# The factor of the expression 2 x 2 + 5 x + 3 . ### 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 99E
To determine

## To calculate: The factor of the expression 2x2+5x+3 .

Expert Solution

The factor of the expression 2x2+5x+3 is (2x+3)(x+1) .

### Explanation of Solution

Given information:

The expression 2x2+5x+3 .

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 2x2+5x+3 .

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=2 , ps+qr=5 and rs=3 .

Here, p=2 , q=1 , r=3 and s=1 , so, 2x2+5x+3 will be factorized as,

2x2+5x+3=2x2+(2+3)x+(1)(3)=2x2+2x+3x+3=2x(x+1)+3(x+1)=(2x+3)(x+1)

Thus, the factor of expression 2x2+5x+3 is (2x+3)(x+1) .

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