1. Describe how factoring a quadratic expression ax2 + bx + c, where a ≠ 1, is different from factoring x2 + bx + c.

2. Two students factored 2x2 + 6x - 20. Keiko said that the factorization was (2x - 4) (x + 5). Ray gave the factorization as (x - 2) (2x + 10). Confirm that both of these factorizations are correct. Then explain why they are not complete.

3. Explain the relationship between the factors of a quadratic expression, the roots of the related quadratic equation, and the x-intercepts of the graph of the related function.

Question

Mathematics

Stanley

16 October, 09:33

1. Describe how factoring a quadratic expression ax2 + bx + c, where a ≠ 1, is different from factoring x2 + bx + c.

2. Two students factored 2x2 + 6x - 20. Keiko said that the factorization was (2x - 4) (x + 5). Ray gave the factorization as (x - 2) (2x + 10). Confirm that both of these factorizations are correct. Then explain why they are not complete.

3. Explain the relationship between the factors of a quadratic expression, the roots of the related quadratic equation, and the x-intercepts of the graph of the related function.

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Answers (1)

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Mark Porter · Answer 1

1. Factoring a quadratic expression ax2 + bx + c, where a ≠ 1, is different from factoring x2 + bx + c because for the former type of expression you have to factor out the value of "a". Then, proceed to the factoring steps as usual.

2. To confirm the equations to be equal with the parent function we do as follows:

(2x - 4) (x + 5) = 2x^2 + 10x - 4x - 20 = 2x^2 + 6x - 20

(x - 2) (2x + 10) = 2x^2 + 10x - 4x - 20 = 2x^2 + 6x - 20

3. The roots of the quadratic expression represents the values of x that would satisfy the expression. The x-intercepts are the values of x when y is equal to zero, it is where the plot touches intersects the x-axis.