Answer:
The all integer values of n are -76, -4, 4, 76
Step-by-step explanation:
∵ The factors of 7 are 1 and 7
∵ The factors of 11 are 1 and 11
- The last term of the quadratic is negative, that means the two
linear factors have different middle sign
∴ The factors are (7x ± 1)(x ± 11) OR (7x ± 11)(x ± 1)
Let us take one by one
The middle term of the quadratic is the sum of the product of nears and ext-reams
In (7x + 1)(x - 11)
∵ The product of ext-reams is 7x × -11 = -77x
∵ The product of nears is 1 × x = x
∵ Their sum is -77x + x = -76x
∴ n = -76
In (7x - 1)(x + 11)
∵ The product of ext-reams is 7x × 11 = 77x
∵ The product of nears is -1 × x = -x
∵ Their sum is 77x + -x = 76x
∴ n = 76
In (7x + 11)(x - 1)
∵ The product of ext-reams is 7x × -1 = -7x
∵ The product of nears is 11 × x = 11x
∵ Their sum is -7x + 11x = 4x
∴ n = 4
In (7x - 11)(x + 1)
∵ The product of ext-reams is 7x × 1 = 7x
∵ The product of nears is -11 × x = -11x
∵ Their sum is 7x + -11x = -4x
∴ n = -4
The all integer values of n are -76, -4, 4, 76
