0 + f**7/980 - f**6/840 - 8*f**3/3 - 13. Let x(u) be the third derivative of k(u). Solve x(y) = 0.
0, 1
Factor -48/11*v + 0 - 76/11*v**2 + 14/11*v**3.
2*v*(v - 6)*(7*v + 4)/11
What is p in 48*p + 7*p**2 + 11*p**2 + 2*p**2 - 23*p**2 - 192 = 0?
8
Suppose -5 - 14 = -2*u - 3*r, 5*r - 23 = u. Let c(w) be the third derivative of 1/21*w**3 + 0*w + 0 + 1/42*w**4 + 1/210*w**5 - 3*w**u. Factor c(s).
2*(s + 1)**2/7
Let z be (-2)/(-1 + 1 + -1). Let i be 1/4*-6*z. Let v(w) = w**2 + 1. Let u(b) = 3*b**3 - 3*b - 6. Let r(y) = i*v(y) - u(y). Find p such that r(p) = 0.
-1, 1
Suppose 2*v + 10 = 7*v. Factor -3*n**v + 0*n + 0*n - 2*n**3 - n**2.
-2*n**2*(n + 2)
Let d(c) = c**2 + 136*c - 417. Let f be d(3). Solve -8/5*v**3 + 4/5 + 8/5*v + f*v**2 - 4/5*v**4 = 0 for v.
-1, 1
Suppose 5*g = 25, -2*s - 7*g + 54 = -3*g. Let c(i) = i**3 - 19*i**2 + 33*i + 17. Let r be c(s). Factor r*u**2 + 4/3*u**3 - 4/3*u + 0.
4*u*(u - 1)*(u + 1)/3
Determine x so that 28/9*x - 2/9*x**2 - 16/3 = 0.
2, 12
Let f(w) be the second derivative of -3*w**5/20 + 9*w**4/4 - 27*w**3/2 + 81*w**2/2 + 448*w - 2. What is u in f(u) = 0?
3
Let c = 53/133 + 4/133. Suppose 3*a = 5*b - 29, 4*a + 11*b - 6*b = 43. Let 9/7*w + c + 6/7*w**a = 0. Calculate w.
-1, -1/2
Let u(w) be the first derivative of -w**4/7 - 44*w**3/21 - 52*w**2/7 - 64*w/7 - 26. Factor u(a).
-4*(a + 1)*(a + 2)*(a + 8)/7
Let t = 34906/9 - 3878. Factor 4/9*n + 0*n**2 - t*n**3 + 2/9 - 2/9*n**4.
-2*(n - 1)*(n + 1)**3/9
Let i = 10 + -6. Let b = -91 + 94. Factor -b*u - 3*u**3 - 1 - 1 + i*u**3.
(u - 2)*(u + 1)**2
Let r be (-20)/(-6) - 9/27. Let 0*a**5 + 3*a**r + 3*a**5 - 2*a**5 + 3*a**4 + 3*a**2 - 2*a**2 = 0. Calculate a.
-1, 0
Let y be (-371)/(-126) - (-10)/(-4). Factor -y*u + 34/9*u**2 + 0.
2*u*(17*u - 2)/9
Let c(k) be the third derivative of k**7/16380 - k**6/2340 + 7*k**4/12 + 4*k**2. Let s(q) be the second derivative of c(q). Factor s(t).
2*t*(t - 2)/13
Determine l, given that 40 + 40*l**2 + 4*l**3 + 65 - 2 + 16 + 112*l - 23 = 0.
-6, -2
Let b = -12 - -15. Suppose 0 = 4*n - 20, 0*q + 13 = -q + b*n. Factor -8/3 - 1/3*a**3 - 4*a - 2*a**q.
-(a + 2)**3/3
Let p be -1 + (-4 - -2) + 15. Let t = p - 10. Factor 4*s + 6*s**3 - 17*s**4 + 9*s**4 + 6*s**4 - 2*s**5 + 10*s**t.
-2*s*(s - 2)*(s + 1)**3
Let p = 1640 - 1637. Solve -9/2*h - 1/2*h**3 + p*h**2 + 2 = 0 for h.
1, 4
Let i(a) = -a**3 - 24*a**2 + 25*a + 2. Let w be i(-25). Factor 11 + 0*l**w - 3*l**2 - 11*l + 4 - l.
-3*(l - 1)*(l + 5)
Let u be (-17)/680*-295 + 1 + -5. Let m(j) be the first derivative of -j - 5 - u*j**4 + 5/4*j**2 + 4*j**3. Find y, given that m(y) = 0.
-1/3, 2/9, 1
Let o(h) be the third derivative of -h**5/60 - 5*h**4/2 - 150*h**3 + 3*h**2 + 3. Factor o(t).
-(t + 30)**2
Suppose 5041/2 + 71*t + 1/2*t**2 = 0. Calculate t.
