
Concept explainers
To calculate: The factors of the polynomial 15x2−8x+1 .

Answer to Problem 4CCYP
The factors of the polynomial 15x2−8x+1 are 5x−1 and 3x−1 .
Explanation of Solution
Given information:
The expression 15x2−8x+1 .
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 (r⋅s=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 15x2−8x+1 .
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 (r⋅s=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=15 , ps+qr=−8 and rs=1 .
Here, p=−5 , q=−3 , r=1 and s=1 , so, 15x2−8x+1 will be factorized as,
15x2−8x+1=15x2−5x−3x+1=5x(3x−1)−1(3x−1)=(5x−1)(3x−1)
Thus, the factors of polynomial 15x2−8x+1 are 5x−1 and 3x−1 .
Chapter 5 Solutions
Algebra 2
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