find the HCF and LCM of 16(x⁴+64x) and 24(x³+9x²+20x)
Answers
Step-by-step explanation:
The given Expressions are 16(x^4+64x),24(x^3+9x^2+20x)
16(x^4+64x) has factors i.e 16x(x + 4)(x^2 - 4x + 16)
24(x^3+9x^2+20x) has factors i.e 24x(x + 4)(x + 5)
By finding the GCF of given expressions we get that the gcf is 8x^2 + 32x
There are 2 number of expressions are given.
To find the LCM we have to first multiply all the expressions (16(x^4+64x))(24(x^3+9x^2+20x)) = 384x^7 + 3456x^6 + 7680x^5 + 24576x^4 + 221184x^3 + 491520x^2
To find the LCM we have devide 2-1 power of gcf from 384x^7 + 3456x^6 + 7680x^5 + 24576x^4 + 221184x^3 + 491520x^2
So by dividing 8x^2 + 32x from 384x^7 + 3456x^6 + 7680x^5 + 24576x^4 + 221184x^3 + 491520x^2 = (384x^7 + 3456x^6 + 7680x^5 + 24576x^4 + 221184x^3 + 491520x^2)/(8x^2 + 32x) = 48x^5 + 240x^4 + 3072x^2 + 15360x
So the LCM of 16(x^4+64x),24(x^3+9x^2+20x) is 48x^5 + 240x^4 + 3072x^2 + 15360x
mark me braniest
Answer:
Step-by-step explanation:
fx=16(x⁴+64x)
=16(x(x³+4³))
=16(x+4)(x²+4⁴-(x)(4))
fx=(x+4)(x²+16-4x)
gx=24(x³+9x²+20x
=24(x(x²+9x+20)
=24(x(x²+4x+5x+20))
=24(x(x+4)(x+5)
H.C.F of fx and gx= 8(x(x+4))
L.C.M = (fx)(gx)/H.C.F of fx and gx
= 16x(x+4)(x²+16-4x)