BuyFind

Precalculus: Mathematics for Calcu...

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

Precalculus: Mathematics for Calcu...

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

Solutions

Chapter 1.3, Problem 102E
To determine

To calculate: The factor of the expression 8x2+10x+3 .

Expert Solution

Answer to Problem 102E

The factor of the expression 8x2+10x+3 is (4x+3)(2x+1) .

Explanation of Solution

Given information:

The expression 8x2+10x+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 8x2+10x+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=8 , ps+qr=10 and rs=3 .

So, 8x2+10x+3 will be factorized as,

  8x2+10x+3=(8x2+(6+4)x+(1)(3))=(8x2+4x+6x+3)=[4x(2x+1)+3(2x+1)]=(4x+3)(2x+1)

Thus, the factor of expression 8x2+10x+3 is (4x+3)(2x+1) .

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