Polynomials: JAMB Mathematics Questions, Answers & Notes

What Polynomials covers in the JAMB Mathematics syllabus

A polynomial is an expression of terms in powers of x. Change the subject of a formula by doing inverse operations to isolate the required variable. Expand brackets using the distributive law; key identities include (a+b)² = a²+2ab+b², (a−b)² = a²−2ab+b² and the difference of two squares a²−b² = (a+b)(a−b). Factorise a quadratic x²+bx+c by finding two numbers that multiply to c and add to b. Solve quadratics by factorising or with the formula x = (−b ± √(b²−4ac))/2a; the discriminant b²−4ac tells you the nature of the roots. For ax²+bx+c=0, the sum of roots = −b/a and the product = c/a.

For Polynomials, JAMB expects you to be able to:

• Change the subject of a formula and evaluate functions
• Expand and factorise algebraic expressions including quadratics
• Solve quadratic equations and use the sum and product of roots

Key facts & revision notes: Polynomials

These are the recurring points our Polynomials questions test — revise them until each feels automatic, then practise the questions above to lock them in.

• Divide by m: x = (y − c)/m.
• (x+3)(x+5) = x² + 5x + 3x + 15 = x² + 8x + 15.
• This is a difference of two squares: x² − 9 = x² − 3² = (x + 3)(x − 3).
• Find two numbers that multiply to 12 and add to 7: 3 and 4.
• So x² + 7x + 12 = (x+3)(x+4).
• Factorise: (x−2)(x−3) = 0, so x = 2 or x = 3 (numbers multiplying to 6, adding to 5).
• f(2) = 2(2²) − 3(2) + 1 = 8 − 6 + 1 = 3.
• (2x−1)² = (2x)² − 2(2x)(1) + 1² = 4x² − 4x + 1.
• The quadratic formula is x = (−b ± √(b² − 4ac))/2a.
• For ax²+bx+c=0, sum of roots = −b/a = −(−7)/1 = 7.
• Product of roots = c/a = 10/1 = 10.
• Cancel (x+2): (x+2)(x−2)/(x+2) = x − 2.
• Common factor is 2x: 2x² + 6x = 2x(x + 3).
• If (x−2) is a factor, then x = 2 makes the expression 0: 2² + 2k − 6 = 0 → 4 + 2k − 6 = 0 → 2k = 2 → k = 1.
• 3x − 2x = 9 − 2, so x = 7.
• f(x+1) = (x+1)² + 1 = x² + 2x + 1 + 1 = x² + 2x + 2.
• Discriminant = b² − 4ac = 2² − 4(1)(5) = 4 − 20 = −16.
• Two numbers multiplying to −6 and adding to −1: −3 and +2.
• Equation: x² − (sum)x + (product) = x² − 7x + 10 = 0.
• (x+2)(x+4) = x² + 4x + 2x + 8 = x² + 6x + 8.
• Difference of two squares: x² − 16 = (x − 4)(x + 4).
• 4 and 5 multiply to 20 and add to 9.
• (x − 3)(x − 4) = 0, so x = 3 or x = 4.
• (3x+1)² = 9x² + 2(3x)(1) + 1 = 9x² + 6x + 1.

Worked examples

Three Polynomials questions with the answer and a short explanation, so you can see how the topic is set before you practise the full set.

How Polynomials is tested in JAMB Mathematics

Our Polynomials bank holds 40 questions (14 easy, 21 medium, 5 hard). JAMB Mathematics typically returns to Polynomials year after year, so steady practice on this topic is high-value revision. Questions are multiple-choice with four options, and at UTME pace you get roughly 40 seconds each — which is why timed practice matters.

How to answer Polynomials questions

Work the stem first and predict the answer before you look at the options; then eliminate the ones that contradict the key facts above. Watch for “which is not…”, “all of the above” and “except” style stems, which are where rushed candidates lose easy marks on Polynomials. If a calculation or a precise definition is involved, work it from first principles rather than guessing from a half-remembered rule. When two options look right, re-read the stem for the qualifier that separates them — JAMB rarely repeats an option by accident. If you are still unsure, eliminate the two weakest choices to lift your odds, flag the question, and move on; never burn a full minute on one Mathematics item when the exam gives you about forty seconds each. Then come back to flagged questions with whatever time remains. The single most reliable way to get faster at Polynomials is repeated timed practice, so use the button above until the recurring patterns feel automatic.

Common mistakes to avoid in Polynomials

The errors that cost marks on Polynomials are usually careless rather than conceptual: misreading a negative stem, confusing two similar terms, or rushing a definition you actually know. Candidates also over-rely on “expo” and last-minute cramming instead of understanding the topic — which fails the moment JAMB rephrases a familiar idea. Treat every option as a claim to be checked against the facts above, keep your working tidy for any calculation, and don’t change a considered answer on a hunch. Above all, revise Polynomials actively by answering questions, not just by re-reading notes — recall under time is what the exam rewards.

Frequently asked questions

Is Polynomials part of the JAMB Mathematics syllabus?

Yes. Polynomials is a recognised topic in the JAMB Mathematics syllabus, covering change the subject of a formula and evaluate functions. You should be able to recall its key facts and apply them to multiple-choice questions.

How many Polynomials questions can I practise on Belmadeng?

There are 40 original, JAMB-standard Polynomials questions in our free bank, each with the correct answer and a worked explanation. You can practise them untimed or as a timed test.

What are the most important points to know about Polynomials?

A polynomial is an expression of terms in powers of x. Change the subject of a formula by doing inverse operations to isolate the required variable. Expand brackets using the distributive law; key identities include (a+b)² = a²+2ab+b², (a−b)² = a²−2ab+b² and the difference of two squares a²−b² = (a+…

How do I answer Polynomials questions quickly in JAMB?

Read the stem carefully, eliminate clearly wrong options, and match the remaining choices to the key facts for Polynomials. Practising timed Polynomials questions builds the speed you need for UTME's pace of about 40 seconds per question.

Are these JAMB Mathematics Polynomials questions past questions or original?

They are original questions written to JAMB (UTME) standard and mapped to the official syllabus — not reproduced past papers. This keeps them legal to use freely while closely mirroring how the real exam tests the topic.

Where can I practise Polynomials questions free without signing up?

Right here — tap “Start Polynomials practice” on this page to begin instantly. Belmadeng's CBT practice is completely free and needs no sign-up, download or subscription.

About these questions: original, JAMB-standard items written from the official UTME Mathematics syllabus (last reviewed 2026-09-18). Belmadeng is an independent study platform and is not affiliated with JAMB. Spotted an error? Use the report link.