Solve (g-2)(2g^2-3g-3)

Question

Simplify the expression

2 g^{3} - 7 g^{2} + 3 g + 6

Evaluate

(g - 2) (2 g^{2} - 3 g - 3)

Apply the distributive property

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

Multiply the terms

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Evaluate

g \times 2 g^{2}

Use the commutative property to reorder the terms

2 g \times g^{2}

Multiply the terms

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Evaluate

g \times g^{2}

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

g^{1 + 2}

Add the numbers

g^{3}

2 g^{3}

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

Multiply the terms

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Evaluate

g \times 3 g

Use the commutative property to reorder the terms

3 g \times g

Multiply the terms

3 g^{2}

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

Use the commutative property to reorder the terms

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

Multiply the numbers

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

Multiply the numbers

2 g^{3} - 3 g^{2} - 3 g - 4 g^{2} - (- 6 g) - (- 2 \times 3)

Multiply the numbers

2 g^{3} - 3 g^{2} - 3 g - 4 g^{2} - (- 6 g) - (- 6)

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

2 g^{3} - 3 g^{2} - 3 g - 4 g^{2} + 6 g + 6

Subtract the terms

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Evaluate

- 3 g^{2} - 4 g^{2}

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

(- 3 - 4) g^{2}

Subtract the numbers

- 7 g^{2}

2 g^{3} - 7 g^{2} - 3 g + 6 g + 6

Solution

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Evaluate

- 3 g + 6 g

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

(- 3 + 6) g

Add the numbers

3 g

2 g^{3} - 7 g^{2} + 3 g + 6

Show Solution

Find the roots

g_{1} = \frac{3 - 33}{4}, g_{2} = 2, g_{3} = \frac{3 + 33}{4}

Alternative Form

g_{1} \approx - 0.686141, g_{2} = 2, g_{3} \approx 2.186141

Evaluate

(g - 2) (2 g^{2} - 3 g - 3)

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

(g - 2) (2 g^{2} - 3 g - 3) = 0

Separate the equation into 2 possible cases

g - 2 = 0 2 g^{2} - 3 g - 3 = 0

Solve the equation

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Evaluate

g - 2 = 0

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

g = 0 + 2

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

g = 2

g = 2 2 g^{2} - 3 g - 3 = 0

Solve the equation

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Evaluate

2 g^{2} - 3 g - 3 = 0

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

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

Simplify the expression

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

Simplify the expression

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Evaluate

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

Multiply

(- 3)^{2} - (- 24)

Rewrite the expression

3^{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

3^{2} + 24

Evaluate the power

9 + 24

Add the numbers

33

g = \frac{3 \pm 33}{4}

Separate the equation into 2 possible cases

g = \frac{3 + 33}{4} g = \frac{3 - 33}{4}

g = 2 g = \frac{3 + 33}{4} g = \frac{3 - 33}{4}

Solution

g_{1} = \frac{3 - 33}{4}, g_{2} = 2, g_{3} = \frac{3 + 33}{4}

Alternative Form

g_{1} \approx - 0.686141, g_{2} = 2, g_{3} \approx 2.186141

Show Solution