factorize the following.
1) 4x^2-2x+5=0
2) 6x^2+5x-4=0
3) x^2=3x
4) x(x-3)=-2
5) 4x^2+11x=-6
1)Please check that you entered this answer correctly, as it is written now I'm not convinced it can be factored.
2)6x^2+5x-4=0
(3x+4)(2x-1)
3)x^2=3x
x^2-3x=0
x(x-3)
4)x(x-3)=-2
x^2-3x=-2
x^2-3x+2
(x-2)(x-1)
5)4x^2+11x+6
(4x+3)(x+2)
To factorize the given quadratic equations, you need to follow these steps:
1) 4x^2 - 2x + 5 = 0
Unfortunately, the given equation cannot be factored further using real numbers, as it does not have any real roots.
2) 6x^2 + 5x - 4 = 0
To factorize this quadratic equation, you can either use the quadratic formula or try factoring it by trial and error. In this case, the quadratic formula would be easier.
Using the quadratic formula, the roots can be found using the formula:
x = (-b ± sqrt(b^2 - 4ac)) / (2a)
For this equation, a = 6, b = 5, and c = -4.
Substituting the values into the formula:
x = (-5 ± sqrt(5^2 - 4 * 6 * -4)) / (2 * 6)
Simplifying:
x = (-5 ± sqrt(25 + 96)) / 12
x = (-5 ± sqrt(121)) / 12
x = (-5 ± 11) / 12
So, the two roots are:
x = (-5 + 11) / 12 = 6/12 = 1/2
x = (-5 - 11) / 12 = -16/12 = -4/3
Therefore, the factored form of the equation is:
6x^2 + 5x - 4 = (2x - 1)(3x + 4)
3) x^2 = 3x
In this equation, you can factor out the common term "x" from both sides:
x(x - 3) = 0
So, the factored form of the equation is:
x(x - 3) = 0
4) x(x - 3) = -2
To factorize this equation, you can multiply the terms inside the parentheses:
x^2 - 3x = -2
Rearranging the equation:
x^2 - 3x + 2 = 0
Now, you can use either the quadratic formula or factoring by trial and error to find the roots.
Factoring by trial and error, the equation can be rewritten as:
(x - 2)(x - 1) = 0
Therefore, the factored form of the equation is:
x(x - 3) = -2 has the factorization (x - 2)(x - 1) = 0.
5) 4x^2 + 11x = -6
To factorize this equation, you can rearrange it to set it equal to 0:
4x^2 + 11x + 6 = 0
Using factoring by trial and error, the equation can be rewritten as:
(2x + 3)(2x + 2) = 0
So, the factored form of the equation is:
4x^2 + 11x = -6 has the factorization (2x + 3)(2x + 2) = 0.