27/4 + 1/4*t**5 - 9/2*t**2.
(t - 3)**3*(t - 1)*(t + 1)/4
Suppose -12624*r + 12592*r = -64. Let s(j) be the first derivative of 38 + 1/21*j**3 + 0*j + 1/7*j**r. Factor s(n).
n*(n + 2)/7
Let b = 31 - 22. Let h(l) = l**2 - 9*l + 3. Let z be h(b). What is f in 9 - 247*f + 268*f + 15*f**2 + 3*f**z + 0*f**3 = 0?
-3, -1
Let q(f) be the third derivative of 1/14*f**7 + 4 - 11/25*f**5 + 0*f - 84/5*f**4 + 7/10*f**6 + 26*f**2 + 288/5*f**3. Factor q(u).
3*(u + 4)**2*(5*u - 6)**2/5
What is v in 10*v**2 + 1/4*v**5 - 1/2*v**3 - 5*v**4 + 1/4*v - 5 = 0?
-1, 1, 20
Let f = -4022 + 4027. Suppose -4*y**2 - 16/3 - 56/3*y + 46/3*y**3 + 32/3*y**4 + 2*y**f = 0. Calculate y.
-2, -1/3, 1
Let u be (-5)/(285/(-6) + -5). Let -8/3*l + 32/21*l**2 + 0 - u*l**3 = 0. Calculate l.
0, 2, 14
Let z be 28/(-2 - -4) + (-29 - -15). Determine i so that 33*i**3 + 0 + z*i + 3/2*i**4 + 363/2*i**2 = 0.
-11, 0
Let y(d) be the second derivative of 25/48*d**4 + 41/6*d**3 - 18*d - 5 - 27/80*d**5 + 3/2*d**2. Factor y(q).
-(q - 3)*(q + 2)*(27*q + 2)/4
Suppose 19 - 19 = 91*i. Let q(p) be the third derivative of 0*p + i*p**5 + 16/9*p**3 - 4/9*p**4 + 0 - 1/315*p**7 + 1/45*p**6 - 17*p**2. Factor q(h).
-2*(h - 2)**3*(h + 2)/3
Let y(t) = -28*t**4 - 374*t**3 - 26941*t**2 - 627277*t - 1149971. Let w(m) = 2*m**4 - 2*m**3 + m**2 + m - 1. Let b(i) = -26*w(i) - 2*y(i). Factor b(u).
4*(u + 2)*(u + 66)**3
Solve 6*k**2 - 2 + 47/2*k = 0.
-4, 1/12
Find b such that -3*b**2 + 139*b - 5*b**2 + 3*b**2 - 7*b + b**2 - 1008 = 0.
12, 21
Suppose 6*c + 5*k - 870 = c, k = -2*c + 348. Suppose 7*q**5 - 1329*q + 306*q - 10*q**5 - 363 + 57*q**4 - c*q**3 - 894*q**2 = 0. What is q?
-1, 11
Suppose 0 = 36*s - 31*s - 20. Factor -4*x**4 - 6*x**4 + 11*x**4 - 3*x**5 + 3*x**s - 16*x**2 + 2*x**5 + 16*x.
-x*(x - 2)**3*(x + 2)
Let i(w) = 212*w**2 + 8408*w + 17056. Let u(q) = -33*q**2 - 1293*q - 2624. Let f(c) = -5*i(c) - 32*u(c). Factor f(n).
-4*(n + 2)*(n + 164)
Let z(b) = 75*b**2 + 7*b**3 + 16*b**3 + 6*b**3 + 22 + 93*b - 13*b**3. Let n(a) = 14*a**3 + 74*a**2 + 91*a + 21. Let p(h) = 6*n(h) - 5*z(h). Factor p(w).
(w + 1)*(w + 16)*(4*w + 1)
Let g be 13 - 10 - (-259 - -262). What is h in g + 0*h**4 - 10*h**2 - 35/3*h**3 + 0*h + 5/3*h**5 = 0?
-2, -1, 0, 3
Let z = 1442 - 1442. Let g(t) be the third derivative of 13*t**2 + z*t**3 + 0 + 0*t + 0*t**4 - 1/60*t**5. Factor g(p).
-p**2
Let a = 390 + -388. Factor -33*f**2 - 62*f**2 - 6*f**3 + f**3 + 0*f**a.
-5*f**2*(f + 19)
Suppose 24*g + g**4 - 14*g**2 - 14*g**2 + 18*g**4 - 20*g**3 - 4*g**5 + 9*g**4 = 0. What is g?
-1, 0, 1, 6
Solve 1404488 + 1676*v + 1/2*v**2 = 0.
-1676
Suppose 0 + 0*p - 258/7*p**4 + 744/7*p**3 - 192/7*p**2 + 3*p**5 = 0. What is p?
