can someone correct these. and help me
DIrections:Factor
(3) 4x^2-4x-15
My solving: 4*x*x-4*x-15 (the star means multiply
my final answer: x^3-15 (the ^ means for exponent)
(4) 5x^2-26x+5
my solving: 5*x*x-26*x+5
my final answer: x^3-16
I don't understand what you did. The question asks for factors.
(2x+3)(2x-5)
Check that.
To factor a polynomial, you need to find the expressions that can be multiplied together to get the original polynomial. Let's go through the steps to factor the given polynomials.
For the first polynomial, 4x^2 - 4x - 15:
1. Make sure the polynomial is in standard form, which it already is.
2. Look for common factors. In this case, there are no common factors other than 1.
3. We need to find two binomials whose product equals the original polynomial. Let's assume the factors are in the form (ax + b)(cx + d).
4. The first terms of the binomials should be 4x multiplied by x, which gives 4x^2. So, (ax)(cx) = 4x^2.
5. The last terms of the binomials multiplied together should give -15. So, (b)(d) = -15.
6. Now, we need to find the values of a, b, c, and d that satisfy the steps above. There are multiple possibilities, so we need to figure out the combination that works.
One possible combination is a = 2, b = -3, c = 2, and d = 5. This gives us (2x + 3)(2x - 5).
So, the correct factoring for the first polynomial is (2x + 3)(2x - 5).
Now, let's move on to the second polynomial, 5x^2 - 26x + 5:
1. Ensure the polynomial is in standard form, which it already is.
2. Look for common factors. In this case, there are no common factors other than 1.
3. Assume the factors are in the form (ax + b)(cx + d).
4. The first terms of the binomials multiplied together should give 5x^2. So, (ax)(cx) = 5x^2.
5. The last terms of the binomials multiplied together should give 5. So, (b)(d) = 5.
6. We need to find the values of a, b, c, and d that satisfy the above conditions. There are multiple possibilities, so we need to determine the combination that works.
One possible combination is a = 5, b = 1, c = 1, and d = 5. This gives us (5x + 1)(x + 5).
Therefore, the correct factoring for the second polynomial is (5x + 1)(x + 5).
I hope this helps clarify the factoring process for these polynomials. Let me know if you have any more questions!