1/36. Let u(s) be the second derivative of -1/6*s**2 + 0 + 1/36*s**4 + a*s**3 - 7/120*s**5 - 3*s. Let u(r) = 0. Calculate r.
-1, 2/7, 1
Let t(f) be the third derivative of -5/39*f**4 - 4/39*f**3 + 0 - 7/780*f**6 - 23/390*f**5 + 0*f - 5*f**2. What is i in t(i) = 0?
-2, -1, -2/7
Let 0 - 1/6*q**4 + 1/3*q**5 - q**3 - 1/6*q**2 + 1/3*q = 0. Calculate q.
-1, 0, 1/2, 2
Suppose -330*t - 371 + 1089 = -272. What is o in -2/11*o**t - 2/11 + 2/11*o**2 + 2/11*o = 0?
-1, 1
Let r = 20/29 + -269/348. Let q = 5/12 - r. Suppose -7/4*a + a**2 - q = 0. Calculate a.
-1/4, 2
Let x(v) be the third derivative of 7/100*v**5 + 0*v + 1/200*v**6 + 36*v**2 + 9/10*v**3 - 2 + 3/8*v**4. Determine y so that x(y) = 0.
-3, -1
Let q(n) be the first derivative of n**4/8 - 41*n**3/6 + 470. Let q(h) = 0. Calculate h.
0, 41
Let k be (-4816)/32 - (-3)/(-2). Let i = -452/3 - k. Factor 0*d - 4/3*d**3 + 0 - i*d**2.
-4*d**2*(d + 1)/3
Suppose -74 = -4*o + z, 3*o + z = -o + 78. Suppose 0 = -4*n + 5 + o. Find g such that 0*g - g**3 - n*g**2 + 3*g + 4*g**3 = 0.
0, 1
Let s(b) = -b**3 + 56*b**2 - 111*b + 165. Let m be s(54). Let g be (-1*4)/(12/(-32)). Factor 2/3*k**5 + 38/3*k**m - 50/3*k**2 + g*k - 14/3*k**4 - 8/3.
2*(k - 2)**2*(k - 1)**3/3
Let s(a) be the first derivative of -a**3/4 + 33*a**2/8 - 15*a/2 + 438. Find n such that s(n) = 0.
1, 10
Find v such that -123/2*v + 60 + 3/2*v**2 = 0.
1, 40
Suppose 29 = 17*r - 5. Solve -9*t**4 + 19*t**4 - 4*t**2 - 5*t - 6*t**r + 5*t**5 = 0 for t.
-1, 0, 1
Let x(j) = 2*j**4 - 6*j**3 - 8*j**2 - 6*j. Let l(w) = -w**3 - w**2 - w. Let s(k) = 2*k**3 - 2*k - 1. Let f be s(-1). Let h(z) = f*x(z) + 6*l(z). Solve h(i) = 0.
-1, 0, 1
Let n(m) = -3*m**2 + 11*m + 7. Suppose -15 - 34 = 7*l. Let o(d) = 2*d**2 - 6*d - 4. Let r(u) = l*o(u) - 4*n(u). Factor r(z).
-2*z*(z + 1)
Suppose -5*n - 2*d + 57 = 0, 9*n - 5*d = 4*n + 50. Factor -8*x - 36*x**3 + n*x**2 - 30*x**2 - 25*x**2.
-4*x*(x + 1)*(9*x + 2)
Let c be (-133)/6 + 1/6. Let b be (-84)/c + (-4)/(-22). What is k in 5*k - 8 - b*k + 4*k**2 - 5*k = 0?
-1, 2
Let w(c) be the third derivative of -c**5/540 - 31*c**4/216 - 29*c**3/27 + 13*c**2. Factor w(d).
-(d + 2)*(d + 29)/9
Let y(p) = p**4 + p**3 - p**2 - p + 3. Let t(b) = -4. Let k(q) = q**3 - 8*q**2 - 10*q + 13. Let r be k(9). Let o(j) = r*y(j) + 3*t(j). Factor o(x).
