# The factor of the expression 2 x 2 + 7 x − 4 . ### 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 100E
To determine

## To calculate: The factor of the expression 2x2+7x−4 .

Expert Solution

The factor of the expression 2x2+7x4 is (2x1)(x+4) .

### Explanation of Solution

Given information:

The expression 2x2+7x4 .

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+7x4 .

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=7 and rs=4 .

Here, p=2 , q=1 , r=1 and s=4 , so, 2x2+7x4 will be factorized as,

2x2+7x4=2x2+(81)x+(1)(4)=2x2+8xx4=2x(x+4)1(x+4)=(2x1)(x+4)

Thus, the factor of expression 2x2+7x4 is (2x1)(x+4) .

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