Final Answer:
x - 2
──────────────────────────────────────
Explanation:
Let’s solve (2x² - 5x + 3) ÷ (2x - 1) step by step.
Step 1: Look at the first terms.
Divide 2x² by 2x → that gives you x.
Write “x” on top (that’s your first part of the answer).
Step 2: Multiply “x” by the whole divisor (2x - 1).
x × (2x - 1) = 2x² - x.
Step 3: Subtract that from the original polynomial.
(2x² - 5x + 3) - (2x² - x) =
2x² - 5x + 3 - 2x² + x =
(-5x + x) + 3 = -4x + 3.
Step 4: Bring down the next term (we already did — it’s all there).
Now divide -4x by 2x → that gives you -2.
Write “-2” next to the “x” on top.
Step 5: Multiply -2 by (2x - 1).
-2 × (2x - 1) = -4x + 2.
Step 6: Subtract that from (-4x + 3).
(-4x + 3) - (-4x + 2) =
-4x + 3 + 4x - 2 = 1.
We’re left with 1, which is smaller than the divisor (2x - 1), so we stop.
Answer: x - 2 with a remainder of 1.
But since the problem just says “divide,” and in many school problems they want the quotient only, we say:
Final Answer: x - 2
(If you need to include the remainder, it would be x - 2 + 1/(2x - 1), but for this level, x - 2 is what’s expected.)
Parent Tip: Review the logic above to help your child master the concept of division of polynomials worksheet with answer.
