*3*(4*i - 1)**2/5
Let s(k) be the second derivative of -k**4/54 + 106*k**3/27 - 2809*k**2/9 + 256*k. Factor s(h).
-2*(h - 53)**2/9
Let a(x) be the second derivative of -x**5/30 + 62*x**4/3 - 15376*x**3/3 + 1906624*x**2/3 + 3*x - 101. What is s in a(s) = 0?
124
Suppose 12*p**3 + 3*p**2 + 21/4*p**4 + 0 + 0*p = 0. What is p?
-2, -2/7, 0
Let a(q) be the third derivative of 0*q + 5/3*q**3 + 17*q**2 - 1/24*q**6 + 5/8*q**4 + 0*q**5 + 0. Factor a(n).
-5*(n - 2)*(n + 1)**2
Suppose 2*b - 10 = -2*d, 5 = b - 4*d + 15. Suppose -7 = 5*r - 27. Factor -2*m**5 - 24*m**2 + 6*m**r + b + 21*m - 7 - m**5 + 6*m**3 - 1.
-3*(m - 1)**4*(m + 2)
Let s(x) = 30*x - 4. Let m be s(4). Suppose 0 = p + p - m. Factor -4*b**3 + 2*b**2 - 4 - p*b + 2*b**2 + 78*b + 16.
-4*(b - 3)*(b + 1)**2
Let f(o) be the second derivative of o**5/10 - 2*o**4/3 - 11*o**3/3 - 6*o**2 - 28*o. Find r, given that f(r) = 0.
-1, 6
Let j(w) be the first derivative of 1/5*w**2 - 13 - 1/5*w**4 + 1/15*w**6 - 4/5*w + 8/15*w**3 - 4/25*w**5. Let j(r) = 0. Calculate r.
-1, 1, 2
Let f = -83 + 89. What is l in 21*l**2 - 4*l**4 + 31*l - 5*l**4 + f*l**3 - 25*l = 0?
-1, -1/3, 0, 2
Let z be (-18*2)/(-3) + -4. What is q in 5*q**2 - 4*q - 5*q - z*q + 2*q - 20 = 0?
-1, 4
Suppose -5*s = -l + 57, -44 - 21 = -l - 3*s. Let r = 62 - l. Determine m so that 2/5*m**3 - 2/5*m + r + 0*m**2 = 0.
-1, 0, 1
Let t(k) be the third derivative of -k**6/24 - 7*k**5/12 - 25*k**4/12 + k**2 - 306. Determine d so that t(d) = 0.
-5, -2, 0
Factor 9/8*h + 3/4 + 3/8*h**2.
3*(h + 1)*(h + 2)/8
Let o(h) = -20*h + 10. Let n be o(-3). Let c = -68 + n. Factor 4/5 + c*g + 6/5*g**2 - 2/5*g**3 - 2/5*g**4.
-2*(g - 2)*(g + 1)**3/5
Let f(j) be the second derivative of -j**5/102 + j**4/102 - 5*j**2 - j. Let q(a) be the first derivative of f(a). Factor q(t).
-2*t*(5*t - 2)/17
Let d(f) be the first derivative of -28*f**3/9 + 5*f**2/3 + 2*f/3 + 39. Factor d(k).
-2*(2*k - 1)*(7*k + 1)/3
Let a(o) = -o**3 + o**2 + o. Let k(q) be the first derivative of 9*q**4/4 + q**3 + q**2/2 - 7. Let c(b) = -14*a(b) - 2*k(b). Determine h so that c(h) = 0.
-4, -1, 0
Let f(y) be the first derivative of y**4/8 - 13*y**3/12 + 3*y**2/4 + 45*y/4 + 191. Determine j, given that f(j) = 0.
-3/2, 3, 5
Let c = -1469/42 + 246/7. Let i(j) be the second derivative of -c*j**4 + 0*j**3 + 0 + j**2 - 5*j. Factor i(d).
-2*(d - 1)*(d + 1)
Let t(c) be the third derivative of c**9/12096 - c**8/3360 + c**7/3360 + 3*c**3/2 - 15*c**2. Let i(v) be the first derivative of t(v). Let i(z) = 0. What is z?
0, 1
Let s(m) be the third derivative of -m**7/560 - 13*m**6/240 - 3*m**5/20 - 16*m**3/3 + 55*m**2. Let y(b) be the first derivative of s(b). Solve y(t) = 0.
-12, -1, 0
Let i(c) be the third derivative of -c**8/5600 + c**7/504 + c**6/300 + c**5/30 + 7*c**2. Let l(s) be the third derivative of i(s). Factor l(t).
