Suppose n(r) = 0. Calculate r.
104
Let p(c) be the second derivative of 0*c**5 + 0*c**2 - 1/72*c**4 - 20*c + 0 + 1/180*c**6 + 0*c**3. What is j in p(j) = 0?
-1, 0, 1
Suppose 66*y - 54*y = 48. Let l(k) be the first derivative of -5/2*k**2 - k**5 + 0*k + 5/4*k**4 - y + 5/3*k**3. Determine q, given that l(q) = 0.
-1, 0, 1
Let g(y) be the second derivative of -y**7/630 + y**6/72 + y**5/20 - y**4/12 + 12*y. Let u(q) be the third derivative of g(q). Suppose u(f) = 0. Calculate f.
-1/2, 3
Let m = -353 + 7061/20. Let b(u) be the second derivative of 0 + 27/2*u**2 + 9/2*u**3 - 2*u + 3/4*u**4 + m*u**5. Find z, given that b(z) = 0.
-3
Determine r, given that -382/3*r**3 + 440/3*r**4 - 12*r**2 - 42*r**5 + 16/3 + 88/3*r = 0.
-2/7, -2/9, 1, 2
Let a(q) = 75*q**2 + 3582*q - 138624. Let b(v) = -9*v**2 - 448*v + 17328. Let h(k) = -4*a(k) - 33*b(k). Factor h(p).
-3*(p - 76)**2
Let p(g) = -g + 14. Let f be p(11). Suppose -v + 1 = t, 0 = -5*t - 2*v + 4 + 10. Factor -3*a**3 + 3*a**f - a**2 + 4*a**t - 3*a**4.
a**2*(a - 1)*(a + 1)
Let w(q) be the third derivative of -14*q**2 + 5/42*q**7 - 5/6*q**4 - 1/8*q**6 + 0*q + 0 - q**5 + 0*q**3. Let w(y) = 0. Calculate y.
-1, -2/5, 0, 2
Let o(t) be the second derivative of 0*t**2 + 0*t**4 + 1/9*t**3 + 5*t + 0 - 1/30*t**5. What is m in o(m) = 0?
-1, 0, 1
Let s(f) = 30*f**2 + 90*f + 25. Let z(o) = 15*o**2 + 47*o + 13. Let q(a) = 3*s(a) - 5*z(a). Solve q(v) = 0.
-2, -1/3
Let o(z) = z**2 + 3*z - 1. Let k(t) = -t**2 - 9*t - 16. Let m be k(-3). Let u = -12 + 9. Let d(b) = b**2 + 2*b - 1. Let s(a) = m*o(a) + u*d(a). Factor s(v).
-(v - 1)*(v + 1)
Let x(j) be the third derivative of -j**6/60 - 23*j**5/10 - 22*j**4 - 260*j**3/3 + 465*j**2. Factor x(k).
-2*(k + 2)**2*(k + 65)
Suppose l - 2*l + 8*l = 0. Suppose -15*r + 11*r + 8 = l. Factor -2/11*p**4 + 0*p + 0*p**3 + 0 + 2/11*p**r.
-2*p**2*(p - 1)*(p + 1)/11
Let y(c) be the second derivative of c**8/1344 - c**7/504 - c**6/72 - c**4/6 - 13*c. Let g(f) be the third derivative of y(f). Let g(a) = 0. What is a?
-1, 0, 2
Let w(l) be the third derivative of l**6/80 - 7*l**5/40 - 111*l**2. Factor w(j).
3*j**2*(j - 7)/2
Let u(x) be the first derivative of -x**5 - 15*x**4/2 - 15*x**3 - 23. Let u(w) = 0. Calculate w.
-3, 0
Determine l, given that -30/19*l**3 + 2/19*l**4 + 0 + 54/19*l**2 - 26/19*l = 0.
0, 1, 13
Let q(h) be the third derivative of 0*h - 1/360*h**6 - 1/18*h**5 + 0 + 40*h**2 - 4/9*h**4 - 16/9*h**3. Suppose q(d) = 0. Calculate d.
-4, -2
Let -2/7*t**3 - 16/7*t - 40/7 + 22/7*t**2 = 0. What is t?
-1, 2, 10
Suppose 4536*q**2 - 1268*q**3 - 3*q**5 - 601*q - 1246*q**3 - 1371*q - 380*q + 165*q + 168*q**4 = 0. What is q?
0, 1, 27
Let -3*t + 3*t**5 + 25*t**3 + 9*t**4 - 12*t**3 + 5*t**2 - t**5 - 2 = 0. Calculate t.
-2, -1, 1/2
Let a be (-58)/(-204) + (-176)/1496. Solve -1/2*f + 0 - a*f**2 = 0 for f.
