6. Suppose u(k) = 0. Calculate k.
29
Let w(i) be the first derivative of -i**5/2 - 35*i**4/4 - 125*i**3/6 - 15*i**2 + 469. Solve w(j) = 0.
-12, -1, 0
Suppose 14*n = 8*n + 30. Let x(j) be the third derivative of 0*j + 3/50*j**n + 4/15*j**3 + 1/5*j**4 + 0 - j**2. Factor x(z).
2*(3*z + 2)**2/5
Let u be (-80)/(-32) + (-1)/(-2). Suppose -3*s = v - 5, 8*s - u*s + 3*v - 15 = 0. Factor s*o + 10/3*o**3 + 4/3*o**2 + 0.
2*o**2*(5*o + 2)/3
Suppose 4*s - 4*x = 1 + 19, 2*x = 4*s - 18. Suppose 0 = 4*l - 3*g + 3, -3*g + 25 = 2*g. Solve -8/5*o**l - 2/5*o**s - 8/5*o - 2/5 - 12/5*o**2 = 0.
-1
Let l = 275 + -271. Let h(y) be the second derivative of -1/21*y**7 - 1/3*y**3 + 0 + 1/30*y**6 + 1/5*y**5 + 1/2*y**2 - 1/6*y**l + 5*y. What is p in h(p) = 0?
-1, 1/2, 1
Determine c, given that 600/7 - 170*c - 248/7*c**3 - 2/7*c**5 + 36/7*c**4 + 804/7*c**2 = 0.
1, 3, 4, 5
Let l(q) be the third derivative of q**5/90 - 5*q**4/36 + 21*q**2. Factor l(o).
2*o*(o - 5)/3
Suppose 3*i - 5 - 1 = 0. Suppose s**i - 6*s**2 + 8 + 11*s**2 + s**3 + 12*s = 0. Calculate s.
-2
Let q(j) = 2*j**3 - j - 4. Let b(u) = 11*u**3 + 32*u**2 - 5*u - 20. Let p(c) = 2*b(c) - 10*q(c). Factor p(v).
2*v**2*(v + 32)
Let w(v) be the second derivative of -v**6/240 - 23*v**5/160 - 143*v**4/96 - 121*v**3/48 + 160*v. Factor w(c).
-c*(c + 1)*(c + 11)**2/8
Suppose -67*m + 61*m = 216. Let r be (-54)/m*8/6. Find f such that 2/7*f**r + 4/7*f - 6/7 = 0.
-3, 1
Let n(m) be the first derivative of -2*m**6/15 + 3*m**5/5 - m**4 + 2*m**3/3 - 7*m + 3. Let c(o) be the first derivative of n(o). Factor c(l).
-4*l*(l - 1)**3
Let z(a) be the third derivative of 7/24*a**6 + 4*a**2 + 31/50*a**5 + 4/15*a**3 + 0*a + 7/150*a**7 + 0 + 17/30*a**4. Factor z(y).
(y + 1)*(y + 2)*(7*y + 2)**2/5
Let q(d) be the third derivative of -d**6/300 - d**5/150 + 236*d**2. Factor q(f).
-2*f**2*(f + 1)/5
Factor 3/7 + 0*f - 3/7*f**2.
-3*(f - 1)*(f + 1)/7
Let m(w) be the second derivative of -w**6/840 + w**5/70 + 5*w**4/56 - 3*w**3/2 - 7*w. Let j(u) be the second derivative of m(u). Find n, given that j(n) = 0.
-1, 5
Let p(k) be the second derivative of 0*k**2 + 1/2*k**3 - 1/8*k**4 + 0 + 9*k. Factor p(v).
-3*v*(v - 2)/2
Find w such that 1146/7*w**3 - 1146/7*w - 335/7*w**2 + 328/7 + w**4 = 0.
-164, -1, 2/7, 1
Find g such that -2/7*g**5 + 16/7*g**3 + 18/7*g + 4/7*g**4 - 36/7*g**2 + 0 = 0.
-3, 0, 1, 3
Let f be (3*9/(-120))/(30/(-40)). Let s(a) be the first derivative of 1/20*a**4 - 6 - f*a**2 + 2/5*a + 0*a**3. Factor s(j).
(j - 1)**2*(j + 2)/5
Let q be 7/6 + (-105)/(-70). Factor -q*d + 1/3*d**2 + 16/3.
(d - 4)**2/3
Let o(l) = l**3 + l**2 + 3. Let f be o(0). Let u(w) be the second derivative of 0*w**4 + 2/5*w**2 + 3*w + 0 - 1/5*w**f + 1/50*w**5. Factor u(c).
