5
Let w(y) be the third derivative of -y**7/105 - 7*y**6/60 + 13*y**5/10 - 53*y**4/12 + 22*y**3/3 + 82*y**2. Let w(u) = 0. What is u?
-11, 1, 2
Let o(w) = -w**2 + 10*w - 6. Let k be o(13). Let t = -30 - k. Find q, given that q**2 + t*q**2 + 4*q - 2 + 2 = 0.
-1/4, 0
Factor -1/4*r**2 - 25/2 - 15/4*r.
-(r + 5)*(r + 10)/4
Let v(x) be the second derivative of -32*x**5/75 - 104*x**4/45 - 37*x**3/9 - 10*x**2/3 + 113*x. Determine p, given that v(p) = 0.
-2, -5/8
Let j be 156/72 - (3 - 18/12). Solve -2/3 - j*f**2 + 4/3*f = 0.
1
Suppose 4*o = -5*s + 28, -4*o + 652*s - 651*s = -4. Solve 0*m**o + 0 + 2/11*m**4 + 0*m - 2/11*m**3 = 0.
0, 1
Factor -172*i + 34814*i**2 - 34809*i**2 - 473*i.
5*i*(i - 129)
Let z(j) be the first derivative of 2*j**3/27 + 242*j**2/9 + 29282*j/9 - 478. Factor z(s).
2*(s + 121)**2/9
Let -8*g + 79/4*g**4 + 0 - 51*g**3 + 41*g**2 - 7/4*g**5 = 0. What is g?
0, 2/7, 1, 2, 8
Let b(j) be the third derivative of 0*j**6 - 2/3*j**4 + 0*j - j**3 + 1/105*j**7 - j**2 + 0 - 1/5*j**5. Factor b(c).
2*(c - 3)*(c + 1)**3
Let c = -24359 - -24362. Factor 0*i**c + 2/3*i**2 - 1/3 - 1/3*i**4 + 0*i.
-(i - 1)**2*(i + 1)**2/3
Let v(j) be the first derivative of -5*j**6 - 5/2*j**4 - 38 + 0*j + 0*j**3 + 0*j**2 - 7*j**5. Let v(n) = 0. What is n?
-2/3, -1/2, 0
Let r(d) be the second derivative of 1/66*d**4 + 0 - 4/33*d**3 + 4/11*d**2 + 11*d. Let r(j) = 0. What is j?
2
Factor 0 - 10/7*h**2 + 2/7*h**4 - 6/7*h - 2/7*h**3.
2*h*(h - 3)*(h + 1)**2/7
Let g(f) be the second derivative of 25*f**7/168 - 79*f**6/24 + 2179*f**5/80 - 4685*f**4/48 + 350*f**3/3 - 125*f**2/2 + 221*f. Factor g(x).
(x - 5)**3*(5*x - 2)**2/4
Let p = 3236/35 + -462/5. Let v(u) be the first derivative of 0*u**2 + 1/14*u**4 + 0*u + 0*u**3 - 6 - p*u**5. What is k in v(k) = 0?
0, 1
Let j(g) be the first derivative of -g**6/36 + 7*g**5/30 + g**4/24 - 7*g**3/18 + 259. Determine x so that j(x) = 0.
-1, 0, 1, 7
Let m be -2*(-2 + 3)/(2 + 0 + -15). Factor -m*h**4 - 32/13*h + 0 - 48/13*h**2 - 18/13*h**3.
-2*h*(h + 1)*(h + 4)**2/13
Let b = -29 + 25. Let g(q) = -5*q**2. Let x(k) = 5*k**2 + k. Let v(h) = b*g(h) - 5*x(h). Determine u so that v(u) = 0.
-1, 0
Let r(j) = -j**2 + 11*j - 9. Let m be r(9). Solve -m*i + 6 - 13*i**2 + 10*i**2 + 3*i**5 - 9*i**4 - 3 + 9*i**2 + 6*i**3 = 0 for i.
-1, 1
Let m be (-206)/(-309) + (-1 - -1) - -1. Factor -m*p**2 - 10/3 - 9*p.
-(p + 5)*(5*p + 2)/3
Suppose -o - 3*o = -24. Suppose 0 = -o*a + 2*a + 12. Factor 6*i**3 + a*i**2 - i**2 - 2*i - 2*i**4 - 4*i**3.
-2*i*(i - 1)**2*(i + 1)
Let o be 10/(-3)*3/(-2). Suppose -2*g - k + o*k + 20 = 0, 4*g = -5*k - 25. Solve 1 + g - 4 + 6*r - 3*r**2 = 0.
1
Let h(t) be the first derivative of 4*t**5/5 - 18*t**4 + 68*t**3/3 - 84. Solve h(s) = 0.
