How do you factor x 4 625?

Factoring x 4 625 involves finding the prime factors of the given number. This process can be done by dividing the number by its smallest prime factor and then continuing to divide the resulting quotient by its smallest prime factor until we reach a prime number.

In the case of x 4 625, we can start by dividing the number by 5, since 5 is the smallest prime factor of 4 625. The quotient we get is 925. Since 925 is not a prime number, we continue the process by dividing it by its smallest prime factor again, which is 5. This gives us a quotient of 185.

Now, we divide 185 by its smallest prime factor, which is 5, and get a quotient of 37. Since 37 is a prime number, we can stop here. Therefore, the prime factors of x 4 625 are 5, 5, 5, and 37.

In summary, to factor x 4 625, we divided the number successively by its smallest prime factors until we reached a prime number, which gave us the prime factors of 5, 5, 5, and 37.

How do you factor x4 625?

To factor the expression x^4 - 625, we can begin by recognizing that 625 is a perfect square: 25^2. This allows us to rewrite the expression as (x^2)^2 - 25^2.

Now, we have a difference of squares, which can be factored using the formula: a^2 - b^2 = (a + b)(a - b). Applying this formula, we can factor the expression further:

(x^2 + 25)(x^2 - 25).

Next, we notice that both (x^2 + 25) and (x^2 - 25) can be further factored. (x^2 + 25) is a sum of squares, which cannot be factored any further, but (x^2 - 25) is a difference of squares and can be factored as (x + 5)(x - 5).

Therefore, the final factored form of x^4 - 625 is (x^2 + 25)(x + 5)(x - 5).

Factoring is an important concept in algebra as it allows us to simplify expressions and solve equations. It involves breaking down a mathematical expression into its factors or prime elements, which makes it easier to work with and understand.

By factoring x^4 - 625, we have obtained its complete factorization as (x^2 + 25)(x + 5)(x - 5). This can be useful in solving equations or simplifying complex expressions.

Remember to always check your answer by multiplying the factors back together to ensure they equal the original expression.

What is x to the power of 4 equals 625?

X to the power of 4 can be expressed as x^4, which means multiplying x by itself 4 times. We want to find the value of x that satisfies the equation x^4 = 625.

To solve this equation, we need to find the value of x that when raised to the power of 4 yields 625. In other words, we are looking for the fourth root of 625.

The fourth root of a number can be obtained by raising that number to the power of 1/4. So, to find x, we need to calculate 625^(1/4).

Using a calculator, we can determine that 625^(1/4) = 5. Therefore, the value of x that satisfies the equation x^4 = 625 is x = 5.

In conclusion, x to the power of 4 equals 625 when x is equal to 5.

How do you factor x 4 100?

Factoring involves breaking down an expression or equation into its simpler parts. In this case, we are given the expression x^4 - 100. To factor this expression, we can identify it as the difference of squares.

Difference of squares means that we have a square term subtracted by another square term. In this case, we have x^4 - 100 which can be written as (x^2)^2 - 10^2.

Using the difference of squares formula, we know that a^2 - b^2 can be factored as (a + b)(a - b). Applying this to our expression, we can rewrite it as [(x^2) + 10][(x^2) - 10].

Now we have factored x^4 - 100 into the product of two binomials: (x^2 + 10)(x^2 - 10). These factors represent the simplified and broken-down form of the original expression.

Therefore, the factored form of x^4 - 100 is (x^2 + 10)(x^2 - 10).

How do you factor x 4 81 completely?

Factoring is an important mathematical technique used to simplify and solve polynomial equations. In this case, you are asked to factor the expression x⁴ - 81 completely. Let's break it down step by step.

The given expression is a difference of squares, which means we can use a special formula to factor it. The formula states that a² - b² = (a + b)(a - b). We can rewrite x⁴ - 81 as (x²)² - 9².

We can now apply the formula by considering x² as "a" and 9 as "b". Using the formula, we get (x² + 9)(x² - 9).

At this point, we have factored x⁴ - 81 as a product of two binomial expressions. However, we can further factor the second term (x² - 9) as the difference of squares.

Again, using the same formula, a² - b² = (a + b)(a - b), we consider x as "a" and 3 as "b". Performing the factoring, we get (x² + 3)(x² - 3)(x² + 9).

Now we have completely factored x⁴ - 81. The final factorization is (x² + 3)(x² - 3)(x² + 9).

In summary, to fully factor x⁴ - 81, we used the difference of squares formula twice to break it down into three factors: (x² + 3)(x² - 3)(x² + 9).