Question

1. 3x2 - 10x +32. 5x2 – x - 42 3. 2х² + 3х – 5​

Answer 1

Ответ:

3*x^2 - 10*x + 3 = 0

d = 100 - 3 * 3 * 4 = 64

х1 = (10 - 8) / 6 = 1/3

x2 = (10 + 8) / 6 = 3

3*x^2 - 10*x + 3 = 3(x - 1/3)(x - 3)

x ^ 2 - 9 = (x - 3)(x + 3)

Сокращаем на х - 3, получаем (3x - 1)/(x + 3)

2) 5 * x ^ 2 + x - 4 = 0

D = 1 + 4 * 4 * 5 = 81

x1 = (-1 + 9)/10 = 4/5 = 0.8

x2 = (-1 - 9)/10 = -1

5 * x ^ 2 + x - 4 = 5 * (x - 0.8)*(x + 1)

x^2 + x = x*(x+1)

Answer 2

It seems like you have three quadratic expressions. Let's take a look at each of them:

1. 3x^2 - 10x + 32: This is a quadratic expression. It can be factored further if possible. To factor it, we look for two numbers that multiply to the constant term (32) and add up to the coefficient of the linear term (-10). In this case, those two numbers are -8 and -4 because (-8) * (-4) = 32 and (-8) + (-4) = -10.

   So, you can factor it as: 3x^2 - 10x + 32 = 3x^2 - 8x - 4x + 32

   Now, you can factor by grouping: = (3x^2 - 8x) - (4x - 32)

   Factor each group separately: = x(3x - 8) - 4(3x - 8)

   Now, notice that you have a common factor of (3x - 8): = (3x - 8)(x - 4)

2. 5x^2 - x - 42: This is another quadratic expression. To factor it, we look for two numbers that multiply to the constant term (-42) and add up to the coefficient of the linear term (-1). In this case, those two numbers are 6 and -7 because 6 * (-7) = -42 and 6 + (-7) = -1.

   So, you can factor it as: 5x^2 - x - 42 = 5x^2 + 6x - 7x - 42

   Now, you can factor by grouping: = (5x^2 + 6x) - (7x + 42)

   Factor each group separately: = x(5x + 6) - 7(5x + 6)

   Now, notice that you have a common factor of (5x + 6): = (5x + 6)(x - 7)

3. 2x^2 + 3x - 5: This is also a quadratic expression. To factor it, we look for two numbers that multiply to the leading coefficient (2) times the constant term (-5), which is -10, and add up to the coefficient of the linear term (3). Unfortunately, there are no such numbers, so this expression cannot be factored further using integer coefficients.

So, the factored forms of these quadratic expressions are:

1. 3x^2 - 10x + 32 = (3x - 8)(x - 4)
2. 5x^2 - x - 42 = (5x + 6)(x - 7)
3. 2x^2 + 3x - 5 (cannot be factored further with integer coefficients)