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Factorisation by Common Factors

5x2-9x+3, 10x...

Question

$(5 x^{2} - 9 x + 3), (10 x^{4} + 17 x^{3} - 62 x^{2} + 30 x - 3)$

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Solution

Degree $\to$ highest coefficient in the polynomial.
$5 x^{2} - 9 x + 3 \to$ degree $= 2$
$10 x^{4} + 17 x^{3} - 62 x^{2} + 30 x - 3 ⟹$ degree $= 4$ .

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$2 x^{2} + 7 x - 1$ completely divides $10 x^{4} + 17 x^{3} - 62 x^{2} + 30 x - 3$ .

10 x^{4} + 17 x^{3} - 62 x^{2} + 30 x - 3

2 x^{2} + 7 x - 1

Q. If we divide

(10 x^{4} + 17 x^{3} - 62 x^{2} + 30 x - 3)

(2 x^{2} + 7 x - 1)

, then the quotient is __________.

Q. Apply division algorithm to find the quotient q(x) and remainder r(x) on dividing

f (x) = 10 x^{4} + 17 x^{3} - 62 x^{2} + 30 x - 3

g (x) = 2 x^{2} - x + 1

Q. Apply division algorithm to find the quotient q(x) and remainder r(x) in dividing f(x) by g(x) in each of the following :

(i) f(x) = x³ − 6x² + 11x − 6, g(x) = x² + x + 1
(ii) f(x) = 10x⁴ + 17x³ − 62x² + 30x − 3, g(x) = 2x² + 7x + 1
(iii) f(x) = 4x³+ 8x + 8x² + 7, g(x) = 2x² − x + 1
(iv) f(x) = 15x³ − 20x² + 13x − 12, g(x) = 2 − 2x + x²

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