0, 1, 17
Let r(z) be the second derivative of -12*z + 5/9*z**3 - 2*z**2 - 1/18*z**4 + 0. Factor r(j).
-2*(j - 3)*(j - 2)/3
Let o = -2483 + 24831/10. Find c, given that -c**2 - 1/2*c**4 + c**3 - o + 1/2*c + 1/10*c**5 = 0.
1
Let h(w) be the third derivative of -w**7/70 - 3*w**6/40 - 3*w**5/20 - w**4/8 + 108*w**2. Factor h(q).
-3*q*(q + 1)**3
Factor 22/7*y**5 + 6/7*y + 4/7 - 12*y**4 - 64/7*y**2 + 116/7*y**3.
2*(y - 1)**4*(11*y + 2)/7
Let r = 104 + -1350/13. Factor -r*j**3 + 0*j + 2/13*j**2 + 0.
-2*j**2*(j - 1)/13
Let b(v) be the first derivative of -v**6/14 - 3*v**5/7 - 6*v**4/7 - 4*v**3/7 + 10. Suppose b(o) = 0. What is o?
-2, -1, 0
Factor 2 + 35/2*h**2 - 13*h + 49/4*h**3.
(h + 2)*(7*h - 2)**2/4
Let o(l) be the second derivative of -32/3*l**6 - 94/5*l**5 + 0*l**2 + 0 - 16*l**4 - 6*l**3 + 6*l - 50/21*l**7. Factor o(w).
-4*w*(w + 1)**2*(5*w + 3)**2
Suppose 10*l = 5*l + 25. Suppose 12 = -l*v + 67. Factor -a**4 - v + a**5 - 2*a**3 + 11.
a**3*(a - 2)*(a + 1)
Let k(l) be the first derivative of l**6/14 + 12*l**5/35 + 3*l**4/7 - 2*l**3/7 - 15*l**2/14 - 6*l/7 - 171. Let k(b) = 0. Calculate b.
-2, -1, 1
Let l = 48972/5 - 9794. Let -2/5*z**4 + 0*z + l*z**3 - 2/5*z**5 + 2/5*z**2 + 0 = 0. What is z?
-1, 0, 1
Let h(s) be the third derivative of s**5/48 + 605*s**4/48 + 73205*s**3/24 - 23*s**2 + s. What is u in h(u) = 0?
-121
Let b = 351 - 347. Let l(v) be the first derivative of 0*v + 1/3*v**2 - 1/6*v**b + 0*v**3 - 5. Suppose l(s) = 0. Calculate s.
-1, 0, 1
Solve 1326 - 20*a - a**2 - 1326 = 0.
-20, 0
Factor 4*o - 342 + 342 + 5*o**2 + o**3.
o*(o + 1)*(o + 4)
Suppose 0 = -3*l - 3, 0 = -v - 3*l - 10 + 16. What is q in -72/7*q + 219/7*q**3 - 51/7*q**2 - 21*q**5 + v*q**4 - 12/7 = 0?
-1, -2/7, 1
Let b(m) = -m**2 + 18*m + 24. Let v be b(19). Solve -15*f**3 + 2*f**v - 81*f - 10*f**4 + 20*f**2 + 3*f**5 + 101*f = 0.
-1, 0, 2
Let i(w) be the second derivative of 1/110*w**5 - 21*w + 0 - 1/11*w**4 + 0*w**2 - 7/33*w**3. Factor i(l).
2*l*(l - 7)*(l + 1)/11
Let o(p) = p**2 - 7*p - 4. Let y be o(6). Let h = y - -15. Factor -h*l**3 + 2*l**3 + 3*l + 1 - 2 + 2*l**4 - l**2.
(l - 1)**2*(l + 1)*(2*l - 1)
Let d(q) = -q**2 - 148*q + 2807. Let f be d(17). Let 8/5*n**f + 4/5 + 12/5*n = 0. What is n?
-1, -1/2
Let q = 19449/35 - 3887/7. Let -4/5*y + q*y**2 + 0 = 0. What is y?
0, 2
Let l be (-1)/(-2)*(-2)/(-5). Suppose 12*f - 17*f + 15 = 0. Factor -1/5*x**f - 2/5*x**2 + 0 + l*x**4 + 0*x.
x**2*(x - 2)*(x + 1)/5
Suppose -16216 - 18*u + 16000 - 28*u + 2*u**2 = 0. What is u?
-4, 27
Let s(o) be the third derivative of -o**9/7560 + o**8/1680 - o**7/1260 + 5*o**4/12 - 17*o**2. Let g(m) be the second derivative of s(m). Factor g(l).
-2*l**2*(l - 1)**2
Let p(m) be the second derivative of 7*m**5/50 + m**4/15 - 28*m**3/15 - 8*m**2/5 + 31*m + 1. Factor p(t).
