# The factor of the expression 9 x 2 − 36 x − 45 .

### Precalculus: Mathematics for Calcu...

6th Edition
Stewart + 5 others
Publisher: Cengage Learning
ISBN: 9780840068071

### Precalculus: Mathematics for Calcu...

6th Edition
Stewart + 5 others
Publisher: Cengage Learning
ISBN: 9780840068071

#### Solutions

Chapter 1.3, Problem 101E
To determine

## To calculate: The factor of the expression 9x2−36x−45 .

Expert Solution

The factor of the expression 9x236x45 is 9(x+1)(x5) .

### Explanation of Solution

Given information:

The expression 9x236x45 .

Formula used:

To find the factor of the trinomial of the form ax2+bx+c , find the numbers p,q,r and s such that sum of product of two numbers is equal to coefficient of x (ps+qr=b) , product of p and q is equal to the coefficient of x2 pq=a and product of r and s numbers is equal to constant term (rs=c) , such that (px+r) and (qx+s) are the factors of ax2+bx+c .

ax2+bx+c=pqx2+(ps+qr)x+rs=pqx2+psx+qrx+rs=px(qx+s)+r(qx+s)=(px+r)(qx+s)

Calculation:

Consider the given expression 9x236x45 .

Rewrite it as,

9x236x45=9(x24x5)

Recall that to find the factor of the trinomial of the form ax2+bx+c , find the numbers p,q,r and s such that sum of product of two numbers is equal to coefficient of x (ps+qr=b) , product of p and q is equal to the coefficient of x2 (pq=a) and product of r and s numbers is equal to constant term (rs=c) , such that (px+r) and (qx+s) are the factors of ax2+bx+c .

ax2+bx+c=pqx2+(ps+qr)x+rs=pqx2+psx+qrx+rs=px(qx+s)+r(qx+s)=(px+r)(qx+s)

So, find p,q,r and s such that pq=1 , ps+qr=4 and rs=5 .

Here, p=1 , q=1 , r=1 and s=5 , so, 9(x24x5) will be factorized as,

9(x24x5)=9(x2+(5+1)x+(1)(5))=9(x25x+x5)=9[x(x5)+1(x5)]=9(x+1)(x5)

Thus, the factor of expression 9x236x45 is 9(x+1)(x5) .

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