Balaji Class 9 Maths Solutions Chapter 5 Polynomial and their Factors Ex 5.4

Free PDF download of Balaji Publications Mathematics Class 9 Solutions Chapter 1 Real Numbers Ex 5.4 for all the questions enlisted under the chapter. All questions are solved using step by step approach, solving the questions from the Class 9 Maths for helps in grasping the concepts correctly.

Balaji Class 9 Maths Solutions Chapter 5 Polynomial and their Factors Ex 5.4 बहुपद तथा उनके गुणनखण्ड

Ex 5.4 Polynomial and their Factors अतिलघु उत्तरीय प्रश्न (Very Short Answer Type Question)

प्रश्न 1.
8x + 12y के गुणनखण्ड ज्ञात कीजिए।
हलः
8x + 12y = 2 × 2 × 2 × x + 2 × 2 × 3 × y = 4(2x + 3y)

प्रश्न 2.
x³ + x² के गुणनखण्ड ज्ञात कीजिए।
हलः
x³ + x² = x × x × x + x × x = x × x(x + 1) = x²(x + 1)

प्रश्न 3.
x² + x + y + xy के गुणनखण्ड ज्ञात कीजिए।
हल:
x² + x + y + xy = [x² + x] + [y + xy] = x(x + 1) + y(x + 1) = (x + 1)(x + y)

प्रश्न 4.
x² – x + y – xy के गुणनखण्ड ज्ञात कीजिए।
हल:
x² – x + y – xy = x(x – 1) – y(x – 1) = (x – 1)(x – y)

Ex 5.4 Polynomial and their Factors  लघु उत्तरीय प्रश्न – I (Short Answer Type Questions – I)

निम्न बहुपदों के गुणनखण्ड ज्ञात कीजिए

प्रश्न 5.
ax + cx – ay – cy
हलः
ax + cx – ay – cy = x(a + c) – y(a + c) = (a + c)(x – y)

प्रश्न 6.
mx – 2my – nx + 2ny
हल:
mx – 2my – nx + 2ny = mx – nx – 2my + 2ny = x(m – n) – 2y(m – n) = (m – n)(x – 2y)

प्रश्न 7.
ab + cd + ad + bc
हलः
ab + cd + ad + bc = ab + ad + cd + bc = a(b + d) + c(b + d)= (b + d)(a + c)

प्रश्न 8.
ax – bx + by + cy – cx – ay
हलः
ax – bx + by + cy – cx – ay = ax – bx – cx – ay + by + cy
= x(a – b – c) – y(a – b – c) = (a – b – c)(x – y)

प्रश्न 9.
mx + ny – nx – my
हलः
mx – ny – nx + my = mx – nx – my + ny = x(m – n) – y(m – n) = (m – n)(x – y)

प्रश्न 10.
ax + cy – ac – xy
हलः
ax + cy – ac – xy = ax – ac – xy + y = a(x – c) – y(x – c) = (x – c)(a – y)

प्रश्न 11.
9a³b²c – 27a²b³c² – 36a²b²c³
हलः
9a³b²c – 27a²b³c² – 36a²b²c³ = 9a²b²c(a – 3bc – 4c²)

प्रश्न 12.
8a²b(a – b)² – 4a²(a – b)³
हलः
8a²b(a – b)² – 4a² (a – b)³ = 4a²(a – b)²[2b – (a – b)]
= 4a² (a – b)²[2b – a + b] = 4a²(a – b)²[3b – a]

प्रश्न 13.
(p + q + r)² + x[p + q + r) – y(p + q + r)
हलः :
(p + q + r)² + x(p + q + r) – y(p + q + r) = (p + q + r)[p + q + r + x – y]

प्रश्न 14.
(p + q)³ + (p + q)² + (p + q)
हलः
(p + q)³ + (p + q)² + (p + q) = (p + q)[(p + q)² + (p + q) + 1]

Ex 5.4 Polynomial and their Factors  लघु उत्तरीय प्रश्न – II (Short Answer Type Questions – II)

निम्न बहुपदों के गुणनखण्ड कीजिए।
प्रश्न 15.
7(x + y)³ +14(x + y)² +28(x + y)
हलः
7(x + y)³ + 14(x + y)² + 28(x + y) = 7(x + y)[(x + y)² + 2(x + y) + 4]
= 7(x + y)[x² + y² + 2xy + 2x + 2y + 4]

प्रश्न 16.
a³bc + ab³c – abc³
हलः
a³bc + ab³c – abc³ = abc(a² + b² – c²)

प्रश्न 17.
(x² + 3x)² – 5(x² + 3x) – y(x² + 3x) + 5y
हलः
(x² + 3x)² – 5(x² + 3x) – y(x² + 3x) + 5y = (x² + 3x)[x² + 3x – 5] – y[x² + 3x – 5]
= [x² + 3x – 5][x² + 3x – y]

प्रश्न 18.
ab(x² + y²)+ xy(a² + b²)
हलः
ab(x² + y²) + xy(a² + b²)= abx² + aby² + xya² + xyb² = abx² + xya² + aby² + xyb²
= ax(bx + ay ) + by (ay + bx) = (ax + by)(bx + ay)

प्रश्न 19.
x⁵ + x⁴ – 2x² – 2x
हलः
x⁵ + x⁴ – 2x² – 2x = x{x⁴ + x³ – 2x – 2] = x[x³(x + 1) – 2(x + 1)]= x[(x³ – 2)(x + 1)]

प्रश्न 20.
ab(c² + 1) + c(a² + b²)
हलः
ab(c² + 1) + c(a² + b²) = abc² + ab + ca² + cb² = abc² + ca² + ab + cb²
= ac(bc + a) + b(a + bc) = (bc + a)(ac + b)

प्रश्न 21.
x² + + 2 – 3x –
हलः