Answer:

Step-by-step explanation:

5. x² + 2x + 1 = 5x + 6

Transpose expression at the left to right side of the equation.

x² + 2x + 1 - (5x + 6) = 0

x² + 2x + 1 - 5x - 6 = 0

Combine like terms,

x² + 2x - 5x + 1 - 6 = 0

x² - 3x - 5 = 0

• The equation is simplified, and as u can see, the resulting equation is a Quadratic Equation since the leading term has degree/exponent 2. So,

a = 1, b = -3, c = -5

6. (x - 1)(x + 2)= x(x + 5)

Multiply first, use FOIL Method at the left,

First: x • x = x²

Outside: x • 2 = 2x

Inside: -1 • x = -1x or simply -x

Last: (-1)(2) = -2

Combine the results,

x² + 2x - x -2

Combine like terms,

x² + x - 2

Rewrite the equation,

x² + x - 2 = x (x + 5) [Distribute terms]

x² + x - 2 = x (x) + x (5)

x² + x - 2 = x² + 5x

Transpose expression at the left to right side of the equation.

x² + x - 2 - (x² + 5x) = 0

x² + x - 2 - x² - 5x = 0

Combine like terms,

x² - x² + x - 5x - 2 = 0

-4x - 2 = 0,

• Hence, this isn't a Quadratic Equation.

7. (x + 2)(x - 3) = 5

Use FOIL Method at the left side,

First: x • x = x²

Outside: x • -3 = -3x

Inside: 2 • x = 2x

Last: (2)(-3) = -6

Combine the results,

x² - 3x + 2x - 6

Combine like terms,

x² - x - 6

Rewrite the equation,

x² - x - 6 = 5

Transpose 5 to the right side,

x² - x - 6 - 5 = 0

x² - x - 11 = 0

• The equation is simplified, and as u can see, the resulting equation is a Quadratic Equation since the leading term has degree/exponent 2. So,

a = 1, b = -1, c = -11

8. x(x² + 3x - 10) = 0

Distribute the term

x(x²) + x(3x) + x(-10) = 0

x³ + 3x² + (-10x) = 0

x³ + 3x² - 10x = 0,

• Hence, this isn't a Quadratic Equation.

9. (x - 1)² + 3 = 2x + 1

Recalling the PEMDAS Rule, from this equation, we have to expand the expression (x - 1)² with exponent,

Since the expression is a binomial, remember Squaring a Binomial,

(x)² + 2(x)(-1) + (-1)² = x² + (-2x) + 1

= x² - 2x + 1

Rewrite the equation,

(x² - 2x + 1) + 3 = 2x + 1

Transpose expression at the left to right side of the equation.

x² - 2x + 1 + 3 - (2x + 1) = 0

x² - 2x + 1 + 3 - 2x - 1 = 0

Combine like terms,

x² - 2x - 2x + 1 + 3 - 1 = 0

x² - 4x + 3 = 0

• The equation is simplified, and as u can see, the resulting equation is a Quadratic Equation since the leading term has degree/exponent 2. So,

a = 1, b = -4, c = 3

10. (x + 2)³ = x(x² - 10x + 25)

Express it as simplified form,

(x + 2)²(x + 2) = x(x² - 10x + 25)

(x)² + 2(x)(2) + 2² = x(x²) + x(-10x) + x(25)

(x² + 4x + 4)(x + 2) = x³ + (-10x²) + 25x

x(x²) + x(4x) + x(4) + 2(x²) + 2(4x) + 2(4)

= x³ + 4x² + 4x + 2x² + 8x + 8

Combine like terms,

x³ + 4x² + 2x² + 4x + 8x + 8

= x³ + 6x² + 12x + 8

Rewrite the equation,

x³ + 6x² + 12x + 8 = x³ - 10x² + 25x

Transpose expression at the left to right side of the equation,

x³ + 6x² + 12x + 8 - (x³ - 10x² + 25x) = 0

x³ + 6x² + 12x + 8 - x³ + 10x² - 25x = 0

Combine like terms,

x³ - x³ + 6x² + 10x² + 12x - 25x + 8 = 0

16x² - 13x + 8 = 0,

• The equation is simplified, and as u can see, the resulting equation is a Quadratic Equation since the leading term has degree/exponent 2. So,

a = 16, b = -13, c = 8