Solve (x+1)(x^2 -3x+4)+(x+1)(x^2 +2x-1)

Question

Simplify the expression

2 x^{3} + x^{2} + 2 x + 3

Evaluate

(x + 1) (x^{2} - 3 x + 4) + (x + 1) (x^{2} + 2 x - 1)

Expand the expression

More Steps

Calculate

(x + 1) (x^{2} - 3 x + 4)

Apply the distributive property

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

Multiply the terms

More Steps

Evaluate

x \times x^{2}

Use the product rule a^{n} \times a^{m} = a^{n + m} to simplify the expression

x^{1 + 2}

Add the numbers

x^{3}

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

Multiply the terms

More Steps

Evaluate

x \times 3 x

Use the commutative property to reorder the terms

3 x \times x

Multiply the terms

3 x^{2}

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

Use the commutative property to reorder the terms

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

Any expression multiplied by 1 remains the same

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

Any expression multiplied by 1 remains the same

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

Any expression multiplied by 1 remains the same

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

Add the terms

More Steps

Evaluate

- 3 x^{2} + x^{2}

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

(- 3 + 1) x^{2}

Add the numbers

- 2 x^{2}

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

Subtract the terms

More Steps

Evaluate

4 x - 3 x

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

(4 - 3) x

Subtract the numbers

x

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

x^{3} - 2 x^{2} + x + 4 + (x + 1) (x^{2} + 2 x - 1)

Expand the expression

More Steps

Calculate

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

Apply the distributive property

x \times x^{2} + x \times 2 x - x \times 1 + 1 \times x^{2} + 1 \times 2 x - 1 \times 1

Multiply the terms

More Steps

Evaluate

x \times x^{2}

Use the product rule a^{n} \times a^{m} = a^{n + m} to simplify the expression

x^{1 + 2}

Add the numbers

x^{3}

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

Multiply the terms

More Steps

Evaluate

x \times 2 x

Use the commutative property to reorder the terms

2 x \times x

Multiply the terms

2 x^{2}

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

Any expression multiplied by 1 remains the same

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

Any expression multiplied by 1 remains the same

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

Any expression multiplied by 1 remains the same

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

Any expression multiplied by 1 remains the same

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

Add the terms

More Steps

Evaluate

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

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

(2 + 1) x^{2}

Add the numbers

3 x^{2}

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

Add the terms

More Steps

Evaluate

- x + 2 x

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

(- 1 + 2) x

Add the numbers

x

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

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

Add the terms

More Steps

Evaluate

x^{3} + x^{3}

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

(1 + 1) x^{3}

Add the numbers

2 x^{3}

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

Add the terms

More Steps

Evaluate

- 2 x^{2} + 3 x^{2}

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

(- 2 + 3) x^{2}

Add the numbers

x^{2}

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

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

Solution

2 x^{3} + x^{2} + 2 x + 3

Show Solution

Factor the expression

(x + 1) (2 x^{2} - x + 3)

Evaluate

(x + 1) (x^{2} - 3 x + 4) + (x + 1) (x^{2} + 2 x - 1)

Factor out x + 1 from the expression

(x + 1) (x^{2} - 3 x + 4 + x^{2} + 2 x - 1)

Solution

(x + 1) (2 x^{2} - x + 3)

Show Solution

Find the roots

x_{1} = \frac{1}{4} - \frac{23}{4} i, x_{2} = \frac{1}{4} + \frac{23}{4} i, x_{3} = - 1

Alternative Form

x_{1} \approx 0.25 - 1.198958 i, x_{2} \approx 0.25 + 1.198958 i, x_{3} = - 1

Evaluate

(x + 1) (x^{2} - 3 x + 4) + (x + 1) (x^{2} + 2 x - 1)

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

(x + 1) (x^{2} - 3 x + 4) + (x + 1) (x^{2} + 2 x - 1) = 0

Calculate

More Steps

Evaluate

(x + 1) (x^{2} - 3 x + 4) + (x + 1) (x^{2} + 2 x - 1)

Expand the expression

More Steps

Calculate

(x + 1) (x^{2} - 3 x + 4)

Apply the distributive property

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

Multiply the terms

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

Multiply the terms

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

Use the commutative property to reorder the terms

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

Any expression multiplied by 1 remains the same

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

Any expression multiplied by 1 remains the same

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

Any expression multiplied by 1 remains the same

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

Add the terms

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

Subtract the terms

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

x^{3} - 2 x^{2} + x + 4 + (x + 1) (x^{2} + 2 x - 1)

Expand the expression

More Steps

Calculate

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

Apply the distributive property

x \times x^{2} + x \times 2 x - x \times 1 + 1 \times x^{2} + 1 \times 2 x - 1 \times 1

Multiply the terms

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

Multiply the terms

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

Any expression multiplied by 1 remains the same

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

Any expression multiplied by 1 remains the same

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

Any expression multiplied by 1 remains the same

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

Any expression multiplied by 1 remains the same

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

Add the terms

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

Add the terms

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

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

Add the terms

More Steps

Evaluate

x^{3} + x^{3}

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

(1 + 1) x^{3}

Add the numbers

2 x^{3}

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

Add the terms

More Steps

Evaluate

- 2 x^{2} + 3 x^{2}

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

(- 2 + 3) x^{2}

Add the numbers

x^{2}

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

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

Subtract the numbers

2 x^{3} + x^{2} + 2 x + 3

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

Factor the expression

(x + 1) (2 x^{2} - x + 3) = 0

Separate the equation into 2 possible cases

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

Solve the equation

More Steps

Evaluate

x + 1 = 0

Move the constant to the right-hand side and change its sign

x = 0 - 1

Removing 0 doesn't change the value,so remove it from the expression

x = - 1

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

Solve the equation

More Steps

Evaluate

2 x^{2} - x + 3 = 0

Substitute a= 2,b= - 1 and c= 3 into the quadratic formula x = \frac{- b \pm b ^{2} - 4 a c}{2 a}

x = \frac{1 \pm ( - 1 ) ^{2} - 4 \times 2 \times 3}{2 \times 2}

Simplify the expression

x = \frac{1 \pm ( - 1 ) ^{2} - 4 \times 2 \times 3}{4}

Simplify the expression

More Steps

Evaluate

(- 1)^{2} - 4 \times 2 \times 3

Evaluate the power

1 - 4 \times 2 \times 3

Multiply the terms

1 - 24

Subtract the numbers

- 23

x = \frac{1 \pm - 23}{4}

Simplify the radical expression

More Steps

Evaluate

- 23

Evaluate the power

23 \times - 1

Evaluate the power

23 \times i

x = \frac{1 \pm 23 \times i}{4}

Separate the equation into 2 possible cases

x = \frac{1 + 23 \times i}{4} x = \frac{1 - 23 \times i}{4}

Simplify the expression

x = \frac{1}{4} + \frac{23}{4} i x = \frac{1 - 23 \times i}{4}

Simplify the expression

x = \frac{1}{4} + \frac{23}{4} i x = \frac{1}{4} - \frac{23}{4} i

x = - 1 x = \frac{1}{4} + \frac{23}{4} i x = \frac{1}{4} - \frac{23}{4} i

Solution

x_{1} = \frac{1}{4} - \frac{23}{4} i, x_{2} = \frac{1}{4} + \frac{23}{4} i, x_{3} = - 1

Alternative Form

x_{1} \approx 0.25 - 1.198958 i, x_{2} \approx 0.25 + 1.198958 i, x_{3} = - 1

Show Solution