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Important questions based on NCERT syllabus for Class 8 Chapter 14-Factorization:
Question 1: Divide
i) 4x^3 + 6x^2 + 12x by 2x
ii)4a^3 + 8a + 20a^2 by 4a
i)4x^2 + 6x^2 + 12x by 2x
4x^3 + 6x^2 + 12x = 2x(2x^2 + 3x + 6)
Dividing above expression by 2x gives 2x^2 + 3x + 6
ii) 4a^3 + 8a + 20a^2 by 4a
4a^3 + 8a + 20a^2 = 4a(a^2 + 5a + 2)
Dividing above expression by 4a gives a^2+5a+2.
Question 2: Factorize 15x + 3y + xy + 45 and give its value for x = 2 and y = 3.
15x + 3y + xy + 45
xy + 3y + 15x + 45
x = 2, y = 3
= 5 × 18
Question 3: Factorize and then divide 5x^3 + 16x^2 + 12x by (x + 2). Find the value of 5x^3 + 16x^2 + 12x for x = 3.
5x^3 + 16x^2 + 12x
= 5x^3 + 10x^2 + 6x^2 + 12x
= 5x^2(x + 2) + 6x(x + 2)
= (5x^2 + 6x)(x + 2)
Dividing above expression by (x+2) gives 5x^2+6x
Substitute x = 3 in theexpression 5x^3 + 16x^2 + 12x, we get,
= 5(3)^3 + 16(3)^2 + 12(3)