Question

Which expression is a factor of 2x^2 + 5x-63

Answer 1

which quadratic function in vertex form can be represented by the graph that has a vertex at (1, 46) and passes through the point (3, 10)?

Answer 2

To factor the quadratic expression \( 2x^2 + 5x - 63 \), we can use the method of factoring by grouping or the AC method.

1. **Multiply** the coefficient of \( x^2 \) (which is 2) by the constant term (which is -63):
\[ 2 \times -63 = -126 \]

2. **Find two numbers** that multiply to -126 and add up to 5 (the coefficient of \( x \)). The numbers that satisfy this condition are 18 and -7.

3. **Rewrite** the middle term (5x) using these two numbers:
\[
2x^2 + 18x - 7x - 63
\]

4. **Group** the terms:
\[
(2x^2 + 18x) + (-7x - 63)
\]

5. **Factor out** the common factors from each group:
\[
2x(x + 9) - 7(x + 9)
\]

6. Now, **factor out** the common binomial factor \( (x + 9) \):
\[
(2x - 7)(x + 9)
\]

So, the expression \( 2x^2 + 5x - 63 \) can be factored as:
\[
(2x - 7)(x + 9)
\]

Thus, the factors of the expression are \( 2x - 7 \) and \( x + 9 \).