RD SHARMA Solutions for Class 9 Maths Chapter 5 - Factorisation of Algebraic Expressions

Give possible expressions for the length and breadth of the rectangle having

35y² + 13y - 12 as its area.

The factors of x³ - x²y - xy² + y³ are

(a) (x + y)(x² - xy + y²)

(b) (x + y)(x² + xy + y²)

(c) (x + y)²(x - y)

(d) (x - y)²(x + y)

The factors of x³ - 1 + y³ + 3xy are

(a) (x - 1 + y) (x² + 1 + y² + x + y - xy)

(b) (x + y + 1) ( x² + y² + 1 - xy - x - y)

(c) (x - 1 + y) (x² - 1 - y² + x + y + xy)

(d) 3(x + y - 1) (x² + y² - 1)

The factors of 8a³ + b³ - 6ab + 1 are

(a) (2a + b - 1)(4a² + b² + 1 - 3ab - 2a)

(b) (2a - b + 1)(4a² + b² - 4ab + 1 - 2a + b)

(c) (2a + b + 1)(4a² + b² + 1 - 2ab - b - 2a)

(d) (2a - 1 + b)(4a² + 1 - 4a - b - 2ab)

(x + y)³ - (x - y)³ can be factorized as

(a) 2y(3x² + y²)

(b) 2x(3x² + y²)

(c) 2y(3y² + x²)

(d) 2x(x² + 3y²)

The expression (a - b)³ + (b - c)³ + (c - a)³ can be factorized as

(a) (a - b)(b - c)(c - a)

(b) 3(a - b)(b - c)(c - a)

(c) -3(a - b)(b - c)(c - a)

(d) (a + b + c)(a² + b² + c² - ab - bc - ca)

The factors of a² - 1 - 2x - x² are

(a) (a - x + 1)(a - x - 1)

(b) (a + x - 1)(a - x + 1)

(c) (a + x + 1)(a - x - 1)

(d) none of these

The factors of x⁴ + x² + 25 are

(a) x² + 3x + 5)(x² - 3x + 5)

(b) (x² + 3x + 5)(x² + 3x - 5)

(c) (x² + x + 5)(x² - x + 5)

(d) none of these

The factors of x² + 4y² + 4y - 4xy - 2x - 8 are

(a) (x - 2y - 4)(x - 2y + 2)

(b) (x - y + 2)(x - 4y - 4)

(c) (x + 2y - 4)(x + 2y + 2)

(d) none of these

The factors of x³ - 7x + 6 are

(a) x(x - 6)(x - 1)

(b) (x² - 6)(x - 1)

(c) (x + 1)(x + 2)(x - 3)

(d) (x - 1)(x + 3)(x - 2)

The expression x⁴ + 4 can be factorized as

(a) (x² + 2x + 2)(x² - 2x + 2)

(b) (x² + 2x + 2)(x² + 2x - 2)

(c) (x² - 2x - 2)(x² - 2x + 2)

(d) (x² + 2)(x² - 2)

If 3x = a + b + c, then the value of (x - a)³ + (x - b)³ + (x - c)³ - 3(x - a)(x - b)(x - c) is

(a) a + b + c

(b) (a - b)(b - c)(c - a)

(c) 0

(d) none of these

If (x + y)³ - (x - y)³ - 6y(x² - y²) = ky², then k =

(a) 1

(b) 2

(c) 4

(d) 8

If x³ - 3x² + 3x + 7 = (x + 1) (ax² + bx + c), then a + b + c =

(a) 4

(b) 12

(c) -10

(d) 3