#Long Division Basic Example

How to multiply binomials. #multiplybinomials #multiplypolynomials

You Can Divide Polynomials Like Regular Numbers [Part 1/4] Wait... you can divide polynomials the SAME way you divide numbers?! 🤯 (x² + 11x + 30) ÷ (x + 6) = ??? Same long division you learned in 4th grade — just with x's instead of digits 💡 Step 1 is the most important — get the setup wrong and EVERYTHING falls apart 💀 Can you guess the answer before Part 2? Drop it below 👇 🎯 Save this series if you're taking algebra! #Math #Algebra #PolynomialDivision #LongDivision #MathTok #LearnMath #MathTricks #Education #StudyTips #HighSchoolMath #MathShorts #Reels #MathEducation #AlgebraTips

Class 9, POLYNOMIALS MCQ IMPORTANT QUESTION #class9#2026#importantquestions #shortvideo#ncertexamplar

This division problem looks IMPOSSIBLE... until you see the trick 🤯 Divide: a³ + b³ + c³ − 3abc by (a + b + c) Most students see this and freeze. Three variables? Cubic terms? A negative 3abc thrown in? BUT here's the secret — it divides PERFECTLY. Zero remainder. ✅ The trick? Focus on "a." Arrange by powers of a, then long divide step by step: a³ ÷ a = a² ↓ multiply back, subtract ↓ repeat for each layer ↓ each round peels back the answer The final result: (a³ + b³ + c³ − 3abc) ÷ (a + b + c) = a² − ab − ac + b² − bc + c² Zero remainder. A monster expression → something beautiful. 🔥 📸 SAVE THIS — because this exact problem shows up on every algebra exam, competitive math test, and polynomial factoring worksheet. Tag someone who needs this before their next exam 👇

The minus version has a SECRET second divisor 🤫 We know x^n − y^n ÷ (x − y) works ALWAYS ✅ But can (x + y) ALSO divide it? n = 2 → (x² − y²) ÷ (x + y) = x − y ✅ n = 3 → remainder ❌ n = 4 → works ✅ x^n − y^n is divisible by (x + y) ONLY when n is EVEN 🔓 It's like a VIP list — and even numbers get the extra pass 🎫 Comment "VIP" if this blew your mind 🤯 . . . #math #algebra #mathtricks #polynomial #divisibility #evennumbers #mathtok #studytok #education #mathshorts #algebrahelp #examprep #mathteacher #learnmath #highschoolmath #mathpatterns #studygram #polynomialdivision #mathreels #mathhacks

While basic polynomial integration (  ∫xndxintegral of x to the n-th power d x 𝑥𝑛𝑑𝑥 ) is straightforward using the power rule, certain polynomial forms and combinations make integration difficult, often requiring advanced techniques like substitution, partial fractions, or reduction formulas. Here are the polynomial forms that are considered hard to integrate, along with examples: 1. High-Degree Reciprocal Polynomials:  ∫1P(x)dxintegral of the fraction with numerator 1 and denominator cap P open paren x close paren end-fraction d x 1𝑃(𝑥)𝑑𝑥 When a high-degree polynomial is in the denominator, it requires factoring into linear and irreducible quadratic terms, followed by complex partial fraction decomposition. Mathematics Stack Exchange Example:  ∫1x4+1dxintegral of the fraction with numerator 1 and denominator x to the fourth power plus 1 end-fraction d x 1𝑥4+1𝑑𝑥 Why it's hard: Requires factoring  x4+1x to the fourth power plus 1 𝑥4+1 into  (x2+2x+1)(x2−2x+1)open paren x squared plus the square root of 2 end-root x plus 1 close paren open paren x squared minus the square root of 2 end-root x plus 1 close paren (𝑥2+2√𝑥+1)(𝑥2−2√𝑥+1) and solving a complex partial fraction system. 2. Powers of Rational Functions:  ∫(P(x)Q(x))ndxintegral of open paren the fraction with numerator cap P open paren x close paren and denominator cap Q open paren x close paren end-fraction close paren to the n-th power d x 𝑃(𝑥)𝑄(𝑥)𝑛𝑑𝑥 When a polynomial fraction is raised to a high power, it becomes tedious and requires significant algebraic manipulation or reduction formulas. Mathematics Stack Exchange +1 Example:  ∫(x41+x6)2dxintegral of open paren the fraction with numerator x to the fourth power and denominator 1 plus x to the sixth power end-fraction close paren squared d x 𝑥41+𝑥62𝑑𝑥 Example:  ∫(2x2+7)10dxintegral of open paren 2 x squared plus 7 close paren to the tenth power d x (2𝑥2+7)10𝑑𝑥 (requires expansion or reduction formula) Mathematics Stack Exchange +1 3. Roots of Polynomials:  ∫P(x)dxintegral of the square root of cap P open paren x close paren end-root d x 𝑃(𝑥)√𝑑𝑥

Polynomials/ Que based on Remainder Theorem Follow @smartstreetedu . . . #onlineclasses #polynomials #studygram #mathhelp #trending

ZERO of a Polynomial & Number of ZEROes in a Polynomial Full video 👉 https://youtu.be/5AG_GofBAnw?si=pAk5Smx9Ka57ZsNF #polynomials #class10maths #zeroofpolynomial

Second order polynomial 🤩 #math

✨️Quadratic Formula(✨️Code link in bio✨️) — Visual Derivation Using Completing the Square 🌛The quadratic formula is one of the most important results in elementary algebra. It provides the solutions to any quadratic equation of the form ax² + bx + c = 0 (with a ≠ 0). Instead of memorizing the formula, this reel explains how it naturally appears through the completing the square method, using a clear visual, geometric approach. By splitting the linear term, arranging the pieces around the x² term, and adding the missing small square, we transform the expression into a perfect square. Solving this structure step-by-step leads directly to the well-known quadratic formula: x = (-b ± √(b² − 4ac)) / (2a) A key part of the formula is the discriminant, written as Δ = b² − 4ac. • If Δ > 0 → two distinct real roots • If Δ = 0 → one repeated real root • If Δ < 0 → no real roots (two complex conjugates) Graphically, these solutions represent the x-intercepts of the parabola defined by y = ax² + bx + c, showing exactly where the curve crosses the x-axis. This visual explanation is ideal for students, visual learners, math enthusiasts, and anyone preparing for exams who wants to understand the quadratic formula more deeply. #math #mathematics #fyp #studygram #trending

So many students forget when they need to use polynomial long division before integrating! Watch this video so you’ll never forget again! #calculus #integrals #usubstitution #tutor #apcalculus