To factorise the quadratic expression 2x² + 2x – 364, we start by simplifying it. The first step is to factor out the common factor, which is 2:
2(x² + x – 182)
Next, we need to factor the trinomial x² + x – 182. To do this, we look for two numbers that multiply to -182 and add up to 1 (the coefficient of x).
Through inspection, we find that the numbers 14 and -13 fit this requirement because:
- 14 * -13 = -182
- 14 + (-13) = 1
Thus, we can rewrite the trinomial:
x² + x – 182 = (x + 14)(x – 13)
We can now incorporate this back into our expression:
2(x + 14)(x – 13)
In conclusion, the factorised form of 2x² + 2x – 364 is:
2(x + 14)(x – 13)