44/5*k**2.
-2*(k - 3)**2*(k - 1)**2/5
Let j = -2/1977 + 15838/21747. What is x in -1/11*x**3 - 7/11*x + 0 + j*x**2 = 0?
0, 1, 7
Let d(r) be the second derivative of -r**6/75 - 107*r**5/25 - 504*r**4 - 114048*r**3/5 + 746496*r**2/5 - 44*r - 55. Find x such that d(x) = 0.
-72, 2
Let i = 23282 - 23278. Factor -15/4*w + 1/2 + 6*w**2 + i*w**3.
(w + 2)*(4*w - 1)**2/4
Let m(v) = -7*v**2 + 32*v + 317. Let t(q) = -9*q**2 + 31*q + 308. Let u(r) = 4*m(r) - 3*t(r). Let u(l) = 0. What is l?
-8, 43
Let v = -43104 + 43109. Find x such that -25*x - 1/3*x**3 + v*x**2 + 125/3 = 0.
5
Let f(a) be the first derivative of 5*a**4/24 + 265*a**3/12 - 41*a - 85. Let n(t) be the first derivative of f(t). Find z, given that n(z) = 0.
-53, 0
Let h(g) = -g**2 + 234*g - 1142. Let j be h(229). Factor -544/3*b - 1/6*b**j + 67/6*b**2 - 578/3.
-(b - 34)**2*(b + 1)/6
Let f(t) be the third derivative of 0 + 329*t**2 - 77/12*t**4 + 0*t - 98/3*t**3 - 8/15*t**5 - 1/60*t**6. Suppose f(s) = 0. Calculate s.
-7, -2
Let j(o) = -5*o**3 - 34*o**2 + 2*o - 18. Let b be j(-7). Let d = b - 17. Factor -7/2*y**3 + y**4 + 2*y + 2*y**2 + d.
y*(y - 2)**2*(2*y + 1)/2
Solve 0 - 3112/3*d**2 + 688/3*d - 662/3*d**4 + 14/3*d**5 + 884*d**3 = 0 for d.
0, 2/7, 2, 43
Let x(y) be the third derivative of y**8/840 - 4*y**7/21 + 437*y**6/60 + 1559*y**5/15 + 1643*y**4/3 + 22472*y**3/15 - 265*y**2 + 5*y. Factor x(z).
2*(z - 53)**2*(z + 2)**3/5
Let z(w) be the third derivative of -w**6/720 + 43*w**5/360 - 83*w**4/144 + 41*w**3/36 + 12*w**2 - 34. Factor z(d).
-(d - 41)*(d - 1)**2/6
Determine h so that 9*h**3 - 309*h**5 + 170*h**4 + 79*h**4 - 741*h**2 + 618*h**5 - 312*h**5 - 498*h = 0.
-1, 0, 2, 83
Let s(o) be the second derivative of o**6/120 - o**5/20 + o**4/12 + 18*o**2 + 62*o. Let u(q) be the first derivative of s(q). Factor u(f).
f*(f - 2)*(f - 1)
Let p(v) be the third derivative of 0*v + 0 + 2/105*v**7 + 0*v**3 + 25/12*v**4 - 19/60*v**6 + 4/3*v**5 + 22*v**2. Solve p(j) = 0 for j.
-1/2, 0, 5
Let l = 5662 + -5659. Let n(g) be the second derivative of 1/110*g**5 + 0 + 1/33*g**4 + 1/33*g**l - 13*g + 0*g**2. Factor n(d).
2*d*(d + 1)**2/11
Factor -96/13 + 6/13*u**2 - 2/13*u**3 + 32/13*u.
-2*(u - 4)*(u - 3)*(u + 4)/13
Let o(t) = -3*t - 21. Let u be o(-8). Let y be 0 + (-10)/(-15)*u. Factor h**2 - 7*h**2 - 4*h**2 - y*h**3 - 3*h**3.
-5*h**2*(h + 2)
Let r(o) = 4*o**2 - 1556*o + 1578. Let f(w) = w**2 - 390*w + 395. Let g(a) = -26*f(a) + 6*r(a). Suppose g(x) = 0. What is x?
1, 401
Let h(n) = 5*n**5 + n**4 - n**3 + 7*n**2 + 2*n + 16. Let i(c) = -c**5 - c**4 - c**3 - c**2 + c - 2. Let d = 146 - 152. Let l(q) = d*i(q) - h(q). Factor l(g).
(g - 1)*(g + 1)**2*(g + 2)**2
Let w be 17787/385*(0 - 15). Let j = w + 693. Solve 7/9*l - 1/9*l**2 + j = 0 for l.
