So here is the answer to the given trinomial above. <span>2<span>x^2</span>+20x+50=2(<span>x^2</span>+10x+25)</span>
Now, let's factor,<span><span>x^2</span>+10x+25</span>
Since it is a perfect square, then it has the form <span>(a+b<span>)^2</span>=(a+b)(a+b) <span>== </span><span>a^2</span>+2ab+<span>b^2
</span></span>
Taking a=x and b=5:
<span>(x+5<span>)^2 </span>= (x+5)(x+5)=<span>x^2 </span>+ 2∗5∗x+<span>5^2</span></span>
Therefore:
<span>2<span>x^2</span>+20x+50 = 2(<span>x^2</span>+10x+25)= 2(x+5<span>)^2 </span>= 2(x+5)(x+5) So the final answer would be option A. </span><span>2(x + 5)(x + 5) I hope this answers the question. Let me know if you need more help next time.</span>
