.
2*h*(h - 7)*(3*h + 2)/3
Let i(p) be the second derivative of p**5/40 - p**4/24 + 110*p. Let i(r) = 0. What is r?
0, 1
Let o(a) = a**2 + 19*a - 214. Let d be o(-27). Factor -9/2*k**2 - 11/2*k**3 + d + 2*k + 1/2*k**4 + 3/2*k**5.
(k - 2)*(k + 1)**3*(3*k - 2)/2
Let o(s) be the third derivative of 0 - 6*s**2 - 5/8*s**4 + 1/8*s**6 + 0*s - 5/12*s**5 + 10/3*s**3 + 1/42*s**7. Factor o(f).
5*(f - 1)**2*(f + 1)*(f + 4)
Let v(o) be the second derivative of 0*o**3 + 1/14*o**7 + 1/5*o**6 + 0*o**4 + 0*o**5 + 0 - 15*o + 0*o**2. Factor v(k).
3*k**4*(k + 2)
Solve -1/4*l**2 - 2 + 9/4*l = 0.
1, 8
Let h(j) be the second derivative of j**4/4 + 20*j**3 + 600*j**2 - 90*j + 1. Let h(c) = 0. What is c?
-20
Let x(f) be the third derivative of -f**7/210 - 3*f**6/40 - f**5/4 + 25*f**4/24 - 186*f**2. Suppose x(j) = 0. What is j?
-5, 0, 1
Let q(m) = m**2 - 22*m - 44. Let h be q(-2). Suppose 4/5*p**5 - 4*p**2 - 4*p**3 + 4/5*p**h + 16/5*p + 16/5 = 0. Calculate p.
-2, -1, 1, 2
Suppose -9/8*b**2 - 3/8*b**3 + 0*b + 0 = 0. Calculate b.
-3, 0
Let r(c) be the third derivative of -c**8/112 + 11*c**7/70 - 19*c**6/40 + 9*c**5/20 - 48*c**2 - 1. Factor r(f).
-3*f**2*(f - 9)*(f - 1)**2
Suppose -y = 2*b - 74, -4*y + 202 = 4*b - 110. Factor s + 16*s - y - 2*s**2 + 19*s - 80.
-2*(s - 9)**2
Let b(p) be the second derivative of 5*p**5/4 + 15*p**4/4 - 85*p**3/6 + 15*p**2/2 + 3*p - 1. Determine m, given that b(m) = 0.
-3, 1/5, 1
Let g(k) be the second derivative of 0 + 1/72*k**4 - 4/9*k**3 + 16/3*k**2 - 30*k. Factor g(m).
(m - 8)**2/6
Let j = 21 - 21. Factor 3*g**2 + j*g**2 - 1100 + 1175 + 30*g.
3*(g + 5)**2
Suppose 6*l - 8*l**2 + 117*l + 13424 + 133*l + 9*l**2 + 2960 = 0. What is l?
-128
Let f(b) be the first derivative of 5/3*b**3 - b**5 + 0*b + 5/2*b**4 - 34 - 5*b**2. Factor f(n).
-5*n*(n - 2)*(n - 1)*(n + 1)
Let p = 1945 - 1942. Factor 0*q**p + 0*q + 1/4*q**4 - 1/4*q**2 + 0.
q**2*(q - 1)*(q + 1)/4
Let n(v) = -v**3 - v + 7. Let d be (4 + -3)*-1 + 1. Let a be n(d). Find b such that -5*b - 32*b**2 - 12 + 29*b**2 - a*b = 0.
-2
Let p(b) be the first derivative of 3*b**4/2 - 3*b**3 - 177*b**2/2 + 90*b + 132. Find a such that p(a) = 0.
-5, 1/2, 6
Let a = -127 - -129. Let n be 1/((-5)/3)*(-5)/a. Factor -n - 3/2*x**2 - 3*x.
-3*(x + 1)**2/2
Factor 0 + 1/4*k**2 - 17/2*k.
k*(k - 34)/4
Let g(u) be the third derivative of 0 - 1/270*u**5 - 1/108*u**4 + 0*u + 4*u**2 + 2/27*u**3. Factor g(l).
-2*(l - 1)*(l + 2)/9
Let q = -40/71 + 2632/639. Factor q*z + 2/9*z**2 + 128/9.
2*(z + 8)**2/9
Solve 4*u**2 + 2710*u + 2*u**2 - 2*u**2 + 367205 - 2*u**2 + 3*u**2 = 0 for u.
-271
Let g(t) be the third derivative of -9/70*t**7 + 7/40*t**6 + 1/2*t**4 + t**5 - 12*t**2 + 0 + 0*t + 0*t**3. Factor g(a).
-3*a*(a - 2)*(a + 1)*(9*a + 2)
Let o(t) = -2*t**2 + 46*t - 8. Let m(r) = -6*r**2 + 132*r - 24. Let i(k) = 6*m(k) - 17*o(k). What is s in i(s) = 0?