-3, 0
Suppose 5*h = 4*r + 41, r + 6 = 2*h + 2*r. Let g**2 - 36*g**h - 4 + 12 + 80*g**3 - 44*g - 48*g**4 + 39*g**2 = 0. Calculate g.
-2, -1, 1/3, 1
Let h(r) be the first derivative of 1/11*r**4 + 3 - 4/33*r**3 - 2*r + 1/11*r**2 - 2/55*r**5 + 1/165*r**6. Let k(g) be the first derivative of h(g). Factor k(p).
2*(p - 1)**4/11
Suppose -302 = 8*v - 326. Determine w, given that 0*w**v + 0*w**2 + 2/7*w**5 + 0 + 0*w**4 + 0*w = 0.
0
Let d(f) be the third derivative of -f**6/360 + f**5/80 - f**4/48 - 5*f**3/2 - 2*f**2. Let i(s) be the first derivative of d(s). Solve i(n) = 0 for n.
1/2, 1
Let h(y) be the second derivative of 3/10*y**5 + 0 + 1/15*y**6 + 0*y**2 + 0*y**3 + 0*y**4 + y. Let h(b) = 0. What is b?
-3, 0
Suppose 0 = -5*x + w + 109, 3*x = -x + 2*w + 86. Let s = -10 + x. Factor 6*r**3 + s*r + 2 - 13*r**2 - 3 - r**4 - 3.
-(r - 2)**2*(r - 1)**2
Let u(o) = 2*o + 20. Let y be u(-10). Let h be (0 + 1 + y)*5. Factor -5*m**h + 2*m**3 - 2*m**5 + 3*m**5 + 2*m**3.
-4*m**3*(m - 1)*(m + 1)
Factor -18/7*f**4 - 48/7*f - 3/7*f**3 + 0 + 72/7*f**2 - 3/7*f**5.
-3*f*(f - 1)**2*(f + 4)**2/7
Let y(v) be the third derivative of v**8/672 - v**7/84 - 7*v**6/120 - v**5/60 + 13*v**4/48 + 7*v**3/12 - 418*v**2. Find k, given that y(k) = 0.
-1, 1, 7
Let b = 4052/17 - 238. Let -b*a**2 + 8/17 - 2/17*a**3 + 0*a = 0. What is a?
-2, 1
Let k = -4 + 8. Let t(d) = 28*d**5 + 45*d**4 + 24*d**3 + d**2 + 3*d. Let g(h) = -h**5 + h**2 - h. Let r(v) = k*t(v) + 12*g(v). Factor r(s).
4*s**2*(s + 1)*(5*s + 2)**2
Let t(z) be the third derivative of -z**5/420 - z**4/14 - 11*z**3/42 - z**2 + 127. Factor t(p).
-(p + 1)*(p + 11)/7
Let m(t) be the second derivative of -5*t**6/2 - 141*t**5/2 - 2629*t**4/4 - 1974*t**3 - 2646*t**2 - 462*t. Factor m(y).
-3*(y + 1)**2*(5*y + 42)**2
Let o(t) be the first derivative of 8*t**3/3 + 4*t**2 + 4*t + 15. Let z(g) = -17*g**2 - 15*g - 9. Let h(q) = -9*o(q) - 4*z(q). Factor h(i).
-4*i*(i + 3)
Let g(w) be the third derivative of -2*w**7/735 - 4*w**6/105 + 4*w**2 + 67*w. Suppose g(o) = 0. Calculate o.
-8, 0
Suppose -15 = 6*f - 27. Let o(w) be the second derivative of 1/48*w**4 + 0 + 1/8*w**f - 5*w + 1/12*w**3. Determine l, given that o(l) = 0.
-1
Suppose -5*p + 15 = -10. Let v be 2*((-147)/30 + p). Factor 0 - v*h**4 - 3/5*h**3 - 3/5*h**2 - 1/5*h.
-h*(h + 1)**3/5
Let f = -8816 - -44106/5. Factor 2/5*k**4 + f*k + 6*k**2 + 14/5*k**3 + 8/5.
2*(k + 1)**3*(k + 4)/5
Let s(l) = -119*l**3 - 211*l**2 - 100*l - 18. Let x(k) = 356*k**3 + 634*k**2 + 298*k + 55. Let u(j) = 7*s(j) + 2*x(j). Factor u(c).
-(c + 1)*(11*c + 4)**2
Let k(q) = -q**3. Let t(m) = -5*m**3 - m. Let y(u) = -6*k(u) + t(u). Factor y(l).
l*(l - 1)*(l + 1)
Let z(k) be the first derivative of -k**4 + 40*k**3/3 - 86. Factor z(t).
