Question

identifying the factored form of a trinomial

which expression is the factored form of (x^2 - 7x + 10)?

(x + 3)(x + 4)
(x - 3)(x - 4)
(x - 2)(x - 5)
(x + 2)(x + 5)

Explanation:

Identify the trinomial to factor

The given trinomial is:

$$ x^2 - 7x + 10 $$

Find two numbers that multiply to 10 and add to -7

We need factors \(a\) and \(b\) such that:

$$ a \cdot b = 10 \quad \text{and} \quad a + b = -7 $$

The factors of \(10\) that add up to \(-7\) are \(-2\) and \(-5\):

$$ (-2) \cdot (-5) = 10 $$

$$ (-2) + (-5) = -7 $$

Write the factored form

Using the factors \(-2\) and \(-5\), we write the trinomial in its factored form:

$$ x^2 - 7x + 10 = (x - 2)(x - 5) $$

This matches the algebra tile model shown, which has dimensions of \((x - 2)\) and \((x - 5)\).

Answer:

• (A) \((x + 3)(x + 4)\)
• (B) \((x - 3)(x - 4)\)
• (C) \((x - 2)(x - 5)\) (Correct answer)
• (D) \((x + 2)(x + 5)\)