# The factors of the trinomial 8 x 2 − 14 x − 15 . ### 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 69E
To determine

## To calculate: The factors of the trinomial 8x2−14x−15 .

Expert Solution

The factors of the trinomial 8x214x15 are 4x+3 and 2x5 .

### Explanation of Solution

Given information:

The expression 8x214x15 .

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 8x214x15 .

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=8 , ps+qr=14 and rs=15 .

Here, p=4 , q=2 , r=3 and s=5 , so, 8x214x15 will be factorized as,

8x214x15=8x2+(20+6)x+(5)(3)=8x220x+6x15=4x(2x5)+3(2x5)=(4x+3)(2x5)

Thus, the factors of trinomial 8x214x15 are 4x+3 and 2x5 .

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