-2*(t - 3)*(9*t + 2)/5
Suppose 10 + 5/6*u**2 - 20/3*u = 0. What is u?
2, 6
Let r(g) be the first derivative of 1/13*g**4 + 0*g**2 + 0*g - 2/65*g**5 + 0*g**3 + 7. Factor r(l).
-2*l**3*(l - 2)/13
Suppose -4*x + i + 2*i = -14, -11 = -3*x + 2*i. Suppose -6*l**2 - 5*l - 3*l**3 + l**2 + 8*l**3 + x = 0. Calculate l.
-1, 1
Let p(m) be the third derivative of m**8/560 - 3*m**7/350 - 13*m**6/200 + 11*m**5/100 + 3*m**4/5 - 2*m**3 - 106*m**2. Suppose p(u) = 0. Calculate u.
-2, 1, 5
Let x(l) = -9*l**4 + 42*l**3 - 108*l**2 + 6*l. Let j(y) = -y**4 + y**3 + y. Let q(o) = 6*j(o) - x(o). Determine u, given that q(u) = 0.
0, 6
Suppose -24*v + 4 = -25*v. Let p(r) = -r**3 + 3*r**2 - 2*r - 3. Let k(i) = i**3 - 4*i**2 + 3*i + 4. Let b(h) = v*p(h) - 3*k(h). Factor b(g).
g*(g - 1)*(g + 1)
Let u(j) be the second derivative of 12*j**2 + 12*j - 1/5*j**5 + 8/3*j**4 + 0 - 26/3*j**3. Solve u(z) = 0 for z.
1, 6
Let p = 6283/1932 + -1/483. Let w = 125/36 - p. Determine u, given that w*u**3 - 2/9*u - 2/9*u**2 + 2/9 = 0.
-1, 1
Let y(i) be the third derivative of 0 + 1/24*i**6 + 20*i**2 - 5/12*i**5 + 35/24*i**4 + 0*i - 5/2*i**3. Factor y(t).
5*(t - 3)*(t - 1)**2
Let w = 3 + 20. Let j = w + -20. Factor -9/2 - 1/2*a**2 - j*a.
-(a + 3)**2/2
Let c(m) be the third derivative of 0 + 0*m**3 - 1/4*m**5 - 8*m**2 + 1/4*m**4 - 1/20*m**6 + 1/14*m**7 + 0*m. Factor c(a).
3*a*(a - 1)*(a + 1)*(5*a - 2)
Determine c so that 36 - c**2 - c**2 - 2*c**2 = 0.
-3, 3
Let l(z) be the third derivative of 4*z**2 + 0*z + 0*z**3 + 1/40*z**6 + 0 - 1/126*z**7 + 1/1008*z**8 + 1/36*z**4 - 7/180*z**5. Let l(s) = 0. What is s?
0, 1, 2
Let n(z) be the first derivative of 2/57*z**3 + 6/19*z**2 - 44 + 0*z. Solve n(r) = 0 for r.
-6, 0
Factor 320*j - 2*j**4 + 10*j**3 + 4*j**4 - 2*j**2 + 18*j**2 - 312*j.
2*j*(j + 1)*(j + 2)**2
Let h(f) = 5*f**2 + 21*f + 6. Let n be 29/(-5) + 2/(-10). Let y(z) = 20*z**2 + 85*z + 25. Let s(i) = n*y(i) + 25*h(i). Factor s(q).
5*q*(q + 3)
Let j(p) be the second derivative of 4/33*p**3 - 1/22*p**5 + 4/11*p**2 + 0 + 1/165*p**6 - 5/66*p**4 + 1/231*p**7 - 11*p. What is r in j(r) = 0?
-2, -1, 1, 2
Let g(q) be the third derivative of q**8/336 + q**7/14 + 31*q**6/60 + 17*q**5/30 - 21*q**4/8 - 49*q**3/6 - 2*q**2 + 2. Factor g(n).
(n - 1)*(n + 1)**2*(n + 7)**2
Let g(d) be the second derivative of d**5/90 + d**4/6 - 85*d**3/27 + 25*d**2/3 - 53*d + 1. Factor g(w).
2*(w - 5)*(w - 1)*(w + 15)/9
Factor 16/5*v**4 + 28/5*v**3 - 4/5*v + 8/5*v**2 + 0.
4*v*(v + 1)**2*(4*v - 1)/5
Find p, given that -1/8*p**2 + 71/4 + 69/8*p = 0.
-2, 71
Let d be (-12)/(-38)*3382/712. Solve -9/2*p**3 + 0 + 6*p - 3*p**4 + d*p**5 + 6*p**2 = 0.
-1, 0, 2
Let s(w) be the third derivative of -3*w**5/20 + w**4/4 + 4*w**3 - 121*w**2. Let s(v) = 0. What is v?
