Question

The HCF and LCM of two polynomials P(x) and
Q(x) are (2x-1) and (6x³ + 25x² - 24x + 5)
respectively. If P(x) = 2x²+9x – 5, determine
Q(x)
(a) 6x²- 5x+1 (b) 6x² + 5x +1

(c) 6x² - 5x-1 (d) 6x²+ 5x-1​

Answer 1

Answer:

6x^2-5x+1=Q(x)

Step-by-step explanation:

because

Lcm×hcf=ab

lcm×hcf/a=b

Answer 2

Answer:

option (a)

Step-by-step explanation:

HCF * LCM = a*b

HCF * LCM = P(x) * Q(x)

Q(x) = HCF * LCM / P(x)

Q(x) = (2x - 1) * (6x^3+25x^2-24x+5) ÷ (2x^2+9x-5 )

= 12x^4+50x^3-48x^2+10x-6x^3-25x^2+24x-5 /

2x^2 +9x-5

= 12x^4 +44x^3-73x^2+34x-5 / 2x^2+9x-5

After solving by long division method ;

Dividend = 12x^4 +44x^3-73x^2+34x-5

Divisor = 2x^2+9x-5

Remainder = 0

Quotient = 6x^2-5x+1

Therefore ; Q(x) = 6x^2-5x+1