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Marizza181 [45]
2 years ago
15

The EXPAND equation of the polynomial function is f(x)= (x-2)(x-5)(x-sqrt3)(x+sqrt3) 15 POINTS Please explain as well if you can

. Please

Mathematics
1 answer:
Fynjy0 [20]2 years ago
8 0

Answer:

f(x) = x⁴ - 7x³ + 7x² + 21x - 30

Step-by-step explanation:

Given function is f(x) = (x - 2)(x - 5)(x - √3)(x + √3)

f(x) = (x - 2)(x - 5)[(x² - (√3)²]  {By using formula, (a - b)(a + b) = a² - b²]

     = (x - 2)(x - 5)(x² - 3)

     = (x - 2)[x(x² - 3) -5(x² - 3)] [By distributive property]

     = (x - 2)(x³ - 3x - 5x² + 15)

     = (x - 2)(x³ - 5x² - 3x + 15)

     = [x(x³ - 5x² - 3x + 15) - 2(x³ - 5x² - 3x + 15)]

     = x⁴ - 5x³- 3x² + 15x - 2x³ + 10x² + 6x - 30

     = x⁴ - 7x³ + 7x² + 21x - 30

Therefore, expanded form of the polynomial function will be,

f(x) = x⁴ - 7x³ + 7x² + 21x - 30  

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Complete the square than convert to vertex form. y=2x^2+8x-9​
8_murik_8 [283]

y=2x^2+8x-9\\D=b^2-4ac\\D=64-4(2)(-9)\\D=64+72 > 0

There are 2 roots so the only way to complete the square is,

y=2x^2+8x-9\\y=2[(x^2+4x)]-9\\y=2[(x^2+4x+4)-4]-9\\y=2[(x+2)^2-4]-9\\y=2(x+2)^2-8-9\\y=2(x+2)^2-17

Just factor 2 out of 2x^2+8x (just ignore the -9) then find the number that will make the terms be able to complete the square.

then complete the square and multiply 2 inside the brackets.

subtraction as you already get the vertex form and know how to complete the square.

Vertex Form: y=2(x+2)^2-17

3 0
3 years ago
Sweet tea purchased a new pair of jeans to wear to the battle of the bands on sale at 40% off he saved $20 what was the regular
DIA [1.3K]
$50 
20 x 2 = 40, which is 80% 
and then 20 divided by 2 is 10; so you add that to 40 and you get your answer 
8 0
3 years ago
Solve for N: 3n - 7 = 6n - 2n
jonny [76]

Answer:

-7

Step-by-step explanation:

1. Combine Like Terms

3n-7=4n

2. Subtract 3n on both sides.

-7=n

3. You got your answer:)

3 0
3 years ago
(there is an attachment)
lara31 [8.8K]
Area of a Triangle = 1/2 * base * Height

2.5 = 1/2 * 2 * h

2.5 = 1 * h

h = 2.5 /1

h = 2.5 in

In short, Your Answer would be: Option C

Hope this helps!


7 0
3 years ago
7y – 26 = 61 this is for math does anyone know what it is
AlladinOne [14]

Answer:

\frac{87}{7}

Step-by-step explanation:

on the picture

if it's helpful ❤❤❤

THANK YOU

8 0
3 years ago
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