Question

find the common factor in a quadratic polynomial X square + 8 x + 15 and X square + 3 x minus 10​

Answer 1

   Answer:

   $(x+5)$

   Step-by-step explanation:

   $\text{The given equations are:}$  $x^{2} + 8x + 15 = 0 \text{ ---(i)}$

                                           $x^{2} + 3x - 10 =0 \text{ ---(ii)}$

   $\text{in order to find their common factor we must simultaneously solve them}$

   $\text{Substracting (i) and (ii)}$

⇒ $x^{2} + 8x + 15 - x^{2} -3x +10 = 0$

⇒ $5x + 25 = 0$

⇒ $5x = 25$

⇒ ${x=-5}$

⇒ $\boxed{x+5 = 0}$

∴ $(x+5) \text{ is the common factor of (i) and (ii)}$