Question

complete the factorization of (3x^2 - 5x + 2).
which two factors can be multiplied together to make this trinomial?

((x - 2))
((x - 1))
((x + 1))
((3x - 2))
((3x + 2))

Explanation:

Identify the trinomial to factor

The given trinomial is:

$$ 3x^2 - 5x + 2 $$

Find two numbers that multiply to \(ac\) and add to \(b\)

For the quadratic expression \(ax^2 + bx + c\):

$$ a = 3, \quad b = -5, \quad c = 2 $$

The product is:

$$ ac = 3 \times 2 = 6 $$

The sum is:

$$ b = -5 $$

The two numbers that multiply to \(6\) and add to \(-5\) are \(-3\) and \(-2\).

Rewrite and factor by grouping

Rewrite the middle term using \(-3x\) and \(-2x\):

$$ 3x^2 - 3x - 2x + 2 $$

Group the terms:

$$ (3x^2 - 3x) - (2x - 2) $$

Factor out the greatest common factor from each group:

$$ 3x(x - 1) - 2(x - 1) $$

Factor out the common binomial \((x - 1)\):

$$ (3x - 2)(x - 1) $$

The two factors are \((x - 1)\) and \((3x - 2)\).

Answer:

• ☐ \((x-2)\)
• ☑ \((x-1)\) (Correct answer)
• ☐ \((x+1)\)
• ☑ \((3x-2)\) (Correct answer)
• ☐ \((3x+2)\)