1, 4
Let c(w) = 2*w**2 + 10*w. Suppose 5*h + 2*m = 3*h + 4, 0 = -2*h + 2*m. Let i(z) = -z. Let r(d) = h*c(d) + 10*i(d). Solve r(y) = 0.
0
Let a(q) be the second derivative of -q**5/80 + q**4/12 + 9*q**3/8 - 45*q**2/4 + 28*q. Determine s, given that a(s) = 0.
-5, 3, 6
Factor -4 + 32/3*o**2 - 26/3*o**5 + 92/3*o**4 - 36*o**3 + 22/3*o.
-2*(o - 1)**4*(13*o + 6)/3
Suppose 0 = -4*j - x + 38, 2*j - 4*x - 38 = -j. Solve -z**4 - 14*z + 19*z + 5*z**5 + j + 6*z**4 - 10*z**3 + 5*z**4 - 20*z**2 = 0.
-2, -1, 1
Suppose -5*d - 2*c = 100, -5*d - c = 82 + 13. Let g be 2*(d/(-4) + -3). Factor 3 + 2*m**2 - 3 - 6*m**2 + 4*m + 4 - 4*m**g.
-4*(m - 1)*(m + 1)**2
Let n = 2140 + -2135. Factor 2/5*b**2 + 6/5*b**4 + 0 - 6/5*b**3 + 0*b - 2/5*b**n.
-2*b**2*(b - 1)**3/5
Let v = -1/10 + 3/5. Factor v*l**2 + 1/2 - l.
(l - 1)**2/2
Let k = -30 + 130. Find r such that k - 100 - 4*r**4 = 0.
0
Let z = 46 + -42. Factor -z - 4*f**4 - 206*f**2 + 0*f**3 + 214*f**2 + 0*f**3.
-4*(f - 1)**2*(f + 1)**2
Suppose 570*k**2 + 162*k**3 - 57*k + 8 - 578*k**4 - 79*k - 26*k**3 = 0. What is k?
-1, 2/17, 1
Solve 3*p + 1/4*p**2 - 1/4*p**3 + 0 = 0 for p.
-3, 0, 4
Let w(v) = 3*v**3 + 12*v**2 - 5*v - 5. Let z(t) = 6*t**3 + 24*t**2 - 9*t - 9. Let y(p) = -9*w(p) + 5*z(p). Factor y(n).
3*n**2*(n + 4)
Let h = -50545/3 + 16849. Factor -h*n**3 + 16/9*n**2 + 0 - 8/9*n.
-2*n*(n - 2)*(3*n - 2)/9
Let g = 4811 - 4807. Factor 1/4*d**3 - 1/4*d**2 - 1/8*d + 1/8 - 1/8*d**5 + 1/8*d**g.
-(d - 1)**3*(d + 1)**2/8
Determine q so that -4/9 + 46/9*q**2 + 146/9*q**3 - 38/3*q**4 - 74/9*q = 0.
-2/3, -1/19, 1
Factor -1954*p - 2*p**3 + 3*p**2 + 2*p**3 + 1954*p - 3*p**4.
-3*p**2*(p - 1)*(p + 1)
Determine x, given that 3*x**4 - 59*x - 9*x**3 - 8*x**2 + 68*x + 12 - 6*x**2 - x**2 + 0*x**2 = 0.
-1, 1, 4
Let x(d) be the third derivative of d**8/392 - 2*d**7/147 - d**6/70 + 4*d**5/35 + 11*d**4/84 - 2*d**3/7 - 4*d**2 - 16*d. Suppose x(g) = 0. Calculate g.
-1, 1/3, 2, 3
Let b be (14/147 - (2455/1155 + -2))*-6. Solve -b*r**3 - 4/11 + 0*r**2 + 6/11*r = 0.
-2, 1
Let h(v) be the third derivative of 1/140*v**6 - 1/30*v**5 + 0*v + 5/84*v**4 + 4*v**2 + 0 - 1/21*v**3. Let h(c) = 0. Calculate c.
1/3, 1
Factor -7/3*w**3 - 12*w + 1/6*w**4 + 0 + 10*w**2.
w*(w - 6)**2*(w - 2)/6
Let l(y) be the third derivative of -y**5/630 + 5*y**4/252 - 4*y**3/63 - 47*y**2. Solve l(m) = 0 for m.
1, 4
Suppose -5*z = 2*d - 16, -3 = -4*d + 9. Let g(h) be the third derivative of -2/33*h**3 - 6*h**z - 1/132*h**4 + 1/660*h**6 + 1/165*h**5 + 0*h + 0. Factor g(n).
