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Learn/ 9th Mathematics/ Unit 4 /Numericals

Unit 4: Factorization and Algebraic Manipulation — Exercise 4 1

9th Class Mathematics · Unit 4: Factorization and Algebraic Manipulation

4.1.1.Factorize by identifying common factors. (i) 6x + 12 (ii) 15y^2 + 20y (iii) -12x^2 - 3x (iv) 4a^2b + 8ab^2 (v) xy - 3x^2 + 2x (vi) 3a^2b - 9ab^2 + 15ab
Result
(i) 6x+12 = 6(x+2)
(ii) 15y2+20y = 5y(3y+4)
(iii) -12x2-3x = -3x(4x+1)
(iv) 4a2b+8ab2 = 4ab(a+2b)
(v) xy-3x2+2x = x(y-3x+2)
(vi) 3a2b-9ab2+15ab = 3ab(a-3b+5)
4.1.2.Factorize and represent pictorially: (i) 5x + 15 (ii) x^2 + 4x + 3 (iii) x^2 + 6x + 8 (iv) x^2 + 4x + 4
Result
(i) 5x+15 = 5(x+3)
(ii) x2+4x+3 = x2+3x+x+3 = x(x+3)+1(x+3)
(ii) (x+1)(x+3)
(iii) x2+6x+8 = x2+4x+2x+8 = x(x+4)+2(x+4)
(iii) (x+2)(x+4)
(iv) x2+4x+4 = x2+2x+2x+4 = x(x+2)+2(x+2)
(iv) (x+2)(x+2) = (x+2)2
4.1.3.Factorize: (i) x^2 + x - 12 (ii) x^2 + 7x + 10 (iii) x^2 - 6x + 8 (iv) x^2 - x - 56 (v) x^2 - 10x - 24 (vi) y^2 + 4y - 12 (vii) y^2 + 13y + 36 (viii) x^2 - x - 2
(i) x2+x-12 = x2+4x-3x-12 = x(x+4)-3(x+4) = (x+4)(x-3)
(ii) x2+7x+10 = x2+5x+2x+10 = x(x+5)+2(x+5) = (x+5)(x+2)
(iii) x2-6x+8 = x2-4x-2x+8 = x(x-4)-2(x-4) = (x-4)(x-2)
(iv) x2-x-56 = x2-8x+7x-56 = x(x-8)+7(x-8) = (x-8)(x+7)
(v) x2-10x-24 = x2-12x+2x-24 = x(x-12)+2(x-12) = (x-12)(x+2)
(vi) y2+4y-12 = y2+6y-2y-12 = y(y+6)-2(y+6) = (y+6)(y-2)
(vii) y2+13y+36 = y2+9y+4y+36 = y(y+9)+4(y+9) = (y+9)(y+4)
(viii) x2-x-2 = x2-2x+x-2 = x(x-2)+1(x-2) = (x-2)(x+1)
(i) (x+4)(x-3) quad (ii) (x+5)(x+2) quad (iii) (x-4)(x-2) quad (iv) (x-8)(x+7) quad (v) (x-12)(x+2) quad (vi) (y+6)(y-2) quad (vii) (y+9)(y+4) quad (viii) (x-2)(x+1)
4.1.4.Factorize: (i) 2x^2 + 7x + 3 (ii) 2x^2 + 11x + 15 (iii) 4x^2 + 13x + 3 (iv) 3x^2 + 5x + 2 (v) 3y^2 - 11y + 6 (vi) 2y^2 - 5y + 2 (vii) 4z^2 - 11z + 6 (viii) 6 + 7x - 3x^2
(i) 2x2+7x+3 = 2x2+6x+x+3 = 2x(x+3)+1(x+3) = (2x+1)(x+3)
(ii) 2x2+11x+15 = 2x2+6x+5x+15 = 2x(x+3)+5(x+3) = (2x+5)(x+3)
(iii) 4x2+13x+3 = 4x2+12x+x+3 = 4x(x+3)+1(x+3) = (4x+1)(x+3)
(iv) 3x2+5x+2 = 3x2+3x+2x+2 = 3x(x+1)+2(x+1) = (3x+2)(x+1)
(v) 3y2-11y+6 = 3y2-9y-2y+6 = 3y(y-3)-2(y-3) = (3y-2)(y-3)
(vi) 2y2-5y+2 = 2y2-4y-y+2 = 2y(y-2)-1(y-2) = (2y-1)(y-2)
(vii) 4z2-11z+6 = 4z2-8z-3z+6 = 4z(z-2)-3(z-2) = (4z-3)(z-2)
(viii) 6+7x-3x2 = -3x2+9x-2x+6 = 3x(-x+3)+2(-x+3) = (3x+2)(3-x)
(i) (2x+1)(x+3) quad (ii) (2x+5)(x+3) quad (iii) (4x+1)(x+3) quad (iv) (3x+2)(x+1) quad (v) (3y-2)(y-3) quad (vi) (2y-1)(y-2) quad (vii) (4z-3)(z-2) quad (viii) (3x+2)(3-x)