1Cademy - Factoring $$8x^2

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Factoring Trinomials of the Form $ax^2 + bx + c$ Using Trial and Error

Example

Factoring $8x^2 - 14x + 3$

To factor the trinomial $8x^2 - 14x + 3$ completely using trial and error:

Step 1 — Write the trinomial in descending order. The expression $8x^2 - 14x + 3$ is already in descending order.

Step 2 — Identify the factor pairs of the first term, $8x^2$ . The possibilities are $x \cdot 8x$ and $2x \cdot 4x$ .

Step 3 — Identify the factor pairs of the last term, $3$ . Because the constant is positive and the middle coefficient is negative, the factors must both be negative. The only option is $-1$ and $-3$ .

Step 4 — Test the combinations to find the one that produces a middle term of $-14x$ .

For $x$ $x$ and $8x$ $8 x$ :
- $(x - 1)(8x - 3)$ gives a middle term of $-11x$ .
- $(x - 3)(8x - 1)$ gives a middle term of $-25x$ .
For $2x$ $2 x$ and $4x$ $4 x$ :
- $(2x - 1)(4x - 3)$ gives a middle term of $-10x$ .
- $(2x - 3)(4x - 1)$ gives a middle term of $-14x$ . ✓

The correct combination is $(2x - 3)(4x - 1)$ .

Step 5 — Verify the result by multiplying: $(2x - 3)(4x - 1) = 8x^2 - 2x - 12x + 3 = 8x^2 - 14x + 3$ .

The completely factored form is $(2x - 3)(4x - 1)$ .

Updated 2026-06-03

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OpenStax Intermediate Algebra

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