Factorise the expressions and divide them as directed
$(m^{2} - 14 m - 32) \div (m + 2)$

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Solution

$m^{2} - 14 m - 32 = m^{2} + 2 m - 16 m - 32 m (m + 2) - 16 (m + 2) = (m + 2) (m - 16) (m^{2} - 14 m - 32) \div (m + 2) = \frac{(m + 2) (m - 16)}{(m + 2)} = m - 16$

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(m^{2} - 14 m - 32) \div (m + 2)

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12 x y (9 x^{2} - 16 y^{2}) + 4 x y (3 x + 4 y)

Factorise the expressions and divide them as directed.

(i) (y² + 7y + 10) ÷ (y + 5)

(ii) (m² − 14m − 32) ÷ (m + 2)

(iii) (5p² − 25p + 20) ÷ (p − 1)

(iv) 4yz(z² + 6z − 16) ÷ 2y(z + 8)

(v) 5pq(p² − q²) ÷ 2p(p + q)

(vi) 12xy(9x² − 16y²) ÷ 4xy(3x + 4y)

(vii) 39y³(50y²− 98) ÷ 26y²(5y+ 7)

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