-4*t**2*(t - 10)
Let m = -15 - -20. Suppose -m*u - 1 = -11. Determine q so that -q**3 + 2*q**2 + 0*q**3 + 9 - 7*q**u + 0*q**3 - 3*q = 0.
-3, 1
Suppose w + 1 = 3*h + 3, -3*h - 67 = 4*w. Let m = w - -22. Factor -4*b**2 + 5*b**4 - m*b**4 - 8*b**3 + 8*b + 8*b**4.
4*b*(b - 2)*(b - 1)*(b + 1)
Let m(l) be the third derivative of 0 + 19*l**2 + 0*l**6 + 1/105*l**7 + 0*l + 0*l**4 - 1/30*l**5 + 0*l**3. Factor m(u).
2*u**2*(u - 1)*(u + 1)
Let a(z) = z**2 + 3*z - 6. Let l be 10/(-4)*(-8)/(-4). Let h be a(l). Solve -2*i**3 + 10*i**h - 4*i**2 + 10*i**5 + 4*i**3 + 6*i**4 = 0.
-1, 0, 2/5
Let k(c) be the second derivative of c**4/60 + 19*c**3/5 + 3249*c**2/10 + 3*c - 23. Factor k(x).
(x + 57)**2/5
Let f(o) be the first derivative of 2*o**6/3 - 16*o**5/5 + o**4 + 40*o**3/3 - 8*o**2 - 32*o + 52. Solve f(z) = 0.
-1, 2
Let k(s) be the first derivative of 5/3*s**3 + 0*s**2 - 5*s + 1. Factor k(z).
5*(z - 1)*(z + 1)
Let k(o) be the third derivative of o**6/210 + 17*o**5/105 - 3*o**4/7 - 3*o**2 + 20. Find a, given that k(a) = 0.
-18, 0, 1
Let d(k) be the second derivative of -2*k**7/105 + k**6/30 + k**5/15 - k**4/6 - 57*k**2/2 + k - 9. Let y(n) be the first derivative of d(n). Factor y(g).
-4*g*(g - 1)**2*(g + 1)
Let g be 14/(-49) - 1306/35. Let h = g + 38. Suppose -h*u**5 + 2/5*u + 4/5*u**4 - 4/5*u**2 + 0*u**3 + 0 = 0. Calculate u.
-1, 0, 1
Let p(y) be the second derivative of -y**7/21 + 2*y**6/5 - 7*y**5/5 + 8*y**4/3 - 3*y**3 + 2*y**2 + 477*y. Factor p(s).
-2*(s - 2)*(s - 1)**4
Suppose s - 124 = -s. Let j(h) = 15*h**2 + 9*h + 17. Let k be j(-2). Factor -s*r**3 + k*r**3 + 0*r**2 - 3 - 9*r - 9*r**2.
-3*(r + 1)**3
Let f(h) be the second derivative of 0 - 1/3*h**3 - 1/54*h**4 + 23*h - 8/9*h**2. Determine l so that f(l) = 0.
-8, -1
Let h(r) be the third derivative of r**7/14 + 7*r**6/12 + 23*r**5/12 + 10*r**4/3 + 10*r**3/3 - 26*r**2. Factor h(s).
5*(s + 1)**2*(s + 2)*(3*s + 2)
Let s(n) be the second derivative of 2/39*n**4 + 0*n**2 + 2/65*n**5 + 0*n**3 + 1/195*n**6 + 0 + 10*n. Factor s(b).
2*b**2*(b + 2)**2/13
Suppose 2*t - 2*j - 6 = 0, 2*t - 15*j = -9*j + 10. Factor 2/11*r - 2/11*r**t + 0.
-2*r*(r - 1)/11
Let y(x) be the third derivative of x**8/448 + x**7/14 + 97*x**6/160 - 29*x**5/40 - 65*x**4/8 + 25*x**3 + 2*x**2 - 96. What is n in y(n) = 0?
-10, -2, 1
Let d(c) = -31*c + 33*c + 11*c**3 + 4*c**2 + 0 - 2 - 7*c**4. Let p(o) = o**2 - o + 1. Let h(i) = -d(i) - 2*p(i). Factor h(z).
z**2*(z - 2)*(7*z + 3)
Let u(x) be the second derivative of -x**4/36 + 3*x**2/2 - 18*x. Factor u(k).
-(k - 3)*(k + 3)/3
Let s(x) be the third derivative of x**6/540 + 7*x**5/135 - x**4/108 - 14*x**3/27 + 2*x**2 + 184. Factor s(h).
2*(h - 1)*(h + 1)*(h + 14)/9
Let t = -50 + 55. Let j(m) be the first 