All the possible values of b will be ±22 and ±10. Thus, there are 4 possibilities such that x2 + bx + 21 factors.
We have been the equation as
x2 + bx + 21
Now all the possible factors of 21 are ±1, ±3, ±7 and ±21
We can write the linear factors as (x+)(x+) or (x-)(x-) as the coefficient of x2 is 1 .
The possible linear factors are :
(x + 1)(x + 21) = x2 + 22x + 21
(x + 3)(x + 7) = x2 + 10x +21
(x – 1)(x – 21) = x2 – 22x + 20
(x – 3)(x – 7) = x2 – 10x + 20
Hence all the possible values of b will be ±22 and ±10. There are 4 possibilities.
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