0, 7
Let w(u) be the third derivative of -u**8/840 - 107*u**7/525 + 9*u**6/25 - u**2 - 688. Factor w(b).
-2*b**3*(b - 1)*(b + 108)/5
Suppose 0 = -v + 13, -g + v = 170 - 159. Solve 3/8*j**3 - 3*j**g + 57/8*j - 9/2 = 0 for j.
1, 3, 4
Let o = -106 + 104. Let b be (o/(-8))/(4*(-30)/(-640)). Factor 0*m + 2/3*m**5 + 0 + b*m**4 + 2/3*m**3 + 0*m**2.
2*m**3*(m + 1)**2/3
Let h(i) be the third derivative of -i**8/3360 + i**7/150 - 37*i**6/1200 - 19*i**5/75 + 91*i**4/60 + 196*i**3/15 + 2430*i**2. Solve h(a) = 0.
-2, 4, 7
Let q be 0/(9 + 80/(-10)) + 0. Let n(b) be the third derivative of q*b**4 + 0 + 0*b**3 + 0*b + 1/24*b**6 - 5*b**2 - 1/12*b**5. Let n(d) = 0. Calculate d.
0, 1
Let z(k) be the first derivative of k**7/4200 + k**6/1800 - k**5/600 - k**4/120 - 35*k**3 + 102. Let v(p) be the third derivative of z(p). Factor v(h).
(h - 1)*(h + 1)**2/5
Solve -301 - 271*o**2 - 1227*o - 278*o**3 + 281*o**3 - 314 - 439*o**2 + 101*o**2 = 0 for o.
-1, 205
Let v(q) be the first derivative of q**6/10 - 27*q**5/25 - 9*q**4/20 + 29*q**3/5 - 27*q**2/5 + 427. Solve v(p) = 0 for p.
-2, 0, 1, 9
Let j(u) = -7*u**3 + 7*u + 3. Let d(k) be the first derivative of 3/2*k**4 + 0*k**3 - 4 - 2*k - 3*k**2. Let n(b) = 3*d(b) + 2*j(b). Factor n(f).
4*f*(f - 1)*(f + 1)
Determine p so that 164 - 199 - 100*p + 105*p**2 - 5*p**4 + 35 = 0.
-5, 0, 1, 4
Suppose -8*a + 27*a = 76. Let t be 108/10 + (3 - 11)/a. Factor 12/5 + t*v + 7/5*v**2.
(v + 6)*(7*v + 2)/5
Let r(b) = 8*b + 7. Let t be r(-20). Let h be 17/(t/(-78)) + -8. Determine z, given that 0 - 5/3*z**2 + h*z = 0.
0, 2/5
Suppose 17*u = -0*u + 334 + 40. Let c(a) be the second derivative of 10/3*a**3 + 0*a**2 + 0 + u*a + 5/12*a**4. Suppose c(w) = 0. What is w?
-4, 0
Let y(t) be the first derivative of -3/7*t**2 + 2/21*t**3 + 0*t - 5. Let y(c) = 0. What is c?
0, 3
Suppose -15 + 2115/4*k**2 + 1089/4*k**4 - 153/2*k + 22209/8*k**3 = 0. What is k?
-10, -2/11, 1/6
Let o(u) be the first derivative of 3/2*u**4 + 3*u**3 - 234 - 12*u**2 - 3/5*u**5 + 12*u. Determine z so that o(z) = 0.
-2, 1, 2
Let m(p) be the first derivative of -p**5/240 - 5*p**4/96 - 10*p**2 + 8. Let x(f) be the second derivative of m(f). Find t such that x(t) = 0.
-5, 0
Let n(w) be the third derivative of 0*w**5 + 0*w + w**2 + 58 + 1/24*w**4 - 1/120*w**6 + 0*w**3. Determine z so that n(z) = 0.
-1, 0, 1
Let f(b) be the second derivative of -b**5/2 + 47*b**4/6 + 242*b**3/3 - 104*b**2 - 1338*b. Determine a, given that f(a) = 0.
-4, 2/5, 13
Let w = 137 + -132. Suppose 9*o**3 - o**w + 5*o**4 + 3005*o - 3*o**4 - 2*o**2 - 3013*o = 0. What is o?
-2, -1, 0, 1, 4
Suppose -29*j + 26*j = -6. Suppose 2 = 2*b, 2*s - 5*b - 3 = -j*b. What is w in 5*w - 51*w**s - 4 - 5*w**2 + 52*w**3 - w**2 + 4*w = 0?
1, 4
Factor -3072 - 3456*c + 3*c**5 - 55*c**2 + 15*c**4 + 103*c**2 + 366*c**3 - 78*c**4.
