Answer:
1 .4x2-9= 2x+3,2x-3
2 .16x2-1=4x-1,4x+1
3 .16x2-4=4(2x+1)(2x-1)
4 .4x2-1=(2x+1)(2x-1)
Step-by-step explanation:
16x² − 1 = (4x − 1)(4x + 1) ; 16x² − 4 = 4(2x + 1)(2x − 1); 4x² − 1 = (2x + 1)(2x − 1) ;
4x² − 9 = (2x + 3)(2x − 3)
16x² − 1 is the difference of squares. This is because 16x² is a perfect square, as is 1. To find the factors of the difference of squares, take the square root of each square; one factor will be the sum of these and the other will be the difference.
The square root of 16x² is 4x and the square root of 1 is 1; this gives us (4x-1)(4x+1).
16x² − 4 is also the difference of squares. The difference of 16x² is 4x and the square root of 4 is 2; this gives us (4x-2)(4x+2). However, we can also factor a 2 out of each of these binomials; this gives us
2(2x-1)(2)(2x+1) = 2(2)(2x-1)(2x+1) = 4(2x-1)(2x+1)
4x² − 1 is also the difference of squares. The square root of 4x² is 2x and the square root of 1 is 1; this gives us (2x-1)(2x+1).
4x² − 9 is also the difference of squares. The square root of 4x² is 2x and the square root of 9 is 3; this gives us (2x-3)(2x+3).
Answer:
it's a whole number
Step-by-step explanation:
it's a whole number
Answer: Y=-1
Explanation: 2y-3=y-4 (add three on both sides)
2y=y-1 (subtract y on both sides)
y=-1
Using derivatives, it is found that regarding the tangent line to the function, we have that:
- The equation of the line is y = 962x - 5119.
<h3>What is a linear function?</h3>
A linear function is modeled by:
y = mx + b
In which:
- m is the slope, which is the rate of change, that is, by how much y changes when x changes by 1.
- b is the y-intercept, which is the value of y when x = 0, and can also be interpreted as the initial value of the function.
The slope of the line tangent to a function f(x) at x = x' is given by f'(x'). In this problem, the function is given by:
f(x) = 5x³ + 2x + 1.
The derivative is given by:
f'(x) = 15x² + 2.
Hence the slope at x = 8 is:
m = f'(8) = 15(8)² + 2 = 962.
The line goes through the point (8,f(8)), hence:
f(8) = 5(8)³ + 2(8) + 1 = 2577.
Hence:
y = 962x + b
2577 = 962(8) + b
b = -5119.
Hence the equation is:
y = 962x - 5119.
More can be learned about tangent lines at brainly.com/question/8174665
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