Solve (5x^2-x^5)(2x^2-8x-3)

Question

Simplify the expression

10 x^{4} - 40 x^{3} - 15 x^{2} - 2 x^{7} + 8 x^{6} + 3 x^{5}

Evaluate

(5 x^{2} - x^{5}) (2 x^{2} - 8 x - 3)

Apply the distributive property

5 x^{2} \times 2 x^{2} - 5 x^{2} \times 8 x - 5 x^{2} \times 3 - x^{5} \times 2 x^{2} - (- x^{5} \times 8 x) - (- x^{5} \times 3)

Multiply the terms

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Evaluate

5 x^{2} \times 2 x^{2}

Multiply the numbers

10 x^{2} \times x^{2}

Multiply the terms

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Evaluate

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

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

x^{2 + 2}

Add the numbers

x^{4}

10 x^{4}

10 x^{4} - 5 x^{2} \times 8 x - 5 x^{2} \times 3 - x^{5} \times 2 x^{2} - (- x^{5} \times 8 x) - (- x^{5} \times 3)

Multiply the terms

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Evaluate

5 x^{2} \times 8 x

Multiply the numbers

40 x^{2} \times x

Multiply the terms

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Evaluate

x^{2} \times x

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

x^{2 + 1}

Add the numbers

x^{3}

40 x^{3}

10 x^{4} - 40 x^{3} - 5 x^{2} \times 3 - x^{5} \times 2 x^{2} - (- x^{5} \times 8 x) - (- x^{5} \times 3)

Multiply the numbers

10 x^{4} - 40 x^{3} - 15 x^{2} - x^{5} \times 2 x^{2} - (- x^{5} \times 8 x) - (- x^{5} \times 3)

Multiply the terms

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Evaluate

- x^{5} \times 2 x^{2}

Multiply the numbers

- 2 x^{5} \times x^{2}

Multiply the terms

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Evaluate

x^{5} \times x^{2}

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

x^{5 + 2}

Add the numbers

x^{7}

- 2 x^{7}

10 x^{4} - 40 x^{3} - 15 x^{2} - 2 x^{7} - (- x^{5} \times 8 x) - (- x^{5} \times 3)

Multiply the terms

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Evaluate

- x^{5} \times 8 x

Multiply the numbers

- 8 x^{5} \times x

Multiply the terms

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Evaluate

x^{5} \times x

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

x^{5 + 1}

Add the numbers

x^{6}

- 8 x^{6}

10 x^{4} - 40 x^{3} - 15 x^{2} - 2 x^{7} - (- 8 x^{6}) - (- x^{5} \times 3)

Use the commutative property to reorder the terms

10 x^{4} - 40 x^{3} - 15 x^{2} - 2 x^{7} - (- 8 x^{6}) - (- 3 x^{5})

Solution

10 x^{4} - 40 x^{3} - 15 x^{2} - 2 x^{7} + 8 x^{6} + 3 x^{5}

Show Solution

Factor the expression

x^{2} (5 - x^{3}) (2 x^{2} - 8 x - 3)

Evaluate

(5 x^{2} - x^{5}) (2 x^{2} - 8 x - 3)

Solution

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Evaluate

5 x^{2} - x^{5}

Rewrite the expression

x^{2} \times 5 - x^{2} \times x^{3}

Factor out x^{2} from the expression

x^{2} (5 - x^{3})

x^{2} (5 - x^{3}) (2 x^{2} - 8 x - 3)

Show Solution

Find the roots

x_{1} = \frac{4 - 22}{2}, x_{2} = 0, x_{3} = 35, x_{4} = \frac{4 + 22}{2}

Alternative Form

x_{1} \approx - 0.345208, x_{2} = 0, x_{3} \approx 1.709976, x_{4} \approx 4.345208

Evaluate

(5 x^{2} - x^{5}) (2 x^{2} - 8 x - 3)

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

(5 x^{2} - x^{5}) (2 x^{2} - 8 x - 3) = 0

Separate the equation into 2 possible cases

5 x^{2} - x^{5} = 0 2 x^{2} - 8 x - 3 = 0

Solve the equation

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Evaluate

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

Factor the expression

x^{2} (5 - x^{3}) = 0

Separate the equation into 2 possible cases

x^{2} = 0 5 - x^{3} = 0

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

x = 0 5 - x^{3} = 0

Solve the equation

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Evaluate

5 - x^{3} = 0

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

- x^{3} = 0 - 5

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

- x^{3} = - 5

Change the signs on both sides of the equation

x^{3} = 5

Take the 3 -th root on both sides of the equation

3 x^{3} = 35

Calculate

x = 35

x = 0 x = 35

x = 0 x = 35 2 x^{2} - 8 x - 3 = 0

Solve the equation

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Evaluate

2 x^{2} - 8 x - 3 = 0

Substitute a= 2,b= - 8 and c= - 3 into the quadratic formula x = \frac{- b \pm b ^{2} - 4 a c}{2 a}

x = \frac{8 \pm ( - 8 ) ^{2} - 4 \times 2 ( - 3 )}{2 \times 2}

Simplify the expression

x = \frac{8 \pm ( - 8 ) ^{2} - 4 \times 2 ( - 3 )}{4}

Simplify the expression

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Evaluate

(- 8)^{2} - 4 \times 2 (- 3)

Multiply

(- 8)^{2} - (- 24)

Rewrite the expression

8^{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

8^{2} + 24

Evaluate the power

64 + 24

Add the numbers

88

x = \frac{8 \pm 88}{4}

Simplify the radical expression

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Evaluate

88

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

4 \times 22

Write the number in exponential form with the base of 2

2^{2} \times 22

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

2^{2} \times 22

Reduce the index of the radical and exponent with 2

222

x = \frac{8 \pm 2 22}{4}

Separate the equation into 2 possible cases

x = \frac{8 + 2 22}{4} x = \frac{8 - 2 22}{4}

Simplify the expression

x = \frac{4 + 22}{2} x = \frac{8 - 2 22}{4}

Simplify the expression

x = \frac{4 + 22}{2} x = \frac{4 - 22}{2}

x = 0 x = 35 x = \frac{4 + 22}{2} x = \frac{4 - 22}{2}

Solution

x_{1} = \frac{4 - 22}{2}, x_{2} = 0, x_{3} = 35, x_{4} = \frac{4 + 22}{2}

Alternative Form

x_{1} \approx - 0.345208, x_{2} = 0, x_{3} \approx 1.709976, x_{4} \approx 4.345208

Show Solution