Solve (5x-7)(3x^(2)-8x-5)

Question

Simplify the expression

15 x^{3} - 61 x^{2} + 31 x + 35

Evaluate

(5 x - 7) (3 x^{2} - 8 x - 5)

Apply the distributive property

5 x \times 3 x^{2} - 5 x \times 8 x - 5 x \times 5 - 7 \times 3 x^{2} - (- 7 \times 8 x) - (- 7 \times 5)

Multiply the terms

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Evaluate

5 x \times 3 x^{2}

Multiply the numbers

15 x \times x^{2}

Multiply the terms

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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}

15 x^{3}

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

Multiply the terms

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Evaluate

5 x \times 8 x

Multiply the numbers

40 x \times x

Multiply the terms

40 x^{2}

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

Multiply the numbers

15 x^{3} - 40 x^{2} - 25 x - 7 \times 3 x^{2} - (- 7 \times 8 x) - (- 7 \times 5)

Multiply the numbers

15 x^{3} - 40 x^{2} - 25 x - 21 x^{2} - (- 7 \times 8 x) - (- 7 \times 5)

Multiply the numbers

15 x^{3} - 40 x^{2} - 25 x - 21 x^{2} - (- 56 x) - (- 7 \times 5)

Multiply the numbers

15 x^{3} - 40 x^{2} - 25 x - 21 x^{2} - (- 56 x) - (- 35)

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

15 x^{3} - 40 x^{2} - 25 x - 21 x^{2} + 56 x + 35

Subtract the terms

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Evaluate

- 40 x^{2} - 21 x^{2}

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

(- 40 - 21) x^{2}

Subtract the numbers

- 61 x^{2}

15 x^{3} - 61 x^{2} - 25 x + 56 x + 35

Solution

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Evaluate

- 25 x + 56 x

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

(- 25 + 56) x

Add the numbers

31 x

15 x^{3} - 61 x^{2} + 31 x + 35

Show Solution

Find the roots

x_{1} = \frac{4 - 31}{3}, x_{2} = \frac{7}{5}, x_{3} = \frac{4 + 31}{3}

Alternative Form

x_{1} \approx - 0.522588, x_{2} = 1.4, x_{3} \approx 3.189255

Evaluate

(5 x - 7) (3 x^{2} - 8 x - 5)

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

(5 x - 7) (3 x^{2} - 8 x - 5) = 0

Separate the equation into 2 possible cases

5 x - 7 = 0 3 x^{2} - 8 x - 5 = 0

Solve the equation

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Evaluate

5 x - 7 = 0

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

5 x = 0 + 7

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

5 x = 7

Divide both sides

\frac{5 x}{5} = \frac{7}{5}

Divide the numbers

x = \frac{7}{5}

x = \frac{7}{5} 3 x^{2} - 8 x - 5 = 0

Solve the equation

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Evaluate

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

Substitute a= 3,b= - 8 and c= - 5 into the quadratic formula x = \frac{- b \pm b ^{2} - 4 a c}{2 a}

x = \frac{8 \pm ( - 8 ) ^{2} - 4 \times 3 ( - 5 )}{2 \times 3}

Simplify the expression

x = \frac{8 \pm ( - 8 ) ^{2} - 4 \times 3 ( - 5 )}{6}

Simplify the expression

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Evaluate

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

Multiply

(- 8)^{2} - (- 60)

Rewrite the expression

8^{2} - (- 60)

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} + 60

Evaluate the power

64 + 60

Add the numbers

124

x = \frac{8 \pm 124}{6}

Simplify the radical expression

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Evaluate

124

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

4 \times 31

Write the number in exponential form with the base of 2

2^{2} \times 31

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

2^{2} \times 31

Reduce the index of the radical and exponent with 2

231

x = \frac{8 \pm 2 31}{6}

Separate the equation into 2 possible cases

x = \frac{8 + 2 31}{6} x = \frac{8 - 2 31}{6}

Simplify the expression

x = \frac{4 + 31}{3} x = \frac{8 - 2 31}{6}

Simplify the expression

x = \frac{4 + 31}{3} x = \frac{4 - 31}{3}

x = \frac{7}{5} x = \frac{4 + 31}{3} x = \frac{4 - 31}{3}

Solution

x_{1} = \frac{4 - 31}{3}, x_{2} = \frac{7}{5}, x_{3} = \frac{4 + 31}{3}

Alternative Form

x_{1} \approx - 0.522588, x_{2} = 1.4, x_{3} \approx 3.189255

Show Solution