Chapter 7: Q23. (page 398)

Solve each equation.
$5 (t^{2} - 3 t + 2) = t (5 t - 2)$

Short Answer

Expert verified

The solution of the equation is $t = \frac{10}{13}$

Step by step solution

Step 1. State the concept of multiplying a polynomial by a monomial.

To find the product of a polynomial and a monomial use the distributive property. The distributive property is given by:

$\begin{array}{l} a (b + c) = a \times b + a \times c \\ (a + b) c = a \times c + b \times c \end{array}$

Step 2. Apply the distributive property.

First, simplify both sides of the equation by applying the distributive property.

$\begin{array}{l} 5 (t^{2} - 3 t + 2) = t (5 t - 2) \\ 5 t^{2} - 5 (3 t) + 5 (2) = t (5 t) - t (2) \end{array}$

Step 3. Simplify for t.

Further, simplify the expression for t.

$\begin{matrix} 5 t^{2} - 15 t + 10 = 5 t^{2} - 2 t \\ 5 t^{2} - 5 t^{2} + 10 = - 2 t + 15 t \\ 0 + 10 = 13 t \\ t = \frac{10}{13} \end{matrix}$

Therefore, $t = \frac{10}{13}$

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Solve each equation.
$5 (t^{2} - 3 t + 2) = t (5 t - 2)$

Short Answer

Step by step solution

Step 1. State the concept of multiplying a polynomial by a monomial.

Step 2. Apply the distributive property.

Step 3. Simplify for t.

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Solve each equation.5(t2−3t+2)=t(5t−2)

Short Answer

Step by step solution

Step 1. State the concept of multiplying a polynomial by a monomial.

Step 2. Apply the distributive property.

Step 3. Simplify for t.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Geometry

Mechanics Maths

Theoretical and Mathematical Physics

Probability and Statistics

Statistics

Decision Maths

Study anywhere. Anytime. Across all devices.

Solve each equation.
$5 (t^{2} - 3 t + 2) = t (5 t - 2)$