3*(c - 8)**3*(c + 1)*(c + 2)
Let x(i) be the third derivative of 1/60*i**6 - 8*i**2 + 1/10*i**5 + 1 - 2/3*i**3 - 1/12*i**4 - 1/105*i**7 + 0*i. Factor x(r).
-2*(r - 2)*(r - 1)*(r + 1)**2
Let k(v) = -8*v**2 + 1756*v + 826. Let z(l) = -24*l**2 + 5268*l + 2460. Let d(c) = 10*k(c) - 3*z(c). What is s in d(s) = 0?
-1/2, 220
Let p(w) be the first derivative of -w**4/14 + 140*w**3/3 - 976*w**2/7 + 4400. Factor p(d).
-2*d*(d - 488)*(d - 2)/7
Let y(r) be the third derivative of 9/140*r**5 + 121*r**2 + 0 + 1/14*r**4 + 3/140*r**6 + 0*r + 1/490*r**7 + 0*r**3. Factor y(h).
3*h*(h + 1)**2*(h + 4)/7
Let q(j) = -2*j + 2. Let u be (3 + -3)/2 + -10. Let n be q(u). Factor -10*t**3 - 8*t - 4*t**2 + 2*t**4 + n*t**2 - 6*t + 4.
2*(t - 2)*(t - 1)**3
Let t = 183 + -181. Determine z so that -2*z**t + 16*z + 10*z - 128 + 20*z - 14*z = 0.
8
Suppose -31*o + 1155 = 24*o. Let a be 4496/448 + (-6)/o. Let -3/2*r**3 - 27/4 - a*r**2 - 18*r = 0. What is r?
-3, -1/2
Let n(m) be the third derivative of -9/32*m**4 + 0 + 1/160*m**6 - 5/8*m**3 - 3/80*m**5 - 5*m**2 + 5*m. Solve n(y) = 0.
-1, 5
Solve 1/11*m**4 - 48/11 + 6/11*m**3 - 56/11*m - 3/11*m**2 = 0 for m.
-4, -1, 3
Find o, given that -2/15*o**2 - 244/15*o + 0 = 0.
-122, 0
What is r in -5*r + 25*r - 20*r - 11*r - 25*r + 2*r**2 - 350 = 0?
-7, 25
Let t be (-356)/(-3)*16/(240/81). Let m be (-66)/231 - ((-48)/70 - 2). Find o such that m*o**5 + 416*o + 80 + 356*o**3 + t*o**2 + 268/5*o**4 = 0.
-10, -1, -1/3
Let o(g) = -g**3 - 9*g**2 - 9*g - 10. Let z be o(-8). Let f(i) = -6*i + 5. Let h be f(z). Find d, given that -8*d - 6*d + 12*d**2 + 24*d + h*d + 6 = 0.
-2, -1/4
Let g(h) be the third derivative of -1/120*h**5 + 0*h - 109*h**2 + 0*h**3 - 1/32*h**4 + 0. Factor g(d).
-d*(2*d + 3)/4
Let v(b) be the second derivative of -b**7/441 - 22*b**6/63 + 451*b**5/210 - 284*b**4/63 + 76*b**3/21 - 36*b + 3. Suppose v(n) = 0. Calculate n.
-114, 0, 1, 2
Suppose -3*d + 179 = 140. Suppose 0*a + d = 2*a + j, 4*a - j - 11 = 0. Factor -4/9*l + 0 - 2/3*l**2 + 14/9*l**a + 2/3*l**5 + 2/3*l**3.
2*l*(l + 1)**3*(3*l - 2)/9
Let c(h) be the first derivative of -h**6/4 - 33*h**5/20 - h**4 - 25*h + 94. Let n(i) be the first derivative of c(i). Factor n(z).
-3*z**2*(z + 4)*(5*z + 2)/2
Solve -1929 + 1569 - 2*i**2 - 2500 - 162*i = 0 for i.
-55, -26
Let q(b) = 6*b**3 - 2400*b**2 + 3254*b - 1094. Let s(p) = 13*p**3 - 2400*p**2 + 3255*p - 1095. Let n(f) = -7*q(f) + 6*s(f). Find h, given that n(h) = 0.
-68, 2/3
Let u(v) be the first derivative of 4*v**3/3 + 776*v**2 + 4053. Factor u(w).
4*w*(w + 388)
Let j(k) be the first derivative of 7*k**4/8 + 2638*k**3/3 - 6793*k**2/4 + 755*k + 653. Factor j(l).
(l - 1)*(l + 755)*(7*l - 2)/2
Let g(j) be the first derivative of -5*j**6/39