Solve (2x+1)(2x^2+5x-4)

Question

Simplify the expression

Solution

4 x^{3} + 12 x^{2} - 3 x - 4

Evaluate

(2 x + 1) (2 x^{2} + 5 x - 4)

Apply the distributive property

2 x \times 2 x^{2} + 2 x \times 5 x - 2 x \times 4 + 1 \times 2 x^{2} + 1 \times 5 x - 1 \times 4

Multiply the terms

More Steps

Evaluate

2 x \times 2 x^{2}

Multiply the numbers

4 x \times x^{2}

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}

4 x^{3}

4 x^{3} + 2 x \times 5 x - 2 x \times 4 + 1 \times 2 x^{2} + 1 \times 5 x - 1 \times 4

Multiply the terms

More Steps

Evaluate

2 x \times 5 x

Multiply the numbers

10 x \times x

Multiply the terms

10 x^{2}

4 x^{3} + 10 x^{2} - 2 x \times 4 + 1 \times 2 x^{2} + 1 \times 5 x - 1 \times 4

Multiply the numbers

4 x^{3} + 10 x^{2} - 8 x + 1 \times 2 x^{2} + 1 \times 5 x - 1 \times 4

Any expression multiplied by 1 remains the same

4 x^{3} + 10 x^{2} - 8 x + 2 x^{2} + 1 \times 5 x - 1 \times 4

Any expression multiplied by 1 remains the same

4 x^{3} + 10 x^{2} - 8 x + 2 x^{2} + 5 x - 1 \times 4

Any expression multiplied by 1 remains the same

4 x^{3} + 10 x^{2} - 8 x + 2 x^{2} + 5 x - 4

Add the terms

More Steps

Evaluate

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

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

(10 + 2) x^{2}

Add the numbers

12 x^{2}

4 x^{3} + 12 x^{2} - 8 x + 5 x - 4

Solution

More Steps

Evaluate

- 8 x + 5 x

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

(- 8 + 5) x

Add the numbers

- 3 x

4 x^{3} + 12 x^{2} - 3 x - 4

Show Solution

Find the roots

Find the roots of the algebra expression

x_{1} = - \frac{5 + 57}{4}, x_{2} = - \frac{1}{2}, x_{3} = \frac{- 5 + 57}{4}

Alternative Form

x_{1} \approx - 3.137459, x_{2} = - 0.5, x_{3} \approx 0.637459

Evaluate

(2 x + 1) (2 x^{2} + 5 x - 4)

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

(2 x + 1) (2 x^{2} + 5 x - 4) = 0

Separate the equation into 2 possible cases

2 x + 1 = 0 2 x^{2} + 5 x - 4 = 0

Solve the equation

More Steps

Evaluate

2 x + 1 = 0

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

2 x = 0 - 1

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

2 x = - 1

Divide both sides

\frac{2 x}{2} = \frac{- 1}{2}

Divide the numbers

x = \frac{- 1}{2}

Use \frac{- a}{b} = \frac{a}{- b} = - \frac{a}{b} to rewrite the fraction

x = - \frac{1}{2}

x = - \frac{1}{2} 2 x^{2} + 5 x - 4 = 0

Solve the equation

More Steps

Evaluate

2 x^{2} + 5 x - 4 = 0

Substitute a= 2,b= 5 and c= - 4 into the quadratic formula x = \frac{- b \pm b ^{2} - 4 a c}{2 a}

x = \frac{- 5 \pm 5 ^{2} - 4 \times 2 ( - 4 )}{2 \times 2}

Simplify the expression

x = \frac{- 5 \pm 5 ^{2} - 4 \times 2 ( - 4 )}{4}

Simplify the expression

More Steps

Evaluate

5^{2} - 4 \times 2 (- 4)

Multiply

5^{2} - (- 32)

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

5^{2} + 32

Evaluate the power

25 + 32

Add the numbers

57

x = \frac{- 5 \pm 57}{4}

Separate the equation into 2 possible cases

x = \frac{- 5 + 57}{4} x = \frac{- 5 - 57}{4}

Use \frac{- a}{b} = \frac{a}{- b} = - \frac{a}{b} to rewrite the fraction

x = \frac{- 5 + 57}{4} x = - \frac{5 + 57}{4}

x = - \frac{1}{2} x = \frac{- 5 + 57}{4} x = - \frac{5 + 57}{4}

Solution

x_{1} = - \frac{5 + 57}{4}, x_{2} = - \frac{1}{2}, x_{3} = \frac{- 5 + 57}{4}

Alternative Form

x_{1} \approx - 3.137459, x_{2} = - 0.5, x_{3} \approx 0.637459

Show Solution

(2x+1)(2x^2+5x 4)

Simplify the expression

Solution

Find the roots

Find the roots of the algebra expression