i also have theses to solve
Factor the polynomial x2 + 5x + 6 completely
Solve the given equation by using the quadratic formula.
x2 – 7x – 4 = 0
What value is under the square root (or radical) in your answer? (Note: You are asked to identify only the value under the radical, not the solution to the equation.)
The Greatest Common Factor of the polynomial 25x + 50y is
Factor the polynomial x2 + 4x – 5 completely.
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Sure! I apologize for any confusion. Let's go through these questions step by step:
1. Factor the polynomial x^2 + 5x + 6 completely:
To factor this quadratic polynomial, we need to find two binomials whose product gives us the original polynomial. We can try factors of the constant term (6) and coefficients of the linear term (5) to find two binomials that multiply together to give us x^2 + 5x + 6. In this case, the factors that work are (x + 2) and (x + 3). So, the equation is factored as (x + 2)(x + 3).
2. Solve the given equation by using the quadratic formula:
The quadratic formula is the standard method for solving quadratic equations of the form ax^2 + bx + c = 0, where a, b, and c are coefficients. The formula is given by x = (-b ± √(b^2 - 4ac)) / (2a).
For the equation x^2 – 7x – 4 = 0, we can identify a = 1, b = -7, and c = -4. Plugging these values into the quadratic formula, we get:
x = (-(-7) ± √((-7)^2 - 4(1)(-4))) / (2(1))
Simplifying further:
x = (7 ± √(49 + 16)) / 2
x = (7 ± √65) / 2
So, the values of x that solve the equation are:
x = (7 + √65) / 2 and x = (7 - √65) / 2
3. What value is under the square root in your answer?
In the quadratic formula solution above, we have √65 under the square root (or radical). This means that the value under the radical is 65.
4. The Greatest Common Factor of the polynomial 25x + 50y:
To find the Greatest Common Factor (GCF), we need to identify the highest power of each variable that is common to all the terms in the polynomial. In this case, the GCF of 25x and 50y is 25, since both terms have a factor of 25. Therefore, the GCF of the polynomial 25x + 50y is 25.
5. Factor the polynomial x^2 + 4x – 5 completely:
Similar to the first question, we need to find two binomials whose product gives us x^2 + 4x – 5. By factoring, we can find (x + 5) and (x – 1) are the binomials that multiply together to give us the original polynomial. So, the polynomial is factored as (x + 5)(x – 1).
I hope this helps! If you have any further questions, feel free to ask.