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Find two values of "b" so that x^2 + b x + 6 can be factored into binomial factors.​

User Cruz Jean
by
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1 Answer

5 votes

Given:

The expression is


x^2+bx+6

To find:

The values of b so that the given expression can be factored into binomials factors.

Solution:

An expression is
ax^2+bx+c factorable if b is the sum of possible factors of ac.

We have,


x^2+bx+6

Here,
a=1,b=b,c=6.


ac=(1)(6)


ac=6

Some, factor forms of 6 are (1×6) and (2×3).


1+6=7


2+3=5

For b=7,


x^2+7x+6=x^2+x+6x+6


x^2+7x+6=x(x+1)+6(x+1)


x^2+7x+6=(x+1)(x+6)

For b=5,


x^2+5x+6=x^2+2x+3x+6


x^2+5x+6=x(x+2)+3(x+2)


x^2+5x+6=(x+2)(x+3)

Therefore, the two possible values of b are 7 and 5.

User Barry Scott
by
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