-71
Let p(g) be the second derivative of 2*g**6/15 + 2*g**5/5 - g**4 - 8*g**3/3 + 8*g**2 + 153*g. Factor p(w).
4*(w - 1)**2*(w + 2)**2
Let g = 45 - 44. Let q be ((-1)/3)/(2/((-2)/g)). Factor -q*u**2 + 0 - 1/3*u.
-u*(u + 1)/3
What is j in 81*j + 3/2*j**2 + 2187/2 = 0?
-27
Let u be (-2)/1*(1 + 5/(440/(-99))). Solve -2*l - u*l**2 - 4 = 0.
-4
Let a be (-6)/(-39) - (-4)/(-26). Suppose 5*m = m + 4*j, 3*m - j - 10 = a. Factor 0*p - 2/5*p**3 - 2/5*p**4 + 2/5*p**2 + 2/5*p**m + 0.
2*p**2*(p - 1)**2*(p + 1)/5
Let b = 8948 - 35549/4. Let a(m) be the second derivative of 1/84*m**7 + 135/4*m**3 - 11*m - 1/4*m**6 + 0 + 9/4*m**5 - 45/4*m**4 - b*m**2. Factor a(g).
(g - 3)**5/2
Let a(i) be the third derivative of -i**8/168 + i**7/105 + 3*i**6/20 + 11*i**5/30 + i**4/3 - 17*i**2 + 2. Factor a(m).
-2*m*(m - 4)*(m + 1)**3
Let s be 4/(-1) - 4/(28/(-49)). What is u in 402*u**s + 12*u**2 + 395*u**3 - 793*u**3 = 0?
-3, 0
Let n(y) be the second derivative of -1/105*y**6 + 1/42*y**4 + 0 + 17*y + 0*y**3 + 0*y**5 + 0*y**2. Let n(p) = 0. What is p?
-1, 0, 1
Factor 4*f**4 + 0*f**4 + 217970*f + 540*f**2 - 218942*f + 92*f**3 - 11664.
4*(f - 4)*(f + 9)**3
Let u(c) be the first derivative of c**4/30 + 4*c**3/15 - 7*c**2/15 - 50. Factor u(i).
2*i*(i - 1)*(i + 7)/15
Factor -10/11*p**3 - 24/11*p**4 + 0*p + 0 - 14/11*p**5 + 0*p**2.
-2*p**3*(p + 1)*(7*p + 5)/11
Let w(c) = c**2 + 13*c + 15. Let o be w(-11). Let n(f) = f + 9. Let t be n(o). Factor -2/3*k**3 - 2/3 - 2*k**t - 2*k.
-2*(k + 1)**3/3
Suppose 360 = 66*z + 30. Find j such that 0 + 0*j**2 - 3/4*j**z - 3/2*j**4 + 9/4*j**3 + 0*j = 0.
-3, 0, 1
Let -8*i**2 + 7*i**3 + 9*i**2 + 5*i**4 - 4*i**4 - 3*i**3 - 4*i**5 - 2*i**4 = 0. What is i?
-1, -1/4, 0, 1
Factor -285*d + 155 + 91 + 14 + 20 + 5*d**2.
5*(d - 56)*(d - 1)
Suppose 0*f = 3*k - f - 49, 68 = 4*k - 4*f. Suppose -2*u = 3*q + 2*q - k, 5*u = 15. Solve -20/3*r - q - 50/9*r**2 = 0 for r.
-3/5
Let l = 152 + -91. Suppose -l = -19*m - 4. Factor 3/5 - 3/5*w**2 - 3/5*w + 3/5*w**m.
3*(w - 1)**2*(w + 1)/5
Let w(m) = -m**4 - m**3 - 3*m**2 - m. Let r(h) = 5*h**4 + 3*h**3 - 14*h**2 + 14*h. Let o(t) = -r(t) - 2*w(t). Factor o(z).
-z*(z - 2)*(z + 3)*(3*z - 2)
Let s(l) be the third derivative of 0*l**4 + 8*l**2 + 0*l + 0 + 0*l**3 - 1/270*l**5. Factor s(z).
-2*z**2/9
What is z in -29 + 37 - 30 + 24*z + 2*z**2 - 4*z**2 = 0?
1, 11
Let b(p) be the second derivative of -p**4/8 + 3*p**3/4 + 3*p**2 - 38*p. Factor b(z).
-3*(z - 4)*(z + 1)/2
Factor 0 - 2/17*u + 12/17*u**2.
2*u*(6*u - 1)/17
Let h(s) = -4 + 1 - 3*s**2 + 4. Let i(n) = 2*n**2 - 2. Let k be i(0). Let q(w) = 7*w**2 - w - 3. Let f(b) = k*q(b) - 5*h(b). Let f(l) = 0. What is l?
-1
Let f = 74 + -69. What is r in -20*r + 2*r**4 + 5*r**3 + 10*r - f*r**4 + 5*r + r**2 + 2 = 0?