2*(n - 1)*(n + 1)*(n + 2)/11
Let s(c) be the third derivative of c**7/3360 - c**6/1440 - c**5/240 - 5*c**3/6 + 16*c**2. Let k(p) be the first derivative of s(p). Factor k(h).
h*(h - 2)*(h + 1)/4
Let y(q) be the third derivative of 0 + 0*q + 1/420*q**7 + 1/24*q**4 - 5*q**2 + 0*q**5 - 1/120*q**6 - 1/12*q**3. Suppose y(w) = 0. Calculate w.
-1, 1
Let s(w) be the first derivative of -2*w**2 + 26 + 2*w + 2/3*w**3. Find i, given that s(i) = 0.
1
Let t = -3929 + 2714937/691. Let u = 6233/4837 + t. Factor -3/7*i**5 + u*i**3 + 0*i**4 - 6/7*i**2 + 0*i + 0.
-3*i**2*(i - 1)**2*(i + 2)/7
Suppose -13 = -2*c - 3. Let z = 8 - c. Find n, given that -8 + 10 - 2 - 3*n**4 + 6*n**z - 3*n**2 = 0.
0, 1
Let b be ((-238)/34 - 4) + 59/3. Factor 2/9 + b*j + 338/3*j**2 + 4394/9*j**3.
2*(13*j + 1)**3/9
Let z(q) be the third derivative of 0*q**3 + 0 + 1/40*q**6 + 24*q**2 - 3/20*q**5 + 1/4*q**4 + 0*q. Factor z(f).
3*f*(f - 2)*(f - 1)
Let t = -3/12794 - -47979/6397. Factor 3*q**3 - t*q**2 - 6 - 33/2*q.
3*(q - 4)*(q + 1)*(2*q + 1)/2
Let d(a) be the second derivative of -a**5/110 + 51*a**4/22 - 1976*a**3/11 + 5776*a**2/11 + 58*a - 2. Factor d(w).
-2*(w - 76)**2*(w - 1)/11
Suppose -32*u - 3*u = -11 - 129. Let 7/4*k**5 + 0 + 0*k + 3/4*k**2 + 13/4*k**3 + 17/4*k**u = 0. What is k?
-1, -3/7, 0
Let p(z) be the third derivative of -z**6/60 + 37*z**5/90 - 31*z**4/12 + 3*z**3 - z**2 - 104*z. Suppose p(b) = 0. What is b?
1/3, 3, 9
Let p = 60 - 57. Factor -1 - 28*z**2 - 5*z**p - 19 - 2*z**2 - 45*z.
-5*(z + 1)**2*(z + 4)
Let m(y) be the third derivative of y**6/20 - 4*y**5/15 + 7*y**4/12 - 2*y**3/3 + 20*y**2. Suppose m(k) = 0. Calculate k.
2/3, 1
Let d = -12001 - -72007/6. Factor d*y + 0*y**2 - 1/6*y**3 + 0.
-y*(y - 1)*(y + 1)/6
Let v(t) = 49*t**2 + 287*t + 1181. Let c(p) = -17*p**2 - 96*p - 393. Let k(w) = 17*c(w) + 6*v(w). Let k(r) = 0. What is r?
-9
Let w(y) = -24*y**3 + 25*y**2 + 29*y + 4. Let h(u) = u**3 + u. Let n = -47 - -51. Let p(b) = n*w(b) + 12*h(b). Suppose p(q) = 0. Calculate q.
-2/3, -1/7, 2
Let o be 1*3 - 96/(-20). Let t = -37/5 + o. Factor 0 + 0*n**2 + t*n - 2/5*n**3.
-2*n*(n - 1)*(n + 1)/5
Suppose 3*c - 12 = 5*g, -4*c = 4*g + c - 20. Let n(m) be the first derivative of 0*m**3 + 4 + 0*m**2 - 1/4*m**4 + g*m. Factor n(w).
-w**3
Let j(r) be the first derivative of -r**7/7140 - r**6/1530 + r**5/1020 + r**4/102 + 3*r**3 + 8. Let u(f) be the third derivative of j(f). Factor u(l).
-2*(l - 1)*(l + 1)*(l + 2)/17
Let k(o) be the second derivative of o**6/600 - o**5/150 + o**4/120 + 15*o**2/2 - 16*o. Let v(h) be the first derivative of k(h). Factor v(g).
g*(g - 1)**2/5
Let c = -1327 - -1331. Let q(a) be the third derivative of 0*a**5 + 1/80*a**6 + 0*a - 10*a**2 + 0*a**3 - 1/420*a**7 + 0*a**c + 0. Suppose q(k) = 0. What is k?
0, 3
Let c be 35*((-1 - 0/(-4)) + 0). Let h be 7/c*(-5)/3. Factor 1/6*o**3 + 2/3*o**2 + 5/6*o + h.
(o + 1)**2*(o + 2)/6
Let s be (18/12*-1)/((-3)/478). Factor 0*y**3 - 