For simple integer factors as this one has, you want to find two values for the quadratic in the form ax^2+bx+c. Let the two values be j and k. These two values must satisfy two conditions.
jk=ac=10 and j+k=b=11, so j and k must be 1 and 10.
Now replace bx with jx and kx...
2x^2+x+10x+5 now factor 1st and 2nd pair of terms.
Factor by grouping.Tap for fewer steps...For a polynomial of the form <span><span><span><span>a<span>x2</span></span>+<span>bx</span></span>+c</span><span><span><span>a<span>x2</span></span>+<span>bx</span></span>+c</span></span>, rewrite the middle term as a sum of two terms whose product is <span><span><span><span>a⋅c</span>=<span>2⋅5</span></span>=10</span><span><span><span>a⋅c</span>=<span>2⋅5</span></span>=10</span></span> and whose sum is <span><span>b=<span>−11</span></span><span>b=<span>-11</span></span></span>.Tap for fewer steps...Factor <span><span>−11</span><span>-11</span></span> out of <span><span><span>−11</span>x</span><span><span>-11</span>x</span></span>.<span><span><span><span><span>2<span>x2</span></span><span><span>−11</span>x</span></span>+5</span>=0</span><span><span><span><span>2<span>x2</span></span><span><span>-11</span>x</span></span>+5</span>=0</span></span>Rewrite <span><span>−11</span><span>-11</span></span> as <span><span>−10</span><span>-10</span></span> plus <span><span>−1</span><span>-1</span></span><span><span><span><span><span>2<span>x2</span></span>+<span><span>(<span><span>−10</span><span>−1</span></span>)</span>x</span></span>+5</span>=0</span><span><span><span><span>2<span>x2</span></span>+<span><span><span>-10</span><span>-1</span></span>x</span></span>+5</span>=0</span></span>Apply the distributive property.<span><span><span><span><span>2<span>x2</span></span>+<span>(<span><span><span>−10</span>x</span><span><span>−1</span>x</span></span>)</span></span>+5</span>=0</span><span><span><span><span>2<span>x2</span></span>+<span><span><span>-10</span>x</span><span><span>-1</span>x</span></span></span>+5</span>=0</span></span>Remove parentheses.<span><span><span><span><span><span>2<span>x2</span></span><span><span>−10</span>x</span></span><span><span>−1</span>x</span></span>+5</span>=0</span><span><span><span><span><span>2<span>x2</span></span><span><span>-10</span>x</span></span><span><span>-1</span>x</span></span>+5</span>=0</span></span>Factor out the greatest common factor from each group.Tap for fewer steps...Group the first two terms and the last two terms.<span><span><span><span>(<span><span>2<span>x2</span></span><span><span>−10</span>x</span></span>)</span>+<span>(<span><span><span>−1</span>x</span>+5</span>)</span></span>=0</span><span><span><span><span>2<span>x2</span></span><span><span>-10</span>x</span></span>+<span><span><span>-1</span>x</span>+5</span></span>=0</span></span>Factor out the greatest common factor (GCF) from each group.<span><span><span><span><span>2x</span><span>(<span>x<span>−5</span></span>)</span></span><span><span>−1</span><span>(<span>x<span>−5</span></span>)</span></span></span>=0</span><span><span><span><span>2x</span><span>x<span>-5</span></span></span><span><span>-1</span><span>x<span>-5</span></span></span></span>=0</span></span>Factor the polynomial by factoring out the greatest common factor, <span><span>x<span>−5</span></span><span>x<span>-5</span></span></span>.<span><span><span><span>(<span>x<span>−5</span></span>)</span><span>(<span><span>2x</span><span>−1</span></span>)</span></span>=0</span><span><span><span>x<span>-5</span></span><span><span>2x</span><span>-1</span></span></span>=0</span></span>Set <span><span>x<span>−5</span></span><span>x<span>-5</span></span></span> equal to <span>00</span> and solve for <span>xx</span>.Tap for fewer steps...Set the factor equal to <span>00</span>.<span><span><span>x<span>−5</span></span>=0</span><span><span>x<span>-5</span></span>=0</span></span>Since <span><span>−5</span><span>-5</span></span> does not contain the variable to solve for, move it to the right side of the equation by adding <span>55</span> to both sides.<span><span>x=5</span><span>x=5</span></span>Set <span><span><span>2x</span><span>−1</span></span><span><span>2x</span><span>-1</span></span></span> equal to <span>00</span> and solve for <span>xx</span>.Tap for fewer steps...Set the factor equal to <span>00</span>.<span><span><span><span>2x</span><span>−1</span></span>=0</span><span><span><span>2x</span><span>-1</span></span>=0</span></span>Since <span><span>−1</span><span>-1</span></span> does not contain the variable to solve for, move it to the right side of the equation by adding <span>11</span> to both sides.<span><span><span>2x</span>=1</span><span><span>2x</span>=1</span></span>Divide each term by <span>22</span> and simplify.Tap for more steps...<span><span>x=<span>12</span></span><span>x=<span>12</span></span></span>The solution is the result of <span><span><span>x<span>−5</span></span>=0</span><span><span>x<span>-5</span></span>=0</span></span> and <span><span><span><span>2x</span><span>−1</span></span>=0</span><span><span><span>2x</span><span>-1</span></span>=0</span></span>.<span><span>x=5,<span>12</span></span><span>x=5,<span>12</span></span></span>
