Factorise x^2 + 3x - 10
Understand the Problem
The question requires us to factorize the quadratic expression x^2 + 3x - 10. This involves expressing the quadratic as a product of two binomials.
Answer
$(x + 5)(x - 2)$
Answer for screen readers
$(x + 5)(x - 2)$
Steps to Solve
- Identify coefficients
The quadratic expression is in the form $ax^2 + bx + c$, where $a = 1$, $b = 3$, and $c = -10$.
- Find two numbers that multiply to $c$ and add up to $b$
We need to find two numbers that multiply to $-10$ and add to $3$. These numbers are $5$ and $-2$, since $5 \times -2 = -10$ and $5 + (-2) = 3$.
- Write the factored form
Using the two numbers we found, we can write the factored form of the quadratic expression as $(x + 5)(x - 2)$.
$(x + 5)(x - 2)$
More Information
The factored form represents the original quadratic expression as a product of two binomials. Expanding $(x + 5)(x - 2)$ gives $x^2 - 2x + 5x - 10 = x^2 + 3x - 10$, which verifies our factorization.
Tips
A common mistake is getting the signs wrong. For example, using -5 and 2 instead of 5 and -2. This would result in the factors $(x - 5)(x + 2)$, which expands to $x^2 - 3x - 10$, which is not the original expression.
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