)**2
Let g(d) be the second derivative of -5/2*d**3 + 7/12*d**4 + 0 - 1/20*d**5 + 9/2*d**2 + 4*d. Determine p so that g(p) = 0.
1, 3
Suppose 3*n = -n - 5*v - 35, 0 = -2*n + v + 7. Find g, given that n + 4/9*g**2 - 2/9*g**5 + 0*g**3 + 2/9*g - 4/9*g**4 = 0.
-1, 0, 1
Let s(z) be the first derivative of -z**3/3 + z**2/2 + 6*z + 63. Factor s(c).
-(c - 3)*(c + 2)
Suppose 3*k - k = 8. Suppose k*b - 21 = 3*v, -b - b + 21 = -5*v. Suppose 42*h - b*h**3 - 3*h**2 - 42*h = 0. Calculate h.
-1, 0
Let -3/8*y**5 - 9/2*y - 3*y**2 + 0 + 21/8*y**3 + 3/4*y**4 = 0. What is y?
-2, -1, 0, 2, 3
Find v, given that -47*v - v**3 + 36*v + 19*v + 2*v**2 = 0.
-2, 0, 4
Factor -1/3*r**3 + 7/3*r**2 + 17/3*r + 3.
-(r - 9)*(r + 1)**2/3
Let m be (4/40)/(2/20). Let t(v) be the first derivative of -m + 3/5*v**2 - 1/5*v**3 + 0*v. Factor t(o).
-3*o*(o - 2)/5
Let q(i) = -2*i**3 + i - 1. Let s be (-3)/(-4 - 44/(-8)). Let c(u) = u**3 - u. Let n(x) = s*q(x) - 5*c(x). Factor n(r).
-(r - 2)*(r + 1)**2
Let n = -1662 + 1664. Factor -2/13*o**4 - 2/13*o**3 + 2/13*o**n + 2/13*o + 0.
-2*o*(o - 1)*(o + 1)**2/13
Determine h, given that 1/6*h**3 + 0 + 128/3*h + 16/3*h**2 = 0.
-16, 0
Let a = 1601/40 + -40. Let s(n) be the third derivative of 1/200*n**6 + 1/175*n**7 + 0*n + 0 + 0*n**3 - a*n**4 - 1/50*n**5 + n**2. Suppose s(p) = 0. What is p?
-1, -1/2, 0, 1
Let i(c) be the second derivative of 3*c**5/80 - c**4/4 + c**3/2 + 5*c + 11. Find r such that i(r) = 0.
0, 2
Factor -34410*d + 4*d**4 - 4*d**4 - 8*d**3 + 34414*d + 4*d**5.
4*d*(d - 1)**2*(d + 1)**2
Let q(k) be the second derivative of k**6/60 + 3*k**5/20 - k**4/8 - 4*k**3/3 + 3*k**2 - 208*k. Factor q(h).
(h - 1)**2*(h + 2)*(h + 6)/2
Let p(u) be the first derivative of u**4/36 + u**3/6 + u**2/3 + 18*u - 18. Let t(y) be the first derivative of p(y). Factor t(f).
(f + 1)*(f + 2)/3
Let j = -51 + 71. Suppose -8*u = 2*u - j. Find m such that 8/5*m**3 + u*m**2 - 4/5 - 14/5*m = 0.
-2, -1/4, 1
Let z(n) be the third derivative of 0*n - 1/480*n**6 - 1/3*n**3 - 34*n**2 - 1/84*n**7 + 0 - 1/448*n**8 + 1/24*n**4 + 3/40*n**5. Let z(k) = 0. Calculate k.
-2, -1, 2/3, 1
Let f(w) be the first derivative of 4*w**6/21 + 34*w**5/35 + 12*w**4/7 + 26*w**3/21 + 2*w**2/7 + 206. Solve f(r) = 0 for r.
-2, -1, -1/4, 0
Let v(f) be the third derivative of f**5/15 - f**4 + 10*f**3/3 + 13*f**2. Factor v(r).
4*(r - 5)*(r - 1)
Let o(f) be the second derivative of 2*f**6/15 + 12*f**5/5 - f**4 - 76*f**3/3 - 48*f**2 - 3*f - 3. Factor o(c).
4*(c - 2)*(c + 1)**2*(c + 12)
Factor -6/5 - 3/5*k + 6/5*k**2 + 3/5*k**3.
3*(k - 1)*(k + 1)*(k + 2)/5
Let z(v) be the third derivative of 0*v + 1/8*v**6 + 1/42*v**7 + 0 + 29*v**2 + 10/3*v**3 - 5/12*v**5 - 5/8*v**4. Factor z(s).