0, 2/7, 4, 8
Let a(g) be the third derivative of g**5/300 - 91*g**4/60 + 3*g**2 - 257. Solve a(u) = 0.
0, 182
Let a(r) be the first derivative of -17*r**3/6 - 157*r**2 + 37*r/2 - 1141. Factor a(y).
-(y + 37)*(17*y - 1)/2
Suppose -60 = -5*n + s, 4*n + 4*s - 14 - 58 = 0. Suppose 7*y - n = 8. Suppose 5*p**y + 7*p**5 - p**5 - 3*p**5 - 2*p**3 + 6*p**4 = 0. What is p?
-1, 0
Let v(p) = -p**3 - 2*p**2 + p - 2. Let m(z) = -20*z**3 + 420*z**2 + 1408*z - 32. Let x(w) = -m(w) + 16*v(w). Factor x(u).
4*u*(u - 116)*(u + 3)
Suppose -195 = 108*h - 113*h. Determine t so that -13*t - 29*t - t**2 - h*t - 484 + 37*t = 0.
-22
Let w(t) be the second derivative of 5*t**4/36 - 1495*t**3/18 + 745*t**2/3 + 517*t. Factor w(z).
5*(z - 298)*(z - 1)/3
Let d(z) = -16*z - 107. Let r be d(-7). Suppose 2*w + r*x = -0*x + 5, 0 = -4*x + 4. Factor 0*i**2 + 0*i + 1/8*i**4 + 0*i**3 + w.
i**4/8
Let h(l) be the second derivative of -6*l**2 + 3/4*l**5 + 0 + 2/5*l**6 + 50*l - 10*l**3 - 15/4*l**4. Let h(x) = 0. What is x?
-2, -1, -1/4, 2
Let g(m) be the third derivative of -m**6/300 - 3*m**5/50 + 11*m**4/30 + 692*m**2 + 2. Let g(k) = 0. What is k?
-11, 0, 2
Let o(j) be the third derivative of j**5/5 + 50*j**4/3 - 206*j**3/3 + 674*j**2. What is d in o(d) = 0?
-103/3, 1
Suppose 5*b + 10 = 0, 0 = -2*s - 2*b + 6 + 10. Suppose -s*m + 17 = -3. Factor -29*n**3 + 48*n - 12 + 12*n**4 - 36*n**3 + 9*n**m + 26*n**3.
3*(n - 2)**2*(n + 1)*(4*n - 1)
Let q be (-3)/((-6)/8) + -7. Let d = 1 - q. What is z in -15*z**3 + 15*z**2 + 12*z - 6 - 24*z**d - 6 + 21*z**4 + 3*z**5 = 0?
-2, -1, 1, 2
Let v = 254 + -170. Determine g so that g**4 + 48*g - 2*g**5 + 96*g**3 - v*g**3 - 5*g**4 + 56*g**2 - 2*g**4 = 0.
-2, 0, 3
Let v(b) be the first derivative of 34 - 17/46*b**4 - 10/23*b**3 - 3/23*b**2 + 2/23*b - 12/115*b**5. Factor v(n).
-2*(n + 1)**3*(6*n - 1)/23
Let f(z) = -18*z + 14*z + 8 + 23 + 5. Let p be f(8). Factor 801*x**p - 88*x**2 - 135 - 806*x**4 + 50*x**3 + 270*x - 92*x**2.
-5*(x - 3)**3*(x - 1)
Let d(c) be the first derivative of -3 - 1/66*c**4 + 2/11*c**2 + 1/33*c**3 + 8*c. Let y(o) be the first derivative of d(o). Find r such that y(r) = 0.
-1, 2
Let f(c) be the first derivative of c**3/3 - 61*c**2 + 805*c - 4947. Factor f(h).
(h - 115)*(h - 7)
Suppose 0 = -4*a + 4*f + 32, -3*f - 365 + 373 = 5*a. Factor -3/4*y**a + 9/4*y**2 + 3/2*y**3 - 3*y - 3.
-3*(y - 2)**2*(y + 1)**2/4
Let b(d) = -d**3 + 20*d**2 - 101*d + 22. Let k = -29 - -40. Let s be b(k). Let 4/5*f - 4/5*f**3 + 0*f**2 + s = 0. What is f?
-1, 0, 1
Let m(s) be the third derivative of -s**6/90 - 2*s**5/5 - 29*s**4/6 - 140*s**3/9 + 263*s**2 - 3. Determine r so that m(r) = 0.
-10, -7, -1
Let a(d) be the first derivative of -7*d**6/30 + 4*d**5/5 - 11*d**4/12 + d**3/3 - 14*d + 23. Let j(h) be the first derivative of a(h). Factor j(f).
