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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鈭�2)is the factored form ofx2鈭�3x鈭�10.

Short Answer

Expert verified

The statement is false. (x鈭�5)(x+2)is the factored form ofx2鈭�3x鈭�10

Step by step solution

01

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

  1. The product of two factors with like signs is positive, and the product of two factors with unlike signs is negative.
  2. If x is a variable and m, n are positive integers, then(xm脳xn)=xm+n
02

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.

(a+b)(c+d)=(a+b)脳(c+d)=a脳(c+d)+b脳(c+d)=(a脳c+a脳d)+(b脳c+b脳d)=(ac+ad)+(bc+bd)=ac+ad+bc+bd

03

Step 3. Substitute the values.

Substitute the values.

(x+5)(x鈭�2)=(x+5)(x+(鈭�2))=x(x鈭�2)+5(x鈭�2)=x2鈭�2x+5x鈭�10=x2+3x鈭�10

Hence, the given statement is false.

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