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

Question

Simplify the expression

x^{3} - 6 x^{2} + 2 x + 15

Evaluate

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

Apply the distributive property

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

Multiply the terms

More Steps

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}

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

Use the commutative property to reorder the terms

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

Multiply the terms

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

Use the commutative property to reorder the terms

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

Multiply the numbers

x^{3} - 5 x^{2} - x^{2} - (- 5 x) - 3 x - (- 15)

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

x^{3} - 5 x^{2} - x^{2} + 5 x - 3 x + 15

Subtract the terms

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Evaluate

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

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

(- 5 - 1) x^{2}

Subtract the numbers

- 6 x^{2}

x^{3} - 6 x^{2} + 5 x - 3 x + 15

Solution

More Steps

Evaluate

5 x - 3 x

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

(5 - 3) x

Subtract the numbers

2 x

x^{3} - 6 x^{2} + 2 x + 15

Show Solution

Find the roots

x_{1} = \frac{1 - 13}{2}, x_{2} = \frac{1 + 13}{2}, x_{3} = 5

Alternative Form

x_{1} \approx - 1.302776, x_{2} \approx 2.302776, x_{3} = 5

Evaluate

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

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

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

Separate the equation into 2 possible cases

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

Solve the equation

More Steps

Evaluate

x^{2} - x - 3 = 0

Substitute a= 1,b= - 1 and c= - 3 into the quadratic formula x = \frac{- b \pm b ^{2} - 4 a c}{2 a}

x = \frac{1 \pm ( - 1 ) ^{2} - 4 ( - 3 )}{2}

Simplify the expression

More Steps

Evaluate

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

Evaluate the power

1 - 4 (- 3)

Multiply the numbers

1 - (- 12)

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

1 + 12

Add the numbers

13

x = \frac{1 \pm 13}{2}

Separate the equation into 2 possible cases

x = \frac{1 + 13}{2} x = \frac{1 - 13}{2}

x = \frac{1 + 13}{2} x = \frac{1 - 13}{2} x - 5 = 0

Solve the equation

More Steps

Evaluate

x - 5 = 0

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

x = 0 + 5

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

x = 5

x = \frac{1 + 13}{2} x = \frac{1 - 13}{2} x = 5

Solution

x_{1} = \frac{1 - 13}{2}, x_{2} = \frac{1 + 13}{2}, x_{3} = 5

Alternative Form

x_{1} \approx - 1.302776, x_{2} \approx 2.302776, x_{3} = 5

Show Solution