-f*(f - 1)**2*(7*f - 2)
Let h be ((-9261)/162 + 59)/(6/(-8)*12/(-18)). Factor 1/9*s**2 - 34/9 + h*s.
(s - 1)*(s + 34)/9
Let x(q) = 12*q - 2*q**3 + 8*q + q**3 + 12 + 13*q + 8*q**2. Let h be x(11). Let 4*f**3 - 8*f - h - 4*f**2 + 0*f**3 - f - 11*f = 0. Calculate f.
-1, 3
Factor 252/13*s + 38/13*s**2 - 2/13*s**3 - 288/13.
-2*(s - 24)*(s - 1)*(s + 6)/13
Let n(z) be the second derivative of z**6/40 + 61*z**5/20 + 899*z**4/8 - 961*z**3/2 - 36*z**2 - 115*z. Let m(x) be the first derivative of n(x). Solve m(l) = 0.
-31, 1
What is o in 63*o - 4*o**4 + 14*o**2 - 63*o - 52*o**3 - 14*o**2 = 0?
-13, 0
Let u(g) be the first derivative of -1/10*g**5 + 0*g + 1/6*g**3 + 35 - 1/8*g**4 + 0*g**2 + 1/12*g**6. Let u(t) = 0. Calculate t.
-1, 0, 1
Let n(x) = x + 39. Let g be n(-24). Let m = g - 13. Solve 4 - 3*r + 12*r**2 - m*r**3 - 2*r**3 + 4*r - 13*r = 0.
1
Factor 656/17 - 2/17*d**2 + 66/17*d.
-2*(d - 41)*(d + 8)/17
Let j(g) = -g**3 + 10*g**2 + 14*g + 16. Let y be j(11). Let v = y - 48. Determine t so that 1 + t**4 + 406*t**3 - v - t**5 - 404*t**3 = 0.
-1, 0, 2
Let q(x) be the second derivative of x**6/40 - 3*x**5/2 + 36*x**4 - 432*x**3 + 2592*x**2 - 1490*x. Suppose q(l) = 0. Calculate l.
4, 12
Let y(p) = -p**3 + p**2 + p - 2. Let o(i) = -33*i**3 + 177*i**2 - 108*i - 72. Let a(x) = -o(x) + 36*y(x). Factor a(z).
-3*z*(z - 1)*(z + 48)
What is m in m**5 - 170*m**3 + 14*m**4 + 1289*m + 221 + 98*m**2 + 329 - 384*m + 90*m**2 - 16*m**2 = 0?
-22, -1, 5
Let z(f) be the first derivative of -f**6/15 + 3*f**5/10 + 3*f**4/2 + 5*f**3/3 + 11*f + 103. Let j(c) be the first derivative of z(c). Solve j(s) = 0 for s.
-1, 0, 5
Let w(z) be the third derivative of z**7/42 + 179*z**6/12 + 2640*z**5 - 13500*z**4 - 2120*z**2. Determine d so that w(d) = 0.
-180, 0, 2
Let f(x) be the first derivative of 16/45*x**3 - 1/30*x**4 + 226 + 4/3*x - 17/15*x**2. Find v such that f(v) = 0.
1, 2, 5
Let s be ((-496)/440)/(41 + (-20792)/506). Let -12/5*k + 0 + 18/5*k**4 - s*k**2 - 32/5*k**3 = 0. What is k?
-1, -2/9, 0, 3
Let i(z) = z**3 + 7*z**2 + 5*z + 4. Let s be i(-6). Let b(p) = -p**2 + 9*p + 14. Let n be b(s). Suppose -4*l - n + 2*l**3 - 3*l + l = 0. What is l?
-1, 2
Let x(g) be the third derivative of g**6/240 + 1193*g**5/60 + 118405*g**4/4 - 237606*g**3 - 2*g**2 - g + 1784. Factor x(o).
(o - 2)*(o + 1194)**2/2
Let x(v) be the first derivative of -2/9*v**3 - 102 - 1/9*v**2 + 1/18*v**4 + 2/3*v. Factor x(f).
2*(f - 3)*(f - 1)*(f + 1)/9
Let w(v) be the second derivative of v**5/60 - 34*v**4/9 - 139*v**3/6 + 468*v - 4. Factor w(z).
z*(z - 139)*(z + 3)/3
Determine o, given that -417605/4 - 1445/2*o - 5/4*o**2 = 0.
-289
Let t(m) = 2*m - 2 + 0*m - 5*m + m**2 + 4*m**4. Let r(h) = h**4 + h**2 - h - 1. Let i = -223 + 227. Let q(s) = i*t(s) - 12*r(s). Factor q(x).
4*(x - 1)**2*(x + 1)**2
Let u be ((