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>
The everyone of two longer parts has 57 cm length and the shortest part has 42 cm length. less 30cm from 156 and divide the remain amount of 126 into three parts. The answer will be 42 cm, then add 15,15 in longer parts.
