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Factorise the expressions and divide them as directed. (i) `(y^2+7y+10) -: (y+5)` (ii) `(m^2-14m-32) -: (m+2)` (iii) `(5p^2-25p+20) -: (p-1)` (iv) `(4yz(z^2+6z-16) -: 2y (z+8)` (v) `5pq(p^2-q^2) -: 2p(p+q)` (vi) `12xy (9x62-16y^2) -: 4xy (3x+4y)` (vii) `39y^3(50y^2-98) -: 26y^2(5y+7)`

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Let's solve the given expressions step by step. ### (i) Factorise and divide: \((y^2 + 7y + 10) \div (y + 5)\) 1. **Factor the numerator**: - We need to factor \(y^2 + 7y + 10\). - We look for two numbers that multiply to \(10\) (the constant term) and add up to \(7\) (the coefficient of \(y\)). - The numbers \(2\) and \(5\) work because \(2 \times 5 = 10\) and \(2 + 5 = 7\). ...
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