Note: This is the Solution of review exercise 4 from newly published book by PCTB (Punjab Curriculum and Textbook Board, Pakistan) for new 9th session 2025 Onward.
Review Exercise 4
Question # 01: Four option are given against each statement. Encircle the correct option.
\((i)\) The factorization of \(12x+36\) is:
\( a) \quad \) \( 12(x+3) \)
\( b) \quad \) \( 12(3x)\)
\(c) \quad \) \( 12(3x+1)\)
\( d) \quad \) \( x(12+36x)\)
\( \text{Answer/Explanation}\)
\((ii)\) The factors of \(4x^2-12y+9\) are:
\( a) \quad \) \( (2x+3)^2\)
\( b) \quad \) \( (2x-3)^2\)
\(c) \quad \) \((2x-3)(2x+3) \)
\( d) \quad \) \((2+3x)(2-3x)^2 \)
\( \text{Answer/Explanation}\)
\((iii)\) The HCF of \(a^3b^3\) and \(ab^2\) is:
\( a) \quad \) \( a^3b^3\)
\( b) \quad \) \(ab^2 \)
\(c) \quad \) \(a^4b^5 \)
\( d) \quad \) \( a^2b\)
\( \text{Answer/Explanation}\)
\((iv)\)\(\quad\)The LCM of \(16x^2\),\(4x\) and \(30xy\) is:
\( a) \quad \) \(480x^3y \)
\( b) \quad \) \( 240xy\)
\(c) \quad \) \( 240x^2y\)
\( d) \quad \) \( 120x^4y)\)
\( \text{Answer/Explanation}\)
\((v)\) \(\quad\)Product of LCM and HCF = ________ of two polynomials.
\( a) \quad \) Sum
\( b) \quad \) Difference
\(c) \quad \) Product
\( d) \quad \) Quotient
\( \text{Answer/Explanation}\)
\((vi)\) The square root of \(x^2-6x+9\) is:
\( a) \quad \) \( \pm (x-3)\)
\( b) \quad \) \( \pm (x+3)\)
\(c) \quad \) \( x-3\)
\( d) \quad \) \( x+3\)
\( \text{Answer/Explanation}\)
\((vii)\)\(\quad\)If \(A=\{1,2,3,4\} \) and \(B=\{x,y,z\}\), then cartesian product of \(A\) and \(B\) contains exactly _______ elements.
\( a) \quad \) \(13\)
\( b) \quad \) \(12\)
\(c) \quad \) \(10\)
\( d) \quad \) \(6\)
\( \text{Answer/Explanation}\)
\((viii)\)\(\quad\)The LCM of \((a-b)^2\) and \((a-b)^4\) is:
\( a) \quad \) \( (a-b)^2\)
\( b) \quad \) \( (a-b)^3\)
\(c) \quad \) \( (a-b)^4\)
\( d) \quad \) \( (a-b)^6\)
\( \text{Answer/Explanation}\)
\((ix)\)\(\quad\)Cubic polynomial has degree:
\( a) \quad \) \(1\)
\( b) \quad \) \(2\)
\(c) \quad \) \(3\)
\( d) \quad \) \(4\)
\( \text{Answer/Explanation}\)
\((x)\) \(\quad\)One of the factors of \(x^3-27\) is:
\( a) \quad \) \(x-3\) is injective
\( b) \quad \) \(x+3 \) is surjective
\(c) \quad \) \(x^2-3x+9\) is bijective
\( d) \quad \) Both \(a\) and \(c\)
\( \text{Answer/Explanation}\)
Question 2: Factorize the following expressions:
\((i)\) \(\quad\) \(4x^3+18x^2-12x\)
\((ii)\) \(\quad\) \(x^3+64y^3 \)
\((iii)\) \(\quad\) \(x^3y^3-8\)
\((iv)\) \(\quad\) \(-x^2-23x-60 \)
\((v)\) \(\quad\) \(2x^2+7x+3 \)
\((vi)\) \(\quad\) \(\{x^4+64 \)
\((vii)\) \(\quad\) \(x^4+2x^2+9\)
\((viii)\) \(\quad\) \((x+3)(x+4)(x+5)(x+6)-360 \)
\((ix)\) \(\quad\) \((x^2+6x+3)(x^2+6x-9)+36 \)
Question 3: Find LCM and HCF by prime factorization method:
\((i)\) \(\quad\) \(4x^3+12x^2,8x^2+16x \)
\((ii)\) \(\quad\) \(x^3+3x^2-4x,x^2-x-6 \)
\((iii)\) \(\quad\) \(x^2+8x+16,x^2-16 \)
\((iv)\) \(\quad\) \(x^3-9x,x^2-4x+3 \)