Factorize 13y2-4-7y-5 - 27 y- 2-3 y2-2 - 17y- 3- 2y2

The correct option is C (y 2)(y+3) (13y^2 47y+5) (27y 23y^2+2) (17y 3+2y^2)=0 y^2(13+23 2)+y( 47 27 17)+(5 2+3)=0 y^2(1 2)+y( 1)+6=0 ...

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Byju's Answer

Standard VIII

Mathematics

Division of a Polynomial by a Polynomial

Factorize 1...

Question

Factorize $(\frac{1}{3} y^{2} - \frac{4}{7} y + 5) - (\frac{2}{7} y - \frac{2}{3} y^{2} + 2) - (\frac{1}{7} y - 3 + 2 y^{2})$

(y - 2) (y + 3)

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(y - 2) (y - 3)

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(y + 2) (y + 3)

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(y + 2) (y - 3)

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Solution

The correct option is C $(y - 2) (y + 3)$
$(\frac{1}{3} y^{2} - \frac{4}{7} y + 5) - (\frac{2}{7} y - \frac{2}{3} y^{2} + 2) - (\frac{1}{7} y - 3 + 2 y^{2}) = 0$
$⟹ y^{2} (\frac{1}{3} + \frac{2}{3} - 2) + y (\frac{- 4}{7} - \frac{- 2}{7} - \frac{1}{7}) + (5 - 2 + 3) = 0$
$⟹ y^{2} (1 - 2) + y (- 1) + 6 = 0$
$⟹ - y^{2} - y + 6 = 0$
$⟹ y^{2} + y - 6 = 0$
$⟹ y^{2} + 3 y - 2 y - 6 = 0$
$⟹ y (y + 3) - 2 (y + 3) = 0$
$⟹ (y - 2) (y + 3) = 0$

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Similar questions

Find the sum of the following polynomials

y^{2} + 2 y - 5; y^{3} + 2 y^{2} + 3 y + 4; y^{3} + 7 y - 2

Simplify each of the following: $(i) x^{2} - 3 x + 5 - \frac{1}{2} (3 x^{2} - 5 x + 7) (i i) [5 - 3 x + 2 y - (2 x - y)] - (3 x - 7 y + 9) (i i i) \frac{11}{2} x^{2} y - \frac{9}{4} x y^{2} + \frac{1}{4} x y - \frac{1}{14} y^{2} x + \frac{1}{15} y x^{2} + \frac{1}{2} x y (i v) (\frac{1}{3} y^{2} - \frac{4}{7} y + 11) - (\frac{1}{7} y - 3 + 2 y^{2}) - (\frac{2}{7} y - \frac{2}{3} y^{2} + 2) (v) - \frac{1}{2} a^{2} b^{2} c + \frac{1}{3} a b^{2} c - \frac{1}{4} a b c^{2} - \frac{1}{5} c b^{2} a^{2} + \frac{1}{6} c b^{2} a - \frac{1}{7} c^{2} a b + \frac{1}{8} c a^{2} b .$

Q. Evaluate:

2 y^{4} + 7 y^{2} + 8 y^{3} + 4 y + 3 b y (y + 3)

Q. Simplify:

(i) (2 y + 3) (y - 2) - (5 y + 3) (y - 2)

(i i) (3 x - 4 y) (x + y) - (5 x + 7 y) (x - y)

Q. Add

(3 + 2 y - 5 y^{2} + 6 y^{3}), (- 8 + 3 y + 7 y^{3})

and

(5 - 6 y - 8 y^{3} + y^{2})

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Factorize (13y2−47y+5)−(27y−23y2+2)−(17y−3+2y2)

The correct option is C (y−2)(y+3)(13y2−47y+5)−(27y−23y2+2)−(17y−3+2y2)=0⟹y2(13+23−2)+y(−47−−27−17)+(5−2+3)=0⟹y2(1−2)+y(−1)+6=0⟹−y2−y+6=0⟹y2+y−6=0⟹y2+3y−2y−6=0⟹y(y+3)−2(y+3)=0⟹(y−2)(y+3)=0

Factorize $(\frac{1}{3} y^{2} - \frac{4}{7} y + 5) - (\frac{2}{7} y - \frac{2}{3} y^{2} + 2) - (\frac{1}{7} y - 3 + 2 y^{2})$