Punjab Board Class 10 Mathematics — Flashcards for Quick Revision

A: Step 1: Divide 140 by 2 → 70 Step 2: Divide 70 by 2 → 35 Step 3: Divide 35 by 5 → 7 Step 4: 7 is prime, so stop Prime factorization: 140 = 2² × 5 × 7 Verification: 4 × 5 × 7 = 140 ✓

A: Step 1: 3825 ÷ 3 = 1275 Step 2: 1275 ÷ 3 = 425 Step 3: 425 ÷ 5 = 85 Step 4: 85 ÷ 5 = 17 Step 5: 17 is prime Prime factorization: 3825 = 3² × 5² × 17 Verification: 9 × 25 × 17 = 3825 ✓

A: Step 1: Check divisibility by small primes (2, 3, 5, 7, 11...) Step 2: 7429 is odd, so not divisible by 2 Step 3: Sum of digits: 7+4+2+9 = 22 (not divisible by 3) Step 4: Doesn't end in 0 or 5, so not

A: The degree is 3. The degree of a polynomial is the highest power of the variable. Here, x³ has the highest power of 3. The polynomial is also called a cubic polynomial because its degree is 3.

A: Step 1: Substitute x = 2 into the polynomial Step 2: p(2) = (2)² - 3(2) - 4 Step 3: p(2) = 4 - 6 - 4 Step 4: p(2) = -6 Answer: p(2) = -6. This means when x = 2, the polynomial's value is -6.

A: Step 1: Substitute x = 3 into p(x) Step 2: p(3) = (3)² - 5(3) + 6 Step 3: p(3) = 9 - 15 + 6 Step 4: p(3) = 0 Answer: Yes, x = 3 is a zero of the polynomial because p(3) = 0. (A zero means the polynom

A: Step 1: From first equation, express x in terms of y: x = 10 - y Step 2: Substitute in second equation: (10 - y) - y = 2 Step 3: Simplify: 10 - 2y = 2 Step 4: Solve for y: 2y = 8, so y = 4 Step 5: Sub

A: Step 1: Multiply first equation by 2: 4x + 6y = 26 Step 2: Multiply second equation by 3: 9x - 6y = 12 Step 3: Add equations to eliminate y: (4x + 9x) + (6y - 6y) = 26 + 12 Step 4: Simplify: 13x = 38,

A: Use substitution method when: 1. One equation is already solved for one variable (like y = 2x + 5) 2. One variable has coefficient 1 or -1 (easy to isolate) 3. Coefficients are small and don't need mu