = 0, then x = 7 (thrice)
Answer: 7, multiplicity 2; -7 multiplicity 3
4. The zeros of f(x) are √5, -√5, -7
The factors of f(x) are (x-√5)(x+√5)(x+7)
Note that (x-√5)(x+√5) = x² - (√5)² = x² - 5
f(x) = (x²-5)(x+7)
= x³ + 7x² - 5x - 35
Answer: f(x) = x³ + 7x² - 5x - 35
5. Expand (2x + 4)³
From Pascal's Triangle, the coefficients are 1 3 3 1
Therefore
(2x + 4)³ = 1(2x)³(4)⁰ + 3(2x)²(4)¹ + 3(2x)¹(4)² + 1(2x)⁰(4)³
= 8x³ + 48x² + 96x + 64
Answer: 8x³ + 48x² + 96x + 64
Answer:
x-intercept is -1; y-intercept is 0.5.
Step-by-step explanation:
The x-intercept is relatively easy to read off. It's the x-value where the graph crosses the x-axis, and here is (-1,0).
The y-intercept is best estimated as (0,+0.5).
The correct answer is the 3rd one on the list.
B.
4 goes into 75 18 times and has a remainder of 3, so it’s 18 3/4
Some numbers cannot be written as a ratio of two integers they are called irrational numbers.
Example: Pi is a famous irrational number. You cannot write down a simple fraction that equals Pi.
A decimal goes on forever without repeating.
Try breaking these into sections.
Twice: 2 times
The sum of: add
A number: choose a variable, like x
---Thus "the sum of a number and 4" becomes "add x and 4" which, mathematically, is "x+4"
-----Continuing to put it all together, "Twice the sum of a number and four" becomes "2 times (x+4)" which, mathematically, is "2(x+4)"
Is: equals
-------"Twice the sum of a number and four is" becomes "2(x+4)="
23 less than: subtract 23. This one tends to trick people; "23 less than" will become "__ - 23", NOT "23 - __"
three times the number: 3 times x
---"23 less than three times the number" becomes "subtract 23 from 3 times x" which, mathematically, is "3x-23"
-------So the final phrase: 2(x+4)=3x-23"