2*(c - 1)**2*(c + 2)/5
Let c = -1125 - -1127. Determine u so that 0 + 2/7*u - 2/7*u**4 - 2/7*u**3 + 2/7*u**c = 0.
-1, 0, 1
Factor -306*n - 2925 + 580 - 3*n**2 - 3799 - 1659.
-3*(n + 51)**2
Suppose 2*p = 5*r - 14, 4*p - 1 = -3*r - 3. Factor 2/9*h**3 + 96*h + 8*h**r + 384.
2*(h + 12)**3/9
Let y(n) be the third derivative of 17/6*n**4 + 48*n**2 + 0*n + 0 - 6*n**3 - 7/15*n**5 - 1/30*n**6. Suppose y(u) = 0. Calculate u.
-9, 1
Let f(r) = -r**3 + 2*r**2 + 10*r - 4. Let c be f(4). Factor -772*l - l**5 + 784*l - l**c + l**3 + 4 + 0*l**4 - 2*l**4 + 11*l**2.
-(l - 2)*(l + 1)**3*(l + 2)
Let z(r) be the first derivative of -r**8/2016 - r**7/420 - r**6/360 + 7*r**2/2 - 12. Let g(k) be the second derivative of z(k). Factor g(m).
-m**3*(m + 1)*(m + 2)/6
Let h = -4064 + 16265/4. Factor 3/4*b**2 + h*b + 0.
3*b*(b + 3)/4
Factor 0 - 20*i - 875/3*i**3 - 440/3*i**2 - 245/3*i**4.
-5*i*(i + 3)*(7*i + 2)**2/3
Let u(q) = -4*q**2 + 8*q. Let a(w) = 18 + 2*w**2 - 38 - 4*w + 20. Let d(v) = 13*a(v) + 6*u(v). Factor d(n).
2*n*(n - 2)
Let x(t) be the third derivative of -t**5/12 + 35*t**4/12 + 25*t**3/2 - 190*t**2 - 2*t. Factor x(u).
-5*(u - 15)*(u + 1)
Let d(y) be the second derivative of 1/2*y**3 + y + 1/12*y**4 + 0 + y**2. Determine k so that d(k) = 0.
-2, -1
Let o(i) = 2*i**3 + 39*i**2 + 20*i. Let b(h) = h. Let m(r) = b(r) - o(r). Factor m(w).
-w*(w + 19)*(2*w + 1)
Let w be 15/25*-2*65/(-2). Suppose 0 = -w*k + 37*k + 6. Find a such that -1/5*a**5 + 0*a**2 + 0*a**4 + 0 - 1/5*a + 2/5*a**k = 0.
-1, 0, 1
Suppose -126*y**2 - 6*y**3 + 21*y + 60 - 15*y**5 - 161*y**4 - 15 + 242*y**4 = 0. Calculate y.
-1, -3/5, 1, 5
Let q(x) = -2*x**3 - 2*x**2 + 2*x. Let g(b) = b**3 - 284*b**2 - 9220*b - 98304. Let v(w) = -g(w) - 2*q(w). Factor v(r).
3*(r + 32)**3
Let d be (20/(-12))/((280/72)/(-7)). Solve 5*b**5 + 0*b + 14/3*b**4 - b**d + 0 - 2/3*b**2 = 0.
-1, -1/3, 0, 2/5
Let -4*q**2 + 8*q**3 + 510*q - 6*q**3 - 510*q = 0. Calculate q.
0, 2
Let x = -396 + 396. Let h(v) be the first derivative of v**3 - 3/4*v**4 - 6 + 0*v**2 + x*v. Factor h(j).
-3*j**2*(j - 1)
Let z(f) = 48*f - 582. Let y(k) = -7*k + 83. Let h(b) = -36*y(b) - 5*z(b). Let n be h(7). Let -9/4 + 0*w**3 + 3/4*w**4 - 9/2*w**2 + n*w = 0. Calculate w.
-3, 1
Suppose -3/2*z**4 + 3/4*z**3 - 3/4*z**5 + 3/2*z**2 + 0*z + 0 = 0. What is z?
-2, -1, 0, 1
Let g(b) be the first derivative of -b**5/20 + b**4/12 - b**3/18 - b**2 - 2. Let l(u) be the second derivative of g(u). Factor l(m).
-(3*m - 1)**2/3
Let o(d) be the first derivative of 5*d**6/36 + 80*d**5/3 + 6400*d**4/3 + 819200*d**3/9 + 6553600*d**2/3 + 83886080*d/3 + 242. Determine f so that o(f) = 0.
-32
Let v(h) = -h**2 + 2*h. Let y be v(2). Suppose -30*r + 131*r - 202 = 0. Solve -2/5*w**r + y + 0*w = 0.
