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Solve the product $\left(x+1\right)\left(x-4\right)$

Step-by-step Solution

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Final answer to the problem

$x^2-3x-4$
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Step-by-step Solution

How should I solve this problem?

  • FOIL Method
  • Product of Binomials with Common Term
  • Find the integral
  • Find the derivative
  • Factor
  • Integrate by partial fractions
  • Integrate by substitution
  • Integrate by parts
  • Integrate using tabular integration
  • Integrate by trigonometric substitution
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We can multiply the polynomials $\left(x+1\right)\left(x-4\right)$ by using the FOIL method. The acronym F O I L stands for multiplying the terms in each bracket in the following order: First by First ($F\times F$), Outer by Outer ($O\times O$), Inner by Inner ($I\times I$), Last by Last ($L\times L$)

$\begin{matrix}(F\times F)\:=\:(x)(x)\\(O\times O)\:=\:(x)(-4)\\(I\times I)\:=\:(1)(x)\\(L\times L)\:=\:(1)(-4)\end{matrix}$
2

Then, combine the four terms in a sum

$(F\times F) + (O\times O) + (I\times I) + (L\times L)$
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Substitute the values of the products

$x\cdot x-4x+1x+1\cdot -4$
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Multiply $1$ times $-4$

$x\cdot x-4x+1x-4$
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Any expression multiplied by $1$ is equal to itself

$x\cdot x-4x+x-4$
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Combining like terms $-4x$ and $x$

$x\cdot x-3x-4$
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When multiplying two powers that have the same base ($x$), you can add the exponents

$x^2-3x-4$

Final answer to the problem

$x^2-3x-4$

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Function Plot

Plotting: $x^2-3x-4$

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1
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5
6
7
8
9
0
a
b
c
d
f
g
m
n
u
v
w
x
y
z
.
(◻)
+
-
×
◻/◻
/
÷
2

e
π
ln
log
log
lim
d/dx
Dx
|◻|
θ
=
>
<
>=
<=
sin
cos
tan
cot
sec
csc

asin
acos
atan
acot
asec
acsc

sinh
cosh
tanh
coth
sech
csch

asinh
acosh
atanh
acoth
asech
acsch

How to improve your answer:

Main Topic: Factorization

In mathematics, factorization or factoring is the decomposition of an object (for example, a number, a polynomial, or a matrix) into a product of other objects, or factors, which when multiplied together give the original.

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