Factor
\left(x-1\right)\left(4x+7\right)
Evaluate
\left(x-1\right)\left(4x+7\right)
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4x^{2}+3x-7
Multiply and combine like terms.
a+b=3 ab=4\left(-7\right)=-28
Factor the expression by grouping. First, the expression needs to be rewritten as 4x^{2}+ax+bx-7. To find a and b, set up a system to be solved.
-1,28 -2,14 -4,7
Since ab is negative, a and b have the opposite signs. Since a+b is positive, the positive number has greater absolute value than the negative. List all such integer pairs that give product -28.
-1+28=27 -2+14=12 -4+7=3
Calculate the sum for each pair.
a=-4 b=7
The solution is the pair that gives sum 3.
\left(4x^{2}-4x\right)+\left(7x-7\right)
Rewrite 4x^{2}+3x-7 as \left(4x^{2}-4x\right)+\left(7x-7\right).
4x\left(x-1\right)+7\left(x-1\right)
Factor out 4x in the first and 7 in the second group.
\left(x-1\right)\left(4x+7\right)
Factor out common term x-1 by using distributive property.
4x^{2}-7+3x
Add -9 and 2 to get -7.
Examples
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{ 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}