Factorise:3b^2=31b+22

Question

Use factorisation method

Answer 1

Hmm, a very different problem than the one you posted earlier.

 

3b² = 31b + 22

 

3b² - 31b -22 = 0

 

The only factors of 3b² are 3b*1b.  The only factors of -22 are (-2*11), 2*(-11), (-1)*(22), and (1)*(-22).  The combination that works is:

 

(3b+2)(b-11) = 0

 

Check by FOILing:

 

(3b+2)(b-11) = 3b2 - 33b + 2b -22 = 3b² -31b - 22

Answer 2

1)  Start by moving all terms to one side of the equation.

 

3b^2-31b-22 =0

 

2a)  Then guess some solutions in the form of (ub+w)(xb+y) where w*y=-22, u*x=3, and ux+wy=-22.

 

I tinkered until I arrived at (b-11)(3b+2).

 

2b)  The quadratic formula can also be used.  You will get solutions of -2/3 and +11 which imply that the equation can be factored into 0=(b-11)(3b+2).

 

2c)  One could graph this equation using a graphing calculator or an on-line utility like desmos.com.  A graph of F(b) = 3b^2-31b-22 will cross the b-axis at -2/3 and +11.