2*(t - 2)*(t + 2)*(7*t + 2)/5
Let u(m) be the third derivative of m**7/20160 - m**6/2880 + m**5/960 + 11*m**4/24 - 22*m**2. Let r(h) be the second derivative of u(h). Factor r(l).
(l - 1)**2/8
Let p(y) be the third derivative of y**7/1260 - y**6/180 + y**5/90 + 5*y**3/3 - 7*y**2. Let f(w) be the first derivative of p(w). Solve f(o) = 0 for o.
0, 1, 2
Factor -2/7*d**4 + 36/7*d - 4/7*d**3 + 0 + 18/7*d**2.
-2*d*(d - 3)*(d + 2)*(d + 3)/7
Suppose -4*d + 1 = -3*d. Factor 6*n**2 - d - 4*n**2 - 3 - 2*n.
2*(n - 2)*(n + 1)
Let r(s) = 3*s**3 + 47*s**2 - 148*s - 192. Let f(j) = -2*j**3 - 24*j**2 + 74*j + 96. Let g(m) = 5*f(m) + 3*r(m). What is c in g(c) = 0?
-1, 6, 16
Factor 12/19 + 2/19*g**2 + 10/19*g.
2*(g + 2)*(g + 3)/19
Let v be (-1733)/13864 - 17*(-1)/8. Find a, given that -6/7*a**v + 0 - 2/7*a**3 + 6/7*a**4 - 2/7*a**5 + 4/7*a = 0.
-1, 0, 1, 2
Let f(v) be the first derivative of 8*v**2 - 4/3*v**3 - 8 + 0*v + 1/16*v**4. Factor f(h).
h*(h - 8)**2/4
Let a(d) be the first derivative of d**6/120 + d**5/40 - d**4/16 - d**3/6 - 17*d**2/2 + 29. Let p(r) be the second derivative of a(r). Factor p(q).
(q - 1)*(q + 2)*(2*q + 1)/2
Let j(q) = -3*q + 28. Let a be j(-24). Factor a*w**4 - 64*w**5 + 4*w**2 - 36*w**3 + 26*w**4 - 30*w**4.
-4*w**2*(w - 1)*(4*w - 1)**2
Let q(a) be the second derivative of a**7/42 - a**6/3 + 9*a**5/5 - 9*a**4/2 + 9*a**3/2 + 21*a. Factor q(w).
w*(w - 3)**3*(w - 1)
Let p(f) be the first derivative of -4*f**3/3 + 104*f**2/3 + 48*f + 631. Factor p(l).
-4*(l - 18)*(3*l + 2)/3
Let x(s) be the third derivative of -s**8/252 + 16*s**7/315 - 2*s**6/15 - 2*s**5/45 + 13*s**4/18 - 4*s**3/3 + s**2 + 31*s. Find h such that x(h) = 0.
-1, 1, 6
Let v(m) = 2*m**4 - 2*m**2. Let u(j) = j**4 + j**3 - j**2 - j. Let q(c) = -3*u(c) + 2*v(c). Factor q(o).
o*(o - 3)*(o - 1)*(o + 1)
Let u(t) = -t**2 - 396*t - 13923. Let q be u(-39). Let 2/5*n**5 + 0 + 6/5*n**2 + q*n + 14/5*n**3 + 2*n**4 = 0. What is n?
-3, -1, 0
Factor -4*i**2 - 3*i**2 - 44*i - 24 - 15*i**2 + 6*i**2 + 4*i**3.
4*(i - 6)*(i + 1)**2
Let r = -7951 - -39758/5. Determine j so that 4/5*j + 1/5*j**2 + r = 0.
-3, -1
Let m(c) be the second derivative of 1/42*c**7 + 0 + 1/15*c**6 + 7/6*c**3 - 2/5*c**5 + 1/6*c**4 - 33*c - 2*c**2. Factor m(w).
(w - 1)**3*(w + 1)*(w + 4)
Let k(o) be the third derivative of o**8/15120 - 13*o**7/3780 + o**5/30 - o**4/24 + 14*o**2. Let p(y) be the third derivative of k(y). Factor p(h).
4*h*(h - 13)/3
Let r = 1006/3 - 334. Let y = -26 + 82/3. Factor r*w**3 + y*w + 0 - 8/3*w**2.
4*w*(w - 1)**2/3
Let h = -15 - -23. Let w(c) be the first derivative of 0*c**4 + 2/15*c**5 - 2/9*c**3 + 1/18*c**6 + 0*c - 1/6*c**2 - h. Determine b so that w(b) = 0.
-1, 0, 1
Let k = -93133/7 + 13305. Let -k*n**3 + 0 - 2/7*n**5 + 4/7*n + 6/7*n**2 - 6/7*n**4 = 0. Calculate n