Solve x^4+x^3+2x^2+x+1 x^2+1 x^2+x+1

Question

Simplify the expression

x^{4} + x^{3} + 4 x^{2} + 2 x + 1

Evaluate

x^{4} + x^{3} + 2 x^{2} + x + 1 \times x^{2} + 1 \times x^{2} + x + 1

Any expression multiplied by 1 remains the same

x^{4} + x^{3} + 2 x^{2} + x + x^{2} + 1 \times x^{2} + x + 1

Any expression multiplied by 1 remains the same

x^{4} + x^{3} + 2 x^{2} + x + x^{2} + x^{2} + x + 1

Add the terms

More Steps

Evaluate

2 x^{2} + x^{2} + x^{2}

Collect like terms by calculating the sum or difference of their coefficients

(2 + 1 + 1) x^{2}

Add the numbers

4 x^{2}

x^{4} + x^{3} + 4 x^{2} + x + x + 1

Solution

More Steps

Evaluate

x + x

Collect like terms by calculating the sum or difference of their coefficients

(1 + 1) x

Add the numbers

2 x

x^{4} + x^{3} + 4 x^{2} + 2 x + 1

Show Solution

x \in / R

Evaluate

x^{4} + x^{3} + 2 x^{2} + x + 1 \times x^{2} + 1 \times x^{2} + x + 1

To find the roots of the expression,set the expression equal to 0

x^{4} + x^{3} + 2 x^{2} + x + 1 \times x^{2} + 1 \times x^{2} + x + 1 = 0

Any expression multiplied by 1 remains the same

x^{4} + x^{3} + 2 x^{2} + x + x^{2} + 1 \times x^{2} + x + 1 = 0

Any expression multiplied by 1 remains the same

x^{4} + x^{3} + 2 x^{2} + x + x^{2} + x^{2} + x + 1 = 0

Add the terms

More Steps

Evaluate

x^{4} + x^{3} + 2 x^{2} + x + x^{2} + x^{2} + x + 1

Add the terms

More Steps

Evaluate

2 x^{2} + x^{2} + x^{2}

Collect like terms by calculating the sum or difference of their coefficients

(2 + 1 + 1) x^{2}

Add the numbers

4 x^{2}

x^{4} + x^{3} + 4 x^{2} + x + x + 1

Add the terms

More Steps

Evaluate

x + x

Collect like terms by calculating the sum or difference of their coefficients

(1 + 1) x

Add the numbers

2 x

x^{4} + x^{3} + 4 x^{2} + 2 x + 1

x^{4} + x^{3} + 4 x^{2} + 2 x + 1 = 0

Solution

x \in / R

Show Solution