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1. The first term of both the factor is x.

2. The product of the second terms of the two factors is equal to the third term of the trinomial.

3. The algebraic sum of the second terms of the two factors is equal to the coefficient of x in the trinomial.

The second term of the factors must be such that their product is + 24 and their sum + 11, it is clear that they must be + 8 and + 3.

x

= x

= x (x + 8) + 3 (x + 8)

Or x

=(x + 8) (x + 3)

The second term of the factors must be such that their product is + 24 and their sum -10, it is clear that they must be - 6 and - 4.

x

= x

= x (x - 6) - 4 (x - 6)

Or x

In the given equation the third term is negative. The second terms of the factors must be such that their product is – 35 and their algebraically sum + 2. Hence they must have opposite signs, and the greater of them must be negative in order to give its sign to their sum

= x

= x

= x (x + 7) – 5 (x + 7)

Hence x