Solve (2p^2 + 19/6p + 9/2)(31/6p^2 + 1/2p - 2) - ScanMath

HOME CALCULATOR SOLVER

DOWNLOAD FOR FREE

Algebra
Calculus
Trigonometry
Matrix

Type your math problem... (2p^2 + 19/6p + 9/2)(31/6p^2 + 1/2p - 2)

Question

Simplify the expression

\frac{31}{3} p^{4} + \frac{625}{36} p^{3} + \frac{125}{6} p^{2} - \frac{49}{12} p - 9

Evaluate

(2 p^{2} + \frac{19}{6} p + \frac{9}{2}) (\frac{31}{6} p^{2} + \frac{1}{2} p - 2)

Apply the distributive property

2 p^{2} \times \frac{31}{6} p^{2} + 2 p^{2} \times \frac{1}{2} p - 2 p^{2} \times 2 + \frac{19}{6} p \times \frac{31}{6} p^{2} + \frac{19}{6} p \times \frac{1}{2} p - \frac{19}{6} p \times 2 + \frac{9}{2} \times \frac{31}{6} p^{2} + \frac{9}{2} \times \frac{1}{2} p - \frac{9}{2} \times 2

Multiply the terms

More Steps

\frac{31}{3} p^{4} + 2 p^{2} \times \frac{1}{2} p - 2 p^{2} \times 2 + \frac{19}{6} p \times \frac{31}{6} p^{2} + \frac{19}{6} p \times \frac{1}{2} p - \frac{19}{6} p \times 2 + \frac{9}{2} \times \frac{31}{6} p^{2} + \frac{9}{2} \times \frac{1}{2} p - \frac{9}{2} \times 2

Multiply the terms

More Steps

\frac{31}{3} p^{4} + p^{3} - 2 p^{2} \times 2 + \frac{19}{6} p \times \frac{31}{6} p^{2} + \frac{19}{6} p \times \frac{1}{2} p - \frac{19}{6} p \times 2 + \frac{9}{2} \times \frac{31}{6} p^{2} + \frac{9}{2} \times \frac{1}{2} p - \frac{9}{2} \times 2

Multiply the numbers

\frac{31}{3} p^{4} + p^{3} - 4 p^{2} + \frac{19}{6} p \times \frac{31}{6} p^{2} + \frac{19}{6} p \times \frac{1}{2} p - \frac{19}{6} p \times 2 + \frac{9}{2} \times \frac{31}{6} p^{2} + \frac{9}{2} \times \frac{1}{2} p - \frac{9}{2} \times 2

Multiply the terms

More Steps

\frac{31}{3} p^{4} + p^{3} - 4 p^{2} + \frac{589}{36} p^{3} + \frac{19}{6} p \times \frac{1}{2} p - \frac{19}{6} p \times 2 + \frac{9}{2} \times \frac{31}{6} p^{2} + \frac{9}{2} \times \frac{1}{2} p - \frac{9}{2} \times 2

Multiply the terms

More Steps

\frac{31}{3} p^{4} + p^{3} - 4 p^{2} + \frac{589}{36} p^{3} + \frac{19}{12} p^{2} - \frac{19}{6} p \times 2 + \frac{9}{2} \times \frac{31}{6} p^{2} + \frac{9}{2} \times \frac{1}{2} p - \frac{9}{2} \times 2

Multiply the numbers

More Steps

\frac{31}{3} p^{4} + p^{3} - 4 p^{2} + \frac{589}{36} p^{3} + \frac{19}{12} p^{2} - \frac{19}{3} p + \frac{9}{2} \times \frac{31}{6} p^{2} + \frac{9}{2} \times \frac{1}{2} p - \frac{9}{2} \times 2

Multiply the numbers

More Steps

\frac{31}{3} p^{4} + p^{3} - 4 p^{2} + \frac{589}{36} p^{3} + \frac{19}{12} p^{2} - \frac{19}{3} p + \frac{93}{4} p^{2} + \frac{9}{2} \times \frac{1}{2} p - \frac{9}{2} \times 2

Multiply the numbers

More Steps

\frac{31}{3} p^{4} + p^{3} - 4 p^{2} + \frac{589}{36} p^{3} + \frac{19}{12} p^{2} - \frac{19}{3} p + \frac{93}{4} p^{2} + \frac{9}{4} p - \frac{9}{2} \times 2

Multiply the numbers

More Steps

\frac{31}{3} p^{4} + p^{3} - 4 p^{2} + \frac{589}{36} p^{3} + \frac{19}{12} p^{2} - \frac{19}{3} p + \frac{93}{4} p^{2} + \frac{9}{4} p - 9

Add the terms

More Steps

\frac{31}{3} p^{4} + \frac{625}{36} p^{3} - 4 p^{2} + \frac{19}{12} p^{2} - \frac{19}{3} p + \frac{93}{4} p^{2} + \frac{9}{4} p - 9

Add the terms

More Steps

\frac{31}{3} p^{4} + \frac{625}{36} p^{3} + \frac{125}{6} p^{2} - \frac{19}{3} p + \frac{9}{4} p - 9

Solution

More Steps

\frac{31}{3} p^{4} + \frac{625}{36} p^{3} + \frac{125}{6} p^{2} - \frac{49}{12} p - 9

Show Solution

Factor the expression

\frac{1}{36} (12 p^{2} + 19 p + 27) (31 p^{2} + 3 p - 12)

Show Solution

Find the roots

p_{1} = - \frac{3 + 1497}{62}, p_{2} = \frac{- 3 + 1497}{62}, p_{3} = - \frac{19}{24} - \frac{935}{24} i, p_{4} = - \frac{19}{24} + \frac{935}{24} i

Alternative Form

p_{1} \approx - 0.672437, p_{2} \approx 0.575663, p_{3} \approx - 0.791 \dot{6} - 1.274074 i, p_{4} \approx - 0.791 \dot{6} + 1.274074 i

Evaluate

(2 p^{2} + \frac{19}{6} p + \frac{9}{2}) (\frac{31}{6} p^{2} + \frac{1}{2} p - 2)

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

(2 p^{2} + \frac{19}{6} p + \frac{9}{2}) (\frac{31}{6} p^{2} + \frac{1}{2} p - 2) = 0

Separate the equation into 2 possible cases

2 p^{2} + \frac{19}{6} p + \frac{9}{2} = 0 \frac{31}{6} p^{2} + \frac{1}{2} p - 2 = 0

Solve the equation

More Steps

p = - \frac{19}{24} + \frac{935}{24} i p = - \frac{19}{24} - \frac{935}{24} i \frac{31}{6} p^{2} + \frac{1}{2} p - 2 = 0

Solve the equation

More Steps

p = - \frac{19}{24} + \frac{935}{24} i p = - \frac{19}{24} - \frac{935}{24} i p = \frac{- 3 + 1497}{62} p = - \frac{3 + 1497}{62}

Solution

p_{1} = - \frac{3 + 1497}{62}, p_{2} = \frac{- 3 + 1497}{62}, p_{3} = - \frac{19}{24} - \frac{935}{24} i, p_{4} = - \frac{19}{24} + \frac{935}{24} i

Alternative Form

p_{1} \approx - 0.672437, p_{2} \approx 0.575663, p_{3} \approx - 0.791 \dot{6} - 1.274074 i, p_{4} \approx - 0.791 \dot{6} + 1.274074 i

Show Solution