0
Let m = 7 + -27/4. Let y(h) be the second derivative of m*h**4 + 1/6*h**2 + 1/45*h**6 + 7/60*h**5 - 4*h + 0 + 5/18*h**3. Suppose y(i) = 0. Calculate i.
-1, -1/2
Let t(o) be the second derivative of o**9/3780 - o**8/840 - o**7/210 + 11*o**4/12 - 11*o. Let d(l) be the third derivative of t(l). Factor d(j).
4*j**2*(j - 3)*(j + 1)
Let a(r) be the second derivative of 0*r**5 + 4*r + 1/80*r**6 - 1/2*r**2 + 0*r**4 + 0 + 0*r**3. Let v(q) be the first derivative of a(q). Factor v(f).
3*f**3/2
Let k be 15/(-18) + 1 + (-29)/(-6). Suppose 2*c = k*c - 12. Factor -1/4*y**2 - 3/4*y**3 + 3/4*y + 1/2 - 1/4*y**c.
-(y - 1)*(y + 1)**2*(y + 2)/4
Factor -195/7 - 114/7*f - 15/7*f**2.
-3*(f + 5)*(5*f + 13)/7
Let y(n) = -n**4 + n**2 + n - 1. Let a(h) = -5*h**4 - 12*h**3 - 7*h**2 + 2*h - 2. Let l(m) = -a(m) + 2*y(m). Determine f, given that l(f) = 0.
-3, -1, 0
Suppose -31*y = -34*y + 12. Suppose -15*h = -14*h - y. Determine b, given that -4/5*b**h + 16/5*b**2 + 4/5 + 2/5*b**5 - 14/5*b - 4/5*b**3 = 0.
-2, 1
Suppose s + 3 = 0, 0 = -3*l - 4*s - 0*s - 183. Let k be ((-23)/(-25) - 1)/(l/95). Let -2/15*m**2 + 2/15*m + k*m**4 - 2/15*m**3 + 0 = 0. Calculate m.
-1, 0, 1
Find o such that -3*o**3 - 33/2*o**2 + 27/2 + 3/4*o**5 + 9/4*o + 3*o**4 = 0.
-3, -1, 1, 2
Let c be 9/(45/20) + -2. Let w(l) be the second derivative of -1/18*l**4 + 0 + 2*l + 1/9*l**3 + 0*l**c. Factor w(v).
-2*v*(v - 1)/3
Suppose 3*r - 3*s = 6, -3*s = 3*r + 2*s - 46. Suppose -3*u + r = -5. Suppose -7*v**2 - 2*v**2 - u*v**3 + 4*v**4 + 5*v**2 + 4*v = 0. What is v?
-1, 0, 1
Let o(k) be the third derivative of k**9/40320 - k**7/1120 + k**6/240 - k**5/3 + 29*k**2. Let l(v) be the third derivative of o(v). Suppose l(r) = 0. What is r?
-2, 1
Let g(a) = 9*a**3 - 29*a**2 + 48*a - 32. Let l(f) = 4*f**3 - 14*f**2 + 21 + 0 - 37 + 24*f. Let n(h) = -4*g(h) + 10*l(h). Find y, given that n(y) = 0.
2
Let w(i) = -3*i**2 - 5*i - 6. Let h(x) = -3*x**2 - 6*x - 6. Let q(v) = 4*h(v) - 3*w(v). Suppose q(g) = 0. Calculate g.
-2, -1
Let f(s) be the third derivative of s**6/60 + 7*s**5/30 + s**4/2 - 3*s**2 - 41*s. Factor f(r).
2*r*(r + 1)*(r + 6)
Let i(l) be the second derivative of -l**10/50400 - l**9/6300 - l**8/2240 - l**7/2100 + 19*l**4/12 - 8*l. Let f(m) be the third derivative of i(m). Factor f(d).
-3*d**2*(d + 1)**2*(d + 2)/5
Suppose -608 = -4*j + 412. Let a be 2/10*j/34. Factor 3/2 + a*o**2 - 3*o.
3*(o - 1)**2/2
Suppose 4*c - 47 = -39. Let -7*o**3 - o**5 + 19*o**2 + 2*o**4 + 2*o**2 + 5*o - 7*o**c + 19*o**3 = 0. What is o?
-1, 0, 5
Let w(k) be the second derivative of 0*k**2 + 2/63*k**7 + 1/15*k**5 + 0 + 1/3*k**4 - 5*k - 4/9*k**3 - 2/15*k**6. Solve w(h) = 0 for h.
-1, 0, 1, 2
Let z(u) be the second derivative of -3*u**5/100 - 273*u**4/20 - 24843*u**3/10 - 2260713*u**2/10 - 2*u + 23. Factor z(a).
-3*(a + 91)**3/5
Let q = 707 - 704. Let 