-1, 2/3, 1
Let f(w) = 2*w**3 + 6*w**2 + 2*w + 2. Let c(i) = i**3 + i**2 + 1. Suppose 12*b - 11*b - 4 = 0. Let o(x) = b*c(x) - f(x). Find y such that o(y) = 0.
-1, 1
Factor 676/7*d**4 + 16/7*d**2 + 0 + 0*d - 208/7*d**3.
4*d**2*(13*d - 2)**2/7
Let l(h) be the third derivative of 0*h + 7/96*h**4 - 1/48*h**5 - 1/12*h**3 - 1/96*h**6 - 1/672*h**8 + 1/120*h**7 + 0 + 29*h**2. Suppose l(x) = 0. Calculate x.
-1, 1/2, 1, 2
Suppose 3*q + l = -2, 4*q + 4*l = 2*q - 8. Suppose -9*k + 13*k = q. Factor 0*b + 0*b**2 + k*b**4 - 2/7*b**3 + 2/7*b**5 + 0.
2*b**3*(b - 1)*(b + 1)/7
Solve -22*q - 64/3 - 2/3*q**2 = 0 for q.
-32, -1
Let i(k) be the third derivative of -k**7/126 - 5*k**6/72 - k**5/6 + 5*k**4/18 + 20*k**3/9 - 16*k**2. Suppose i(h) = 0. What is h?
-2, 1
Suppose -n + 34 = 2*p + 32, 3*n = 2*p + 6. Find z such that 2/3 - 2/3*z - n*z**3 - 10/3*z**2 = 0.
-1, 1/3
Let d(p) = 2*p**2 + 328*p - 1690. Let m be d(5). Solve -1/4*r**3 + m*r**2 + 0*r + 1/4*r**4 + 0 = 0.
0, 1
Find r such that 0*r + 24/5*r**2 + 0 + 0*r**4 - 28/5*r**3 + 4/5*r**5 = 0.
-3, 0, 1, 2
Let d = 2456/2005 - 10/401. Factor 9/5*u + 3/5*u**2 + d.
3*(u + 1)*(u + 2)/5
Let d(s) be the first derivative of 2*s**5/35 + 274*s**4/7 + 75076*s**3/7 + 10285412*s**2/7 + 704550722*s/7 + 890. Determine i, given that d(i) = 0.
-137
Let y = 8939/10 - 1787/2. Solve -2*v + 12/5 - y*v**2 = 0 for v.
-6, 1
Let v(r) be the first derivative of -r**3/3 + 7*r**2 - 33*r + 121. Find t such that v(t) = 0.
3, 11
Let f be (-21)/(-12) - (8 - 7). Let o(k) be the first derivative of 0*k**3 - 1 + 0*k**2 - f*k**4 + 0*k. Solve o(a) = 0.
0
Suppose 2*j - 2766 = -h + 610, 5*h - 16805 = 5*j. Let a be (-17)/(h/(-300)) + (-8)/6. Factor -4/11*q**2 + 0*q + 0 + 6/11*q**3 - a*q**4.
-2*q**2*(q - 2)*(q - 1)/11
Let z be ((-12)/14)/(1419/(-154) + 9). Factor 14/3*i**2 - z - 38/3*i.
2*(i - 3)*(7*i + 2)/3
Let q = 191/21 + -6691/798. Let g = 3609/266 - q. Let 12*j**3 - g*j**4 + 0*j - 24/7*j**2 + 0 + 27/7*j**5 = 0. Calculate j.
0, 2/3, 2
Let h(o) be the first derivative of -o**5/20 - o**4/6 - o**3/6 + 34*o - 4. Let i(g) be the first derivative of h(g). Solve i(v) = 0 for v.
-1, 0
Let w(j) be the third derivative of j**6/120 - 17*j**5/420 + j**4/28 + j**2. Solve w(c) = 0 for c.
0, 3/7, 2
Let k(d) be the third derivative of d**5/240 + 5*d**4/32 - 2*d**3/3 + 2*d**2 - 231*d. Determine v, given that k(v) = 0.
-16, 1
Let m = -2232/7 + 2152/7. Let g = m - -369/28. Determine x so that 5/4*x - 1/4*x**3 - g*x**2 - 1/4 + 2*x**4 - x**5 = 0.
-1, 1/2, 1
Let g(a) be the second derivative of 3/10*a**2 + 1/60*a**4 - 2/15*a**3 + 5*a + 0. Suppose g(p) = 0. What is p?
1, 3
Let p(s) = -15*s + 3. Suppose 2*n - 5*b = -16, -3*b + 20 = 2*n + b. Let m(y) = -y**2 - 13*y + 2. Let u(x) = n*p(x) - 3*m(x). Suppose u(o) = 0. Calculate o.
-3, 0
What 