Example 15 - Chapter 12 Class 8 Factorisation
Last updated at July 14, 2026 by Teachoo
Dividing two polynomials
Dividing polynomial by polynomial
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Example 15 Divide 44 (š„^4 ā 5š„^3 ā 24š„^2) by 11x (x ā 8) We first factorize 44 (š„^4 ā 5š„^3 ā 24š„^2) = 44 (š„^2 Ć š„^2 ā 5š„ Ć š„^2 ā 24 Ć š„^2) Taking š„^2 common, = ć44š„ć^2 (š„^2 ā 5š„ ā 24) By middle term splitting, = 44š„^2 (š„^2+3š„ ā 8š„ ā 24) = 44š„^2 [(š„^2+3š„) ā (8š„+24)] Both have x as common factor Both have 8 as common factor Splitting the middle term We need to find two numbers whose Sum = ā5 Product = ā24 So, we write ā5x = 3x ā 8x = 44š„^2 [š„(š„+3) ā8(š„+3)] Taking š„+3 common, = 44š„^2 (š„+3) (š„ ā 8) Dividing (44 (š„^4 ā 5š„^3 ā 24š„^2 ))/(11š„ (š„ ā 8)) = (44 š„^2 (š„ + 3) (š„ ā 8))/(11š„ (š„ ā 8)) = 44/11 Ć š„^2/š„ Ć (š„ + 3) Ć ((š„ ā 8))/((š„ ā 8)) = 4 Ć š„ Ć (š„ + 3) = 4š (š + 3)
