Y = 2x² + x - 10 .(factor and zero prod)

(x-2)(2x+5)

For a polynomial of the form  a x 2 + b x + c

rewrite the middle term as a sum of two terms whose product is  a  x (times) c = 2 − 10 = − 20  and whose sum is  b = 1

2 x 2 − 4 x + 5 x − 10 = 0

2 x ( x − 2 ) + 5 ( x − 2 ) = 0

( x − 2 ) ( 2 x + 5 ) = 0

x − 2 = 0  

2 x + 5 = 0

Set the first factor equal to  0

x − 2 = 0

Add  2  to both sides of the equation.

x = 2

Set the next factor equal to  0  

2 x + 5  =  0

Subtract  5  from both sides of the equation.

2 x = −  5

Divide each term by  2  and simplify.  

x  =  −  5 /2

The final solution is all the values that make   = ( x − 2 )  ( 2 x + 5 )  =  0  = true.

x  =  2 ,  −  5 / 2

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