Chapter 8: Q4. (page 513)

State whether each sentence is true or false. If false, replace the underlined phrase or expression to make a true sentence.
$(x + 5) (x - 2)$ is the factored form of $x^{2} - 3 x - 10$ .

Short Answer

Expert verified

The statement is false. $(x - 5) (x + 2)$ is the factored form of $x^{2} - 3 x - 10$

Step by step solution

Step 1. State the concept for multiplication of algebraic expressions.

The product of two factors with like signs is positive, and the product of two factors with unlike signs is negative.
If x is a variable and m, n are positive integers, then $(x^{m} \times x^{n}) = x^{m + n}$

Step 2. State multiplication of Two Binomials.

Let $(a + b)$ and $(c + d)$ are two binomials. By using the distributive law of multiplication over addition twice, their product as given below.

$\begin{matrix} (a + b) (c + d) = (a + b) \times (c + d) \\ = a \times (c + d) + b \times (c + d) \\ = (a \times c + a \times d) + (b \times c + b \times d) \\ = (a c + a d) + (b c + b d) \\ = a c + a d + b c + b d \end{matrix}$

Step 3. Substitute the values.

Substitute the values.

$\begin{matrix} (x + 5) (x - 2) = (x + 5) (x + (- 2)) \\ = x (x - 2) + 5 (x - 2) \\ = x^{2} - 2 x + 5 x - 10 \\ = x^{2} + 3 x - 10 \end{matrix}$

Hence, the given statement is false.

Unlock Step-by-Step Solutions & Ace Your Exams!

Full Textbook Solutions
Get detailed explanations and key concepts
Unlimited Al creation
Al flashcards, explanations, exams and more...
Ads-free access
To over 500 millions flashcards
Money-back guarantee
We refund you if you fail your exam.

Start your free trial

Over 30 million students worldwide already upgrade their learning with Vaia!

Recommended explanations on Math Textbooks

View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

State whether each sentence is true or false. If false, replace the underlined phrase or expression to make a true sentence.
$(x + 5) (x - 2)$ is the factored form of $x^{2} - 3 x - 10$ .

Short Answer

Step by step solution

Step 1. State the concept for multiplication of algebraic expressions.

Step 2. State multiplication of Two Binomials.

Step 3. Substitute the values.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Theoretical and Mathematical Physics

Decision Maths

Geometry

Calculus

Logic and Functions

Discrete Mathematics

Study anywhere. Anytime. Across all devices.

State whether each sentence is true or false. If false, replace the underlined phrase or expression to make a true sentence.(x+5)(x−2)is the factored form ofx2−3x−10.

Short Answer

Step by step solution

Step 1. State the concept for multiplication of algebraic expressions.

Step 2. State multiplication of Two Binomials.

Step 3. Substitute the values.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Theoretical and Mathematical Physics

Decision Maths

Geometry

Calculus

Logic and Functions

Discrete Mathematics

Study anywhere. Anytime. Across all devices.

State whether each sentence is true or false. If false, replace the underlined phrase or expression to make a true sentence.
$(x + 5) (x - 2)$ is the factored form of $x^{2} - 3 x - 10$ .