5*(s - 1)**2*(s + 1)*(s + 4)
Let -23*h**4 + 24*h**4 + 24*h**2 + 2 + 3*h**2 - 13*h - 15*h**3 - 2 = 0. Calculate h.
0, 1, 13
Suppose 15 = -y + 16. Factor 6*j**3 - y - 3*j**5 + 1 + 365*j - 368*j.
-3*j*(j - 1)**2*(j + 1)**2
Let d be (-623)/(-178) - 1/(-2). Let n(j) be the third derivative of 1/6*j**d + 11*j**2 - 4/3*j**3 + 0*j + 1/15*j**5 + 0. Find i such that n(i) = 0.
-2, 1
Let k = 16860 + -16857. Factor -2/9*u**k - 4/9*u**2 + 16/9 + 8/9*u.
-2*(u - 2)*(u + 2)**2/9
Let n(d) be the first derivative of -3*d**5/10 - 45*d**4/16 - 19*d**3/4 - 9*d**2/4 - 425. Let n(k) = 0. Calculate k.
-6, -1, -1/2, 0
Let o(p) = 2*p**2 + 13*p - 4. Let q be o(-7). Find u such that -3*u**2 - 24*u**q + 7*u**4 + 5*u - 4*u**4 + 42*u**2 - 23*u = 0.
0, 1, 6
Suppose 369547*w - 2*w**3 - 369547*w + 4*w**2 = 0. Calculate w.
0, 2
Let g(l) = l**3 - 11*l**2 + 2*l - 26. Let x be g(11). Let k be x/(-24) - (-3)/(-18). Factor 0*w + 0 + 0*w**2 - 1/5*w**4 + k*w**3.
-w**4/5
Let j(d) be the first derivative of -d**7/3360 - d**6/360 + 43*d**3/3 + 1. Let h(r) be the third derivative of j(r). Factor h(f).
-f**2*(f + 4)/4
Let w(u) be the first derivative of -3 + 0*u**3 + 0*u - 1/2*u**2 + 1/4*u**4. Factor w(l).
l*(l - 1)*(l + 1)
Suppose -4*l + 6*l + 12 = 0. Let s be l/(-5)*80/24. Let 1/2*u**3 - 1/2*u + 0 + 1/2*u**2 - 1/2*u**s = 0. What is u?
-1, 0, 1
Factor -1/2*f - 1 + 1/2*f**2.
(f - 2)*(f + 1)/2
Let b be 416 - (-1 - (0 + (-2)/2)). Find r such that 410*r - 27*r**5 - 45*r**2 - 99*r**4 - 118*r**3 - b*r + 7*r**3 = 0.
-2, -1, -1/3, 0
Let v(j) be the first derivative of 3*j**3 - 27*j**2/5 - 8*j/5 + 492. Suppose v(i) = 0. Calculate i.
-2/15, 4/3
Let c = 83/2604 + -1/124. Let r(d) be the third derivative of 1/735*d**7 - 6*d**2 + 0 + 1/42*d**5 + 0*d**3 - c*d**4 + 0*d - 1/105*d**6. Let r(j) = 0. What is j?
0, 1, 2
Let c(t) be the second derivative of 5*t**7/42 - t**6/6 - 3*t**5/4 + 25*t**4/12 - 5*t**3/3 + 45*t. Factor c(y).
5*y*(y - 1)**3*(y + 2)
Suppose 10*p + 6 = 13*p + 3*z, 5*z + 14 = 3*p. Solve -4*d - 2/5 - 32/5*d**4 - 66/5*d**2 - 16*d**p = 0 for d.
-1, -1/4
Let o(f) be the second derivative of -2*f**7/105 + 6*f**6/25 + 21*f**5/25 + 11*f**4/15 - 12*f + 5. Determine d so that o(d) = 0.
-1, 0, 11
Let t(z) be the first derivative of 2/3*z**6 - 12*z**5 + 450*z**2 + 30*z**4 + 760/3*z**3 - 28 + 324*z. Factor t(i).
4*(i - 9)**2*(i + 1)**3
Let -5*v**3 + 4*v**3 - 306 + 154 + 152 + 28*v**2 = 0. Calculate v.
0, 28
Let i = -1432/35 - -292/7. Factor 56/5*v + 196/5 + i*v**2.
4*(v + 7)**2/5
Let m(w) = -w**2 - 26*w + 360. Let v be m(10). Let -3/5*u**3 + v + 0*u - 9/5*u**2 = 0. Calculate u.
-3, 0
Suppose -4*q + 11 = 2*o + o, 2*q + o = 5. Factor -7 - 5*a**q - 48*a - 8 + 28*a.
-5*(a + 1)*(a + 3)
Let d(p) be the first derivative of 0*p**2 - 9 - 10*p + 5/2*p**3 - 5/8*p**4. Factor d(j).
