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Step-by-step explanation:
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Answer:
The standard form of the equation of the parabola is (y + 2)² = 8 (x - 3)
Step-by-step explanation:
The standard form of the equation of a parabola is (y - k)² = 4p (x - h), where
- The vertex of the parabola is (h , k)
- The focus is (h + p, k)
∵ The vertex of the parabola is (3 , -2)
∴ h = 3 and k = -2
∵ The focus is (5 , -2)
∴ h + p = 5
- Substitute h by 3 to find p
∵ 3 + p = 5
- Subtract 3 from both sides
∴ p = 2
∵ The standard form of the equation of the parabola is (y - k)² = 4p (x - h)
- Substitute the values of h , k , and p in the equation
∴ (y - -2)² = 4(2) (x - 3)
∴ (y + 2)² = 8 (x - 3)
The standard form of the equation of the parabola is (y + 2)² = 8 (x - 3)
Factors of a polynomial together constitute the polynomial by multiplication. The factored form of
is ![= 4c^7(3c^2 + 7)](https://tex.z-dn.net/?f=%3D%204c%5E7%283c%5E2%20%2B%207%29)
<h3>What is distributive property of multiplication over addition?</h3>
Suppose a, b and c are three numbers. Then we have:
![a(b + c) = a\times b + a\times c](https://tex.z-dn.net/?f=a%28b%20%2B%20c%29%20%3D%20a%5Ctimes%20b%20%2B%20a%5Ctimes%20c)
(a(b+c) means a multiplied to (b+c). The sign of multiplication is usually hidden when using symbols and both quantities which are in multiplication are written together without space)
Remember that many times, when using letters or symbols, we hide multiplication and write two things which are multiplied, close to each other. As in ![2 \times x = 2x](https://tex.z-dn.net/?f=2%20%5Ctimes%20x%20%3D%202x)
The given polynomial is ![12c^9 + 28c^7](https://tex.z-dn.net/?f=12c%5E9%20%2B%2028c%5E7)
To factor it, we can use the fact that 12 and 28 are both having 4 as common factor since:
![12 = 4 \times 3 \\28 = 4 \times 7](https://tex.z-dn.net/?f=12%20%3D%204%20%5Ctimes%203%20%5C%5C28%20%3D%204%20%5Ctimes%207)
Thus, the given polynomial is factored as:
![12c^9 + 28c^7 = 4 \times 3 \times c^7 \times c^2 + 4 \times 7 \times c^7 = 4c^7(3c^2 + 7)](https://tex.z-dn.net/?f=12c%5E9%20%2B%2028c%5E7%20%3D%204%20%5Ctimes%203%20%5Ctimes%20c%5E7%20%5Ctimes%20c%5E2%20%2B%204%20%5Ctimes%207%20%5Ctimes%20c%5E7%20%3D%204c%5E7%283c%5E2%20%2B%207%29)
Thus,
The factored form of
is ![= 4c^7(3c^2 + 7)](https://tex.z-dn.net/?f=%3D%204c%5E7%283c%5E2%20%2B%207%29)
Learn more about factors of a polynomial here:
brainly.com/question/16078564
Answer:
(8 + x)(8 - x)
Step-by-step explanation:
Use the DIFFERENCE OF TWO SQUARES METHOD.
Find the like terms. There are NO like terms. We have to use THE DIFFERENCE OF TWO SQUARES FORMULA.
64 - x²
8 - x + 8 + x
(8 + x)(8 - x)
Answer:
GCD(a,b) is multiple of d. It means d divides GCD(a,b).
Step-by-step explanation:
Let a and b are two unknown numbers.
If d divides a and d divides b, then a and b are multiple of d.
![a=d\cdot m=dm](https://tex.z-dn.net/?f=a%3Dd%5Ccdot%20m%3Ddm)
![b=d\cdot n=dn](https://tex.z-dn.net/?f=b%3Dd%5Ccdot%20n%3Ddn)
where, m and n are integers.
The greatest common divisor of a and b is
![GCD(a,b)=d\cdot m\cdot n](https://tex.z-dn.net/?f=GCD%28a%2Cb%29%3Dd%5Ccdot%20m%5Ccdot%20n)
![GCD(a,b)=d\cdot mn](https://tex.z-dn.net/?f=GCD%28a%2Cb%29%3Dd%5Ccdot%20mn)
GCD(a,b) is multiple of d. It means d divides GCD(a,b).
Hence proved.