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

Question

Simplify the expression

Solution

12 x^{3} + 19 x^{2} - 4 x - 2

Evaluate

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

Apply the distributive property

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

Multiply the terms

More Steps

Evaluate

4 x \times 3 x^{2}

Multiply the numbers

12 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}

12 x^{3}

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

Multiply the terms

More Steps

Evaluate

4 x \times 4 x

Multiply the numbers

16 x \times x

Multiply the terms

16 x^{2}

12 x^{3} + 16 x^{2} - 4 x \times 2 + 1 \times 3 x^{2} + 1 \times 4 x - 1 \times 2

Multiply the numbers

12 x^{3} + 16 x^{2} - 8 x + 1 \times 3 x^{2} + 1 \times 4 x - 1 \times 2

Any expression multiplied by 1 remains the same

12 x^{3} + 16 x^{2} - 8 x + 3 x^{2} + 1 \times 4 x - 1 \times 2

Any expression multiplied by 1 remains the same

12 x^{3} + 16 x^{2} - 8 x + 3 x^{2} + 4 x - 1 \times 2

Any expression multiplied by 1 remains the same

12 x^{3} + 16 x^{2} - 8 x + 3 x^{2} + 4 x - 2

Add the terms

More Steps

Evaluate

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

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

(16 + 3) x^{2}

Add the numbers

19 x^{2}

12 x^{3} + 19 x^{2} - 8 x + 4 x - 2

Solution

More Steps

Evaluate

- 8 x + 4 x

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

(- 8 + 4) x

Add the numbers

- 4 x

12 x^{3} + 19 x^{2} - 4 x - 2

Show Solution

Find the roots

Find the roots of the algebra expression

x_{1} = - \frac{2 + 10}{3}, x_{2} = - \frac{1}{4}, x_{3} = \frac{- 2 + 10}{3}

Alternative Form

x_{1} \approx - 1.720759, x_{2} = - 0.25, x_{3} \approx 0.387426

Evaluate

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

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

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

Separate the equation into 2 possible cases

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

Solve the equation

More Steps

Evaluate

4 x + 1 = 0

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

4 x = 0 - 1

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

4 x = - 1

Divide both sides

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

Divide the numbers

x = \frac{- 1}{4}

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

x = - \frac{1}{4}

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

Solve the equation

More Steps

Evaluate

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

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

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

Simplify the expression

x = \frac{- 4 \pm 4 ^{2} - 4 \times 3 ( - 2 )}{6}

Simplify the expression

More Steps

Evaluate

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

Multiply

4^{2} - (- 24)

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

4^{2} + 24

Evaluate the power

16 + 24

Add the numbers

40

x = \frac{- 4 \pm 40}{6}

Simplify the radical expression

More Steps

Evaluate

40

Write the expression as a product where the root of one of the factors can be evaluated

4 \times 10

Write the number in exponential form with the base of 2

2^{2} \times 10

The root of a product is equal to the product of the roots of each factor

2^{2} \times 10

Reduce the index of the radical and exponent with 2

210

x = \frac{- 4 \pm 2 10}{6}

Separate the equation into 2 possible cases

x = \frac{- 4 + 2 10}{6} x = \frac{- 4 - 2 10}{6}

Simplify the expression

x = \frac{- 2 + 10}{3} x = \frac{- 4 - 2 10}{6}

Simplify the expression

x = \frac{- 2 + 10}{3} x = - \frac{2 + 10}{3}

x = - \frac{1}{4} x = \frac{- 2 + 10}{3} x = - \frac{2 + 10}{3}

Solution

x_{1} = - \frac{2 + 10}{3}, x_{2} = - \frac{1}{4}, x_{3} = \frac{- 2 + 10}{3}

Alternative Form

x_{1} \approx - 1.720759, x_{2} = - 0.25, x_{3} \approx 0.387426

Show Solution

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

Simplify the expression

Solution

Find the roots

Find the roots of the algebra expression