4*x*(x - 1)*(x + 1)**2
Let k(c) be the first derivative of -4*c**3/3 - 240*c**2 - 14400*c + 138. Determine n so that k(n) = 0.
-60
Let o(h) be the third derivative of -112/15*h**7 - 41*h**2 + 16/3*h**3 + 0 + 134/15*h**5 - 161/30*h**6 + 0*h + 49/12*h**8 + 34/3*h**4. Let o(l) = 0. What is l?
-2/7, 1
Let m = 14/43 - -74/301. Let q = -14 - -17. Factor 0*k + m - 3/7*k**2 + 1/7*k**q.
(k - 2)**2*(k + 1)/7
Let l = 7972 - 40538/5. Let w = 136 + l. Factor -w*h**2 + 4/5*h + 2/5*h**4 - 4/5*h**3 + 0.
2*h*(h - 2)*(h - 1)*(h + 1)/5
Let b(k) be the third derivative of -13*k**2 - 1/8*k**4 + 0*k + 0 + 1/60*k**5 + 1/3*k**3. Factor b(l).
(l - 2)*(l - 1)
Let l be (-1)/((-12)/8)*(-1 + 7). Suppose 0 = l*v - m - 12, 4*m + m = 2*v - 24. Determine a, given that -1/5 + 0*a + 1/5*a**v = 0.
-1, 1
Determine l, given that 5*l + 110*l**2 + 5 - 3*l**3 - l**3 - 115*l**2 - l**3 = 0.
-1, 1
Let y be (-6)/(25*(-28)/70). Suppose y*a**3 - 192/5 + 9*a**2 + 144/5*a = 0. Calculate a.
-8, 1
Let k(r) = -r - 3. Let p be k(-5). Solve 43*l**5 + 72*l - 120*l**p - 84*l**2 + 29*l**3 - 143*l**5 + 220*l**4 + 15*l**3 = 0 for l.
-1, 0, 3/5, 2
Factor 629*u**2 + 1738*u**2 - 372*u + 12 + 516*u**2.
3*(31*u - 2)**2
Let p(w) be the third derivative of w**8/840 - 2*w**7/105 - 11*w**6/300 - 358*w**2. Find i, given that p(i) = 0.
-1, 0, 11
Let h be 34/70 + 10 + (-720)/70. Let x(m) be the first derivative of -10 + h*m**3 + 12/5*m + 6/5*m**2. Factor x(y).
3*(y + 2)**2/5
Suppose -m - 3 = -5. Let s(v) be the second derivative of 0 + 0*v**2 - 1/6*v**4 + m*v - 1/35*v**6 - 4/35*v**5 - 2/21*v**3. Factor s(x).
-2*x*(x + 1)**2*(3*x + 2)/7
Let g be 6/(-18)*(-9 + (-4 - -7)). Let t = -63 + 67. Determine n so that -1/2*n**3 + 1/4 + 1/4*n**t + 1/4*n**5 + 1/4*n - 1/2*n**g = 0.
-1, 1
Let t(q) be the second derivative of -8*q + 4*q**2 - 22/3*q**3 - 13/3*q**4 + 0. Solve t(l) = 0 for l.
-1, 2/13
Let p be (8/(-18))/((-24)/108). Find g, given that -18*g - 19*g + 6*g**5 - 10*g**3 + 41*g + p*g**2 - 2*g**4 = 0.
-1, -2/3, 0, 1
Let g be (-4)/(-18) - (-250)/90. Let l be 0*(g - 21/6). Factor -34*r - r**2 + 40*r - 9 + l*r**2.
-(r - 3)**2
Let d(w) be the third derivative of -w**7/560 + 3*w**5/40 + w**4/4 + 41*w**2. Factor d(j).
-3*j*(j - 4)*(j + 2)**2/8
Let i be 4396/105 + ((-42)/(-45))/7. Factor 24 - i*q**2 + 40*q**2 - 16.
-2*(q - 2)*(q + 2)
Let i(w) = 18*w + 174. Let t(x) = x**2 - 19*x - 176. Let v(h) = