Principles Of Factoring Quadratic Equations

1. What is the factorization of the quadratic equation x²+5x+6=0?

(x+2)(x+3)=0

(x+1)(x+3)=0

(x+3)(x+1)=0

(x-2)(x-8)=0

(x+2)(x+1)=0

The given quadratic equation is x^2 + 5x + 6 = 0. To find the factorization, we need to determine two binomials that, when multiplied together, will give us the quadratic equation. By looking at the options, we can see that (x+2)(x+3) is the correct factorization. When we expand this expression, we get x^2 + 5x + 6, which matches the original equation. Therefore, the factorization of the quadratic equation x^2 + 5x + 6 = 0 is (x+2)(x+3)=0.

Explanation

The given quadratic equation is x^2 + 5x + 6 = 0. To find the factorization, we need to determine two binomials that, when multiplied together, will give us the quadratic equation. By looking at the options, we can see that (x+2)(x+3) is the correct factorization. When we expand this expression, we get x^2 + 5x + 6, which matches the original equation. Therefore, the factorization of the quadratic equation x^2 + 5x + 6 = 0 is (x+2)(x+3)=0.

2. Before factoring a quadratic equation, the equation must equal (_______).

Before factoring a quadratic equation, the equation must equal zero. This is because factoring involves finding the values of x that make the equation equal to zero, which are called the roots or solutions of the equation. By setting the equation equal to zero, we can then factor it into two binomial expressions or use other methods to solve for x.

Explanation

Before factoring a quadratic equation, the equation must equal zero. This is because factoring involves finding the values of x that make the equation equal to zero, which are called the roots or solutions of the equation. By setting the equation equal to zero, we can then factor it into two binomial expressions or use other methods to solve for x.

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3. Factor the following equation: x²+2x=3. What is the factorization?

(x+3)(x+2)=0

(x+3)(x-1)=0

(x+5)(x-3)=0

X(x-2)=3

2(x-1)=3

The given equation is x^2 + 2x = 3. To factorize this equation, we need to find two binomials that multiply together to give us the original equation. In this case, the correct factorization is (x+3)(x-1)=0. By expanding this factorization, we get x^2 + 2x - 3, which is equal to the original equation. To find the solutions, we set each factor equal to zero, so x+3=0 or x-1=0, giving us x=-3 or x=1.

Explanation

The given equation is x^2 + 2x = 3. To factorize this equation, we need to find two binomials that multiply together to give us the original equation. In this case, the correct factorization is (x+3)(x-1)=0. By expanding this factorization, we get x^2 + 2x - 3, which is equal to the original equation. To find the solutions, we set each factor equal to zero, so x+3=0 or x-1=0, giving us x=-3 or x=1.

4. For the quadratic equation x²-2x+1=0, what is the value of x?

(x-2)(x-1)=0

(x-1)(x-2)=0

X=0

X=2

X=1

The given quadratic equation can be factored as (x-1)(x-1)=0. This means that either (x-1) or (x-1) must equal zero in order for the equation to be true. Therefore, the value of x that satisfies the equation is x=1.

Explanation

The given quadratic equation can be factored as (x-1)(x-1)=0. This means that either (x-1) or (x-1) must equal zero in order for the equation to be true. Therefore, the value of x that satisfies the equation is x=1.

5. For the equation 3x(x+4)=0, what are the two values of x? (Hint: The equation does NOT need to be solved.)

X=2, x=4

X=1, x=-2

X=0, x=0

X=0, x=-4

X=-3, x=2

The equation 3x(x+4)=0 can be factored as 3x(x+4)=0. By applying the zero product property, we know that either 3x=0 or (x+4)=0. Therefore, the two possible values for x are x=0 and x=-4.

Explanation

The equation 3x(x+4)=0 can be factored as 3x(x+4)=0. By applying the zero product property, we know that either 3x=0 or (x+4)=0. Therefore, the two possible values for x are x=0 and x=-4.