Solve (3p - 7) * (2p^2 - 3p - 4)

Question

Simplify the expression

6 p^{3} - 23 p^{2} + 9 p + 28

Evaluate

(3 p - 7) (2 p^{2} - 3 p - 4)

Apply the distributive property

3 p \times 2 p^{2} - 3 p \times 3 p - 3 p \times 4 - 7 \times 2 p^{2} - (- 7 \times 3 p) - (- 7 \times 4)

Multiply the terms

More Steps

Evaluate

3 p \times 2 p^{2}

Multiply the numbers

6 p \times p^{2}

Multiply the terms

More Steps

Evaluate

p \times p^{2}

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

p^{1 + 2}

Add the numbers

p^{3}

6 p^{3}

6 p^{3} - 3 p \times 3 p - 3 p \times 4 - 7 \times 2 p^{2} - (- 7 \times 3 p) - (- 7 \times 4)

Multiply the terms

More Steps

Evaluate

3 p \times 3 p

Multiply the numbers

9 p \times p

Multiply the terms

9 p^{2}

6 p^{3} - 9 p^{2} - 3 p \times 4 - 7 \times 2 p^{2} - (- 7 \times 3 p) - (- 7 \times 4)

Multiply the numbers

6 p^{3} - 9 p^{2} - 12 p - 7 \times 2 p^{2} - (- 7 \times 3 p) - (- 7 \times 4)

Multiply the numbers

6 p^{3} - 9 p^{2} - 12 p - 14 p^{2} - (- 7 \times 3 p) - (- 7 \times 4)

Multiply the numbers

6 p^{3} - 9 p^{2} - 12 p - 14 p^{2} - (- 21 p) - (- 7 \times 4)

Multiply the numbers

6 p^{3} - 9 p^{2} - 12 p - 14 p^{2} - (- 21 p) - (- 28)

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

6 p^{3} - 9 p^{2} - 12 p - 14 p^{2} + 21 p + 28

Subtract the terms

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Evaluate

- 9 p^{2} - 14 p^{2}

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

(- 9 - 14) p^{2}

Subtract the numbers

- 23 p^{2}

6 p^{3} - 23 p^{2} - 12 p + 21 p + 28

Solution

More Steps

Evaluate

- 12 p + 21 p

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

(- 12 + 21) p

Add the numbers

9 p

6 p^{3} - 23 p^{2} + 9 p + 28

Show Solution

Find the roots

p_{1} = \frac{3 - 41}{4}, p_{2} = \frac{7}{3}, p_{3} = \frac{3 + 41}{4}

Alternative Form

p_{1} \approx - 0.850781, p_{2} = 2. \dot{3}, p_{3} \approx 2.350781

Evaluate

(3 p - 7) (2 p^{2} - 3 p - 4)

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

(3 p - 7) (2 p^{2} - 3 p - 4) = 0

Separate the equation into 2 possible cases

3 p - 7 = 0 2 p^{2} - 3 p - 4 = 0

Solve the equation

More Steps

Evaluate

3 p - 7 = 0

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

3 p = 0 + 7

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

3 p = 7

Divide both sides

\frac{3 p}{3} = \frac{7}{3}

Divide the numbers

p = \frac{7}{3}

p = \frac{7}{3} 2 p^{2} - 3 p - 4 = 0

Solve the equation

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Evaluate

2 p^{2} - 3 p - 4 = 0

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

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

Simplify the expression

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

Simplify the expression

More Steps

Evaluate

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

Multiply

(- 3)^{2} - (- 32)

Rewrite the expression

3^{2} - (- 32)

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} + 32

Evaluate the power

9 + 32

Add the numbers

41

p = \frac{3 \pm 41}{4}

Separate the equation into 2 possible cases

p = \frac{3 + 41}{4} p = \frac{3 - 41}{4}

p = \frac{7}{3} p = \frac{3 + 41}{4} p = \frac{3 - 41}{4}

Solution

p_{1} = \frac{3 - 41}{4}, p_{2} = \frac{7}{3}, p_{3} = \frac{3 + 41}{4}

Alternative Form

p_{1} \approx - 0.850781, p_{2} = 2. \dot{3}, p_{3} \approx 2.350781

Show Solution