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

Question

Simplify the expression

Solution

- x^{3} + 4 x^{2} - 7 x + 4

Evaluate

(- 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

Multiply the numbers

- 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

If a negative sign or a subtraction symbol appears outside parentheses, remove the parentheses and change the sign of every term within the parentheses

- 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

4 x^{2}

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

Solution

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

- 7 x

- x^{3} + 4 x^{2} - 7 x + 4

Show Solution

Find the roots

Find the roots of the algebra expression

x_{1} = \frac{3}{2} - \frac{7}{2} i, x_{2} = \frac{3}{2} + \frac{7}{2} i, x_{3} = 1

Alternative Form

x_{1} \approx 1.5 - 1.322876 i, x_{2} \approx 1.5 + 1.322876 i, x_{3} = 1

Evaluate

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

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

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

Change the sign

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

Separate the equation into 2 possible cases

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

Solve the equation

More Steps

Evaluate

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

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

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

Simplify the expression

More Steps

Evaluate

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

Multiply the numbers

(- 3)^{2} - 16

Rewrite the expression

3^{2} - 16

Evaluate the power

9 - 16

Subtract the numbers

- 7

x = \frac{3 \pm - 7}{2}

Simplify the radical expression

More Steps

Evaluate

- 7

Evaluate the power

7 \times - 1

Evaluate the power

7 \times i

x = \frac{3 \pm 7 \times i}{2}

Separate the equation into 2 possible cases

x = \frac{3 + 7 \times i}{2} x = \frac{3 - 7 \times i}{2}

Simplify the expression

x = \frac{3}{2} + \frac{7}{2} i x = \frac{3 - 7 \times i}{2}

Simplify the expression

x = \frac{3}{2} + \frac{7}{2} i x = \frac{3}{2} - \frac{7}{2} i

x = 1 x = \frac{3}{2} + \frac{7}{2} i x = \frac{3}{2} - \frac{7}{2} i

Solution

x_{1} = \frac{3}{2} - \frac{7}{2} i, x_{2} = \frac{3}{2} + \frac{7}{2} i, x_{3} = 1

Alternative Form

x_{1} \approx 1.5 - 1.322876 i, x_{2} \approx 1.5 + 1.322876 i, x_{3} = 1

Show Solution

( X+1)(x^2 3x+4)

Simplify the expression

Solution

Find the roots

Find the roots of the algebra expression