Question

Find the zeros of the polynomials P(x) = x2 +7x – 30

Answer 1

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Answer 2

⇒Multiply the coefficient of the first term by the constant   1 • -30 = -30

⇒nd two factors of  -30  whose sum equals the coefficient of the middle term, which is   -7 .

     -30    +    1    =    -29  

     -15    +    2    =    -13  

     -10    +    3    =    -7    

Rewrite the polynomial splitting the middle term using the two factors found in step 2 above,  -10  and  3  

                    x2 - 10x + 3x - 30

: Add up the first 2 terms, pulling out like factors :

                   x • (x-10)

Add up the last 2 terms, pulling out common factors :

                   3 • (x-10)                                                                                      Add up the four terms of step 4 :

(x+3)  •  (x-10)

                   (x+3)  •  (x-10)