-4/3, 2
Let v(t) be the third derivative of -t**5/120 - 7*t**4/48 - 161*t**2. Factor v(j).
-j*(j + 7)/2
Let p = -3278 + 3280. Find z such that -1/3*z**3 + 0 + 1/3*z + 0*z**p = 0.
-1, 0, 1
Find p, given that -2/5 - 3/5*p - 1/5*p**2 = 0.
-2, -1
Let m(i) be the second derivative of 0*i**4 + 31*i + 1/6*i**6 + 1/4*i**5 + 0*i**2 + 0*i**3 + 0. Let m(d) = 0. What is d?
-1, 0
Let t = -3/493 - -10377/3944. Let -3/4*z**5 + t*z**4 - 39/4*z**2 + 3/2*z + 9 + 9/8*z**3 = 0. Calculate z.
-3/2, -1, 2
Let v = 42 + -33. Let d be (-40)/(-30) + 0 + 6/v. Find y such that -1/3*y**3 + 0*y + 4/3 - y**d = 0.
-2, 1
Let x(n) be the third derivative of n**6/1980 + n**5/220 + n**3/6 + 10*n**2. Let p(d) be the first derivative of x(d). Factor p(q).
2*q*(q + 3)/11
Let i = 1299 - 1299. Let f(x) be the second derivative of i - 9/10*x**6 - 9/20*x**5 + 0*x**2 - 1/2*x**3 + 5/4*x**4 + 7*x. Factor f(l).
-3*l*(l + 1)*(3*l - 1)**2
Let n(i) be the third derivative of -1/60*i**5 - 7*i**2 + 0*i - 3/4*i**4 - 27/2*i**3 + 0. Factor n(t).
-(t + 9)**2
Let x(a) be the third derivative of a**7/840 + 7*a**6/480 + a**5/40 - 46*a**2 - 2*a. Factor x(g).
g**2*(g + 1)*(g + 6)/4
Let v(s) = 16*s**4 - 133*s**3 - 325*s**2 - 176*s + 11. Let i(y) = -3*y**4 + 27*y**3 + 65*y**2 + 35*y - 2. Let w(n) = -11*i(n) - 2*v(n). Factor w(d).
d*(d - 33)*(d + 1)**2
Let z(g) = 5*g**2 + g + 4. Let h(i) = 33*i**2 + 6*i + 25. Let t(j) = 6*h(j) - 39*z(j). Factor t(r).
3*(r - 2)*(r + 1)
Let w(r) be the third derivative of 17*r**2 + 1/120*r**6 + 0*r - 1/336*r**8 + 0*r**3 + 0 + 1/210*r**7 - 1/60*r**5 + 0*r**4. Determine j so that w(j) = 0.
-1, 0, 1
Let y be (-3*4 - 2)*(-2)/4. Suppose -t = -3*t + 6. Factor -5*g**t + y*g**3 + 0*g**2 - g**2 - 3*g**3.
-g**2*(g + 1)
Let m(o) be the second derivative of -12*o**5/5 + 250*o**4 + 503*o**3/2 + 189*o**2/2 + 11*o + 21. Let m(i) = 0. Calculate i.
-1/4, 63
Let g = 1145/721 - -13/103. Solve -g*s**2 + 9/7*s + 3/7 = 0 for s.
-1/4, 1
Let v(u) be the third derivative of -u**6/600 + u**5/60 + u**4/15 - 2*u**3/5 + u**2 - 21. Determine m, given that v(m) = 0.
-2, 1, 6
Let d(t) = 4239*t**3 + 1281*t**2 - 2390*t + 505. Let u(z) = -2120*z**3 - 640*z**2 + 1192*z - 252. Let w(j) = 4*d(j) + 7*u(j). Factor w(y).
4*(y + 1)*(23*y - 8)**2
Let j(a) = -16*a**2 + 83*a + 19. Let q(y) = 82*y**2 - 416*y - 94. Let k(d) = -11*j(d) - 2*q(d). Solve k(r) = 0 for r.
-1/4, 7
Let o(s) be the second derivative of 7*s**5/5 + 25*s**4/3 + 32*s**3/3 - 24*s**2 + 43*s - 5. Factor o(t).
4*(t + 2)**2*(7*t - 3)
Let r(i) be the third derivative of 1/270*i**5 + 16*i**2 + 0 - 1/270*i**6 + 0*i**3 + 1/945*i**7 + 0*i**4 + 0*i. Let r(n) = 0. Calculate n.
0, 1
Let s(o) be the third derivative of -o**5/180 + 133*o**4/36 - 17689*o**3/18