Factorise-1 x2-9 x-182 x2-10 x-93 y2-24 y-1444 5 y2-5 y-105 p2-2 p-356 p2-7 p-447 m2-23 m-1208 m2-25 m-1009 3 x2-14 x-1510 2 x2-x-4511 20 x2-26 x-812 44 x2-x-3

1 #160;x2+9x+18=x2+6x+3x+18=xx+6+3x+6=x+3x+6 nbsp; 2 #160;x2 10x+9=x2 9x x+9=xx 9 1x 9=x 1x 9 3 #160;y2+24y+144= #160;y2+12y+12y+144= #160;yy+12+12 ...

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Byju's Answer

Standard VIII

Mathematics

Factorisation by Regrouping Terms

Factorise.1 x...

Question

Factorise.
(1) x²+ 9x + 18
(2) x²− 10x + 9
(3) y²+ 24y + 144
(4) 5y²+ 5y − 10
(5) p²− 2p − 35
(6) p²− 7p − 44
(7) m²− 23m + 120
(8) m²− 25m + 100
(9) 3x²+ 14x + 15
(10) 2x²+ x − 45
(11) 20x²− 26x + 8
(12) 44x²− x − 3

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Solution

$(1) x^{2} + 9 x + 18 = x^{2} + 6 x + 3 x + 18 = x (x + 6) + 3 (x + 6) = (x + 3) (x + 6)$
$(2) x^{2} - 10 x + 9 = x^{2} - 9 x - x + 9 = x (x - 9) - 1 (x - 9) = (x - 1) (x - 9)$
$(3) y^{2} + 24 y + 144 = y^{2} + 12 y + 12 y + 144 = y (y + 12) + 12 (y + 12) = (y + 12) (y + 12)$
$(4) 5 y^{2} + 5 y - 10 = 5 y^{2} + 10 y - 5 y - 10 = 5 y (y + 2) - 5 (y + 2) = (5 y - 5) (y + 2) = 5 (y - 1) (y + 2)$
$(5) p^{2} - 2 p - 35 = p^{2} - 7 p + 5 p - 35 = p (p - 7) + 5 (p - 7) = (p + 5) (p - 7)$
$(6) p^{2} - 7 p - 44 = p^{2} - 11 p + 4 p - 44 = p (p - 11) + 4 (p - 11) = (p + 4) (p - 11)$
$(7) m^{2} - 23 m + 120 = m^{2} - 15 m - 8 m + 120 = m (m - 15) - 8 (m - 15) = (m - 8) (m - 15)$
$(8) m^{2} - 25 m + 100 = m^{2} - 20 m - 5 m + 100 = m (m - 20) - 5 (m - 20) = (m - 5) (m - 20)$
$(9) 3 x^{2} + 14 x + 15 = 3 x^{2} + 9 x + 5 x + 15 = 3 x (x + 3) + 5 (x + 3) = (3 x + 5) (x + 3)$
$(10) 2 x^{2} + x - 45 = 2 x^{2} + 10 x - 9 x - 45 = 2 x (x + 5) - 9 (x + 5) = (2 x - 9) (x + 5)$
$(11) 20 x^{2} - 26 x + 8 = 20 x^{2} - 16 x - 10 x + 8 = 4 x (5 x - 4) - 2 (5 x - 4) = (4 x - 2) (5 x - 4) = 2 (2 x - 1) (5 x - 4)$
$(12) 44 x^{2} - x - 3 = 44 x^{2} + 11 x - 12 x - 3 = 11 x (4 x + 1) - 3 (4 x + 1) = (11 x - 3) (4 x + 1)$

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Similar questions

Q. Factorize:
(i)

y^{2} + 24 y + 144

(ii)

p^{2} - 7 p - 44

(iii)

3 x^{2} + 14 x + 15

(iv)

44 x^{2} - x - 3

Q. Simplify :
(i)

y^{2} + 24 y + 144

(ii)

p^{2} - 7 p - 44

(iii)

3 x^{2} + 14 x + 15

(iv)

44 x^{2} - x - 3

Q. lf the curves

\frac{x^{2}}{a^{2}} + \frac{y^{2}}{b^{2}} = 1

and

\frac{x^{2}}{p^{2}} - \frac{y^{2}}{m^{2}} = 1

cut each other orthogonally, then

Q. Solve the following quadratic equations by factorisation.
(1) x² – 15x + 54 = 0
(2) x² + x – 20 = 0
(3) 2y² + 27y + 13 = 0
(4) 5m² = 22m + 15
(5) 2x² – 2x +

\frac{1}{2}

= 0
(6)

6 x - \frac{2}{x} = 1

(7)

\sqrt{2} x^{2} + 7 x + 5 \sqrt{2} = 0

to solve this quadratic equation by factorisation, complete the following activity.
(8)

3 x^{2} - 2 \sqrt{6} x + 2 = 0

(9)

2 m (m - 24) = 50

(10)

25 m^{2} = 9

(11)

7 m^{2} = 21 m

(12)

m^{2} - 11 = 0

Q. Divide and write the quotient and the remainder.
(1) (y² + 10y + 24) ÷ (y + 4)
(2) (p² + 7p − 5) ÷ (p + 3)
(3) (3x + 2x² + 4x³) ÷ (x − 4)
(4) (2m³ + m² + m + 9) ÷ (2m − 1)
(5) (3x − 3x² − 12 + x⁴ + x³) ÷ (2 + x²)
(6) (a⁴ − a³ + a² − a + 1) ÷ (a³ − 2)
(7) (4x⁴ − 5x³ − 7x + 1) ÷ (4x − 1)

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Factorise. (1) x2 + 9x + 18 (2) x2 − 10x + 9 (3) y2 + 24y + 144 (4) 5y2 + 5y − 10 (5) p2 − 2p − 35 (6) p2 − 7p − 44 (7) m2 − 23m + 120 (8) m2 − 25m + 100 (9) 3x2 + 14x + 15 (10) 2x2 + x − 45 (11) 20x2 − 26x + 8 (12) 44x2 − x − 3

Factorise.
(1) x²+ 9x + 18
(2) x²− 10x + 9
(3) y²+ 24y + 144
(4) 5y²+ 5y − 10
(5) p²− 2p − 35
(6) p²− 7p − 44
(7) m²− 23m + 120
(8) m²− 25m + 100
(9) 3x²+ 14x + 15
(10) 2x²+ x − 45
(11) 20x²− 26x + 8
(12) 44x²− x − 3