Solve (x-3)(x^(2) 2x 7)

Question

Simplify the expression

14 x^{4} - 42 x^{3}

Evaluate

(x - 3) (x^{2} \times 2 x \times 7)

Remove the parentheses

(x - 3) x^{2} \times 2 x \times 7

Multiply the terms with the same base by adding their exponents

(x - 3) x^{2 + 1} \times 2 \times 7

Add the numbers

(x - 3) x^{3} \times 2 \times 7

Multiply the terms

(x - 3) x^{3} \times 14

Use the commutative property to reorder the terms

(x - 3) \times 14 x^{3}

Multiply the terms

14 x^{3} (x - 3)

Apply the distributive property

14 x^{3} \times x - 14 x^{3} \times 3

Multiply the terms

More Steps

Evaluate

x^{3} \times x

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

x^{3 + 1}

Add the numbers

x^{4}

14 x^{4} - 14 x^{3} \times 3

Solution

14 x^{4} - 42 x^{3}

Show Solution

x_{1} = 0, x_{2} = 3

Evaluate

(x - 3) (x^{2} \times 2 x \times 7)

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

(x - 3) (x^{2} \times 2 x \times 7) = 0

Multiply

More Steps

Multiply the terms

x^{2} \times 2 x \times 7

Multiply the terms with the same base by adding their exponents

x^{2 + 1} \times 2 \times 7

Add the numbers

x^{3} \times 2 \times 7

Multiply the terms

x^{3} \times 14

Use the commutative property to reorder the terms

14 x^{3}

(x - 3) \times 14 x^{3} = 0

Multiply the terms

14 x^{3} (x - 3) = 0

Elimination the left coefficient

x^{3} (x - 3) = 0

Separate the equation into 2 possible cases

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

The only way a power can be 0 is when the base equals 0

x = 0 x - 3 = 0

Solve the equation

More Steps

Evaluate

x - 3 = 0

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

x = 0 + 3

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

x = 3

x = 0 x = 3

Solution

x_{1} = 0, x_{2} = 3

Show Solution