-5*(j - 2)**2*(j + 1)/2
Let l(t) be the first derivative of t**5/40 - 15*t**4/8 + 117*t**3/4 + 1485*t**2/4 + 9801*t/8 + 343. Determine s, given that l(s) = 0.
-3, 33
Let t(q) be the second derivative of -q**6/30 + 7*q**5/60 - q**4/12 - q**3/6 - 45*q**2/2 + 13*q. Let k(u) be the first derivative of t(u). Factor k(m).
-(m - 1)**2*(4*m + 1)
Let g(h) = 19*h**5 - 10*h**4 - 83*h**3 - 19*h**2 + 5*h - 10. Let z(k) = -k**5 - k**3 - k**2 - k + 2. Let b(o) = -g(o) - 5*z(o). Suppose b(w) = 0. Calculate w.
-2, -2/7, 0, 3
Let f(t) = -t**4 + 2*t**3 - 10*t**2 + 14. Let o(i) = i**4 - i**3 + i**2 + 1. Suppose 2*a - 5 = 3, 5*a = 5*q + 30. Let v(x) = q*o(x) - f(x). Solve v(s) = 0.
-2, 2
Let u be (3/(-6))/(1/26). Let o = u - -15. Factor -a**3 - 2*a + o*a**3 + 2*a - a.
a*(a - 1)*(a + 1)
Let g = -164 + 158. Let c be g/(1 + 1) + (-273)/(-91). Solve -2/7*a**2 - 2/7*a + c = 0 for a.
-1, 0
Let g(t) be the third derivative of -t**7/525 - 13*t**6/300 - 8*t**5/25 - 3*t**4/5 + 15*t**2 + 4*t. Factor g(n).
-2*n*(n + 1)*(n + 6)**2/5
Let u(m) = 29*m - 404. Let r be u(14). Find v, given that -3 + 3/4*v**r + 0*v = 0.
-2, 2
Let h(c) be the third derivative of c**5/60 - 5*c**4/12 - 11*c**3/6 - 93*c**2. Factor h(y).
(y - 11)*(y + 1)
Let y(i) be the first derivative of -2*i**3/9 - 17*i**2/3 + 76*i/3 - 171. Factor y(r).
-2*(r - 2)*(r + 19)/3
Let d = 9949/936 - 138/13. Let f(i) be the third derivative of 0*i + 7*i**2 + d*i**4 - 1/180*i**5 + 0 + 1/9*i**3. Solve f(v) = 0 for v.
-1, 2
Let y = 92 + -90. Find n such that -4*n**y + 12*n**2 - n - 4*n**3 - 3*n = 0.
0, 1
Suppose 9 = 2*h - 3. Factor 4*k**5 - 4 - 6*k**2 - 9*k - 2 + 9*k**4 + 3 + h*k**3 - k**5.
3*(k - 1)*(k + 1)**4
Let b(c) be the first derivative of 0*c + 2/3*c**3 - 5*c**2 - 19. Suppose b(k) = 0. What is k?
0, 5
Let u(j) be the second derivative of j**7/14 - j**6/10 - 9*j**5/20 + 5*j**4/4 - j**3 + 14*j + 1. Let u(q) = 0. Calculate q.
-2, 0, 1
Solve 80/3*h + 76/3*h**2 - 3/2*h**4 + 4*h**3 + 8 = 0 for h.
-2, -2/3, 6
Let n(s) be the second derivative of s**8/784 - s**6/70 + s**5/70 + 3*s**4/56 - s**3/7 + 7*s**2/2 - 18*s. Let z(o) be the first derivative of n(o). Factor z(y).
3*(y - 1)**3*(y + 1)*(y + 2)/7
Let l(n) be the first derivative of -n**5/7 - 2*n**4/7 + 44*n**3/21 - 8*n**2/7 + 514. Suppose l(h) = 0. What is h?
-4, 0, 2/5, 2
Let o(l) be the second derivative of -5*l**9/3024 + l**7/84 - l**5/24 + 7*l**3/6 + 9*l. Let d(f) be the second derivative of o(f). Factor d(i).
-5*i*(i - 1)**2*(i + 1)**2
Factor 1/6*n**4 - 95/6*n + 191/6*n**2 - 97/6*n**3 + 0.
n*(n - 95)*(n - 1)**2/6
Suppose 6/5*s**2 + 82/5*s - 88/5 = 0. Calculate s.
-44/3, 1
Solve 1 - 65*i - 22 - 20*i**2 + 6 = 0 for i.
-3, -1/4
Let x(k) be the second derivative of k**5/30 - 17*k**4/18 + 31*k**3/9 - 5*k**2 + 28*k. Let x(w) = 0. Calculate w.
1, 15
Fin