how to factor 2b2 + 4b - 21?

If this expression was set equal to zero, you could find roots only using the quadratic formula, as this expression is not factorable.

Quadratic formula, a=2, b=4, c = -21

-b ± √(b²-4ac) / 2a

[-4 ± √(4² - (4)(2)(-21))] / 4

[-4 ± √(16 - (-168))] / 4

[-4 ± √184] / 4

[-4 ± √(4*46)] / 4

[-4 ± 2√46] / 4

-1 ± (√46)/2

Do you know the add and discard method?

First we will put an extra 2 in

(2x + _____)(2x - ______)


Then multiply 2*-21

-42 then find factors of -42 that add to 4

There are no factors that add to 4

At this point I see that it is not factorable.


I will give you an example of a factorable problem with the add and discard method.

4x^2 +5x-6

put in an extra 4

(4x+____)(4x-_____)

multiply 4 and -6

-24 what are factors of -24 that add to +5

8,-3

Put those in

(4x+8)(4x-3)

Now the discard part. Since we put in an extra 4 we now factor out a 4 and discard it.

4(x+2)(4x-3)

Discard the 4

(x+2)(4x-3)

Can`t be done.

2b^2 + 4b - 21
= cannot be factored

(b-3)(b+7)

Factor 16b² + 10b - 21 ( 8b - 7 )( 2b + 3 ) ANSWER: e) none of these

You have to use quadratic formula for this equation

a = 2
b = 4
c = -21

-b+-root(b^2 - 4ab) / 2a

Use the quadratic formula:
x (b) = -b+/- sq. root (b2 - 4ac)/2a