Score 90+ in FBISE Class 11 Math Unit 5 Polynomials – all exercises key answers!
HSA Notes Features
- 100% NBF/FBISE accurate
- Exercises 5.1–5.3 + Review solved
- Short exam-focused format
- Remainder & Factor theorems
- Synthetic division & factorization
- Word problems on volume/area
- Free PDF with diagrams
- Trusted for top marks
Target Audience
FBISE + Punjab boards. Top schools: Beaconhouse, Roots, LGS, City School, Karachi Grammar, Aitchison, Lawrence, ICG, APS, FPS.
Unit 5 Key Solved Highlights
Ex 5.1 (Remainder Theorem)
Q1(i) Remainder = 5
Q1(ii) Remainder = 35
Q2 x−3 is factor (P(3)=0)
Q3 x−3 not factor (P(3)=−5)
Q5 q = −12
Q6 m = 6
Q7 1 is zero, −2 is not
Q8 Zeros: 2, −½, −3
Q9 f(x) = (x−4)(x²+3x−2)
Q10 Floor area = x²+10x+24
Ex 5.2 (Factor Theorem)
Q1 (y+1)(y−3)(y+2)
Q2 (x−1)(2x−1)(x+1)
Q3 (x−2)(2x+3)(x+3)
Q4 (x−3)(3x²+4x+12)
Q5 (t−1)(t²+2t+5)
Q6 (x−2)(2x+1)(x−6)
Q7 (2x−1)(x−2)(x−5)
Ex 5.3 (Applications)
Q1 Dimensions: 12×2×5 cm
Q2 Tickets sold in 12th game = 650
Q3 Dimensions: 8×6×3
Q4 Dimensions: 25×11×9
Q5 Length ACED = 3x+7; Area square = (x+4)²
Q6 Sides: y−1, y+1
Review Exercise Key
(i) (x+1)(x−2)
(ii) Remainder = 0
(iii) −3
(iv) Divisor & factor
(v) k = −20
(vi) Remainder
(vii) p = 1
(viii) f(2) = 12
View PDF for full solutions, synthetic divisions, proofs.
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