Factor
2\left(x+1\right)\left(x+15\right)
Evaluate
2\left(x+1\right)\left(x+15\right)
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2\left(x^{2}+16x+15\right)
Factor out 2.
a+b=16 ab=1\times 15=15
Consider x^{2}+16x+15. Factor the expression by grouping. First, the expression needs to be rewritten as x^{2}+ax+bx+15. To find a and b, set up a system to be solved.
1,15 3,5
Since ab is positive, a and b have the same sign. Since a+b is positive, a and b are both positive. List all such integer pairs that give product 15.
1+15=16 3+5=8
Calculate the sum for each pair.
a=1 b=15
The solution is the pair that gives sum 16.
\left(x^{2}+x\right)+\left(15x+15\right)
Rewrite x^{2}+16x+15 as \left(x^{2}+x\right)+\left(15x+15\right).
x\left(x+1\right)+15\left(x+1\right)
Factor out x in the first and 15 in the second group.
\left(x+1\right)\left(x+15\right)
Factor out common term x+1 by using distributive property.
2\left(x+1\right)\left(x+15\right)
Rewrite the complete factored expression.
2x^{2}+32x+30=0
Quadratic polynomial can be factored using the transformation ax^{2}+bx+c=a\left(x-x_{1}\right)\left(x-x_{2}\right), where x_{1} and x_{2} are the solutions of the quadratic equation ax^{2}+bx+c=0.
x=\frac{-32±\sqrt{32^{2}-4\times 2\times 30}}{2\times 2}
All equations of the form ax^{2}+bx+c=0 can be solved using the quadratic formula: \frac{-b±\sqrt{b^{2}-4ac}}{2a}. The quadratic formula gives two solutions, one when ± is addition and one when it is subtraction.
x=\frac{-32±\sqrt{1024-4\times 2\times 30}}{2\times 2}
Square 32.
x=\frac{-32±\sqrt{1024-8\times 30}}{2\times 2}
Multiply -4 times 2.
x=\frac{-32±\sqrt{1024-240}}{2\times 2}
Multiply -8 times 30.
x=\frac{-32±\sqrt{784}}{2\times 2}
Add 1024 to -240.
x=\frac{-32±28}{2\times 2}
Take the square root of 784.
x=\frac{-32±28}{4}
Multiply 2 times 2.
x=-\frac{4}{4}
Now solve the equation x=\frac{-32±28}{4} when ± is plus. Add -32 to 28.
x=-1
Divide -4 by 4.
x=-\frac{60}{4}
Now solve the equation x=\frac{-32±28}{4} when ± is minus. Subtract 28 from -32.
x=-15
Divide -60 by 4.
2x^{2}+32x+30=2\left(x-\left(-1\right)\right)\left(x-\left(-15\right)\right)
Factor the original expression using ax^{2}+bx+c=a\left(x-x_{1}\right)\left(x-x_{2}\right). Substitute -1 for x_{1} and -15 for x_{2}.
2x^{2}+32x+30=2\left(x+1\right)\left(x+15\right)
Simplify all the expressions of the form p-\left(-q\right) to p+q.
Examples
Quadratic equation
{ x } ^ { 2 } - 4 x - 5 = 0
Trigonometry
4 \sin \theta \cos \theta = 2 \sin \theta
Linear equation
y = 3x + 4
Arithmetic
699 * 533
Matrix
\left[ \begin{array} { l l } { 2 } & { 3 } \\ { 5 } & { 4 } \end{array} \right] \left[ \begin{array} { l l l } { 2 } & { 0 } & { 3 } \\ { -1 } & { 1 } & { 5 } \end{array} \right]
Simultaneous equation
\left. \begin{cases} { 8x+2y = 46 } \\ { 7x+3y = 47 } \end{cases} \right.
Differentiation
\frac { d } { d x } \frac { ( 3 x ^ { 2 } - 2 ) } { ( x - 5 ) }
Integration
\int _ { 0 } ^ { 1 } x e ^ { - x ^ { 2 } } d x
Limits
\lim _{x \rightarrow-3} \frac{x^{2}-9}{x^{2}+2 x-3}