Q. 3 J4.2( 10 Votes )
Let’s find G.C.D of the following algebraic expression:
x3-16x, 2x3 + 9x2 + 4x, 2x3 + x2-28x
Answer :
Factors of x3-16x
=x(x2-16)
=x(x + 4)(x-4) … (Using a2-b2=(a + b)(a-b))
Factors of 2x3 + 9x2 + 4x
=x(2x2 + 9x + 4)
=x(2x2 + 8x + x + 4)
=x{2x(x + 4) + 1(x + 4)}
=x[{(2x + 1)(x + 4)}]
=x×(2x + 1)×(x + 4)
Factors of 2x3 + x2-28x
=x(2x2 + x-28)
=x(2x2 + 8x-7x-28)
=x{2x(x + 4)-7(x + 4)}
=x[{(2x-7)(x + 4)}]
=x×(2x-7)×(x + 4)
GCD is the greatest common divisor, which is equal to the product of all the common divisors.
∴ the GCD of x3-16x, 2x3 + 9x2 + 4x, 2x3 + x2-28x is x(x + 4)
Rate this question :






















Let's find G.C.D. and L.C.M. of (y3 – 8), (y3 – 4y2 + 4y) and (y2 + y – 6)
West Bengal - MathematicsLet's find the G.C.D. of ax2, a2x3 & a4x.
West Bengal - MathematicsLet's find the G.C.D. of the algebraic expressions x(x2– 9), x2 – x – 12.
West Bengal - MathematicsLet’s find G.C.D of the following algebraic expression:
x2 + xy,xz + yz, x2 + 2xy + y2
West Bengal - Mathematics
Let’s find G.C.D of the following algebraic expressions:
3a2b2c, 12a2b4c2, 9a5b4
West Bengal - Mathematics
Let’s find G.C.D of the following algebraic expressions:
5p2q2, 10p2q2, 25p4q3
West Bengal - Mathematics
Let’s find G.C.D of the following algebraic expressions:
7y3z6, 21y2, 14z2
West Bengal - Mathematics
Let’s find G.C.D of the following algebraic expression:
x2-1, x2-2x + 1, x3 + x2-2x
West Bengal - Mathematics
Let’s find G.C.D of the following algebraic expression:
a2-1, a3-1, a2 + a-2
West Bengal - Mathematics
Let’s find G.C.D of the following algebraic expression:
x3-3x2y, x2-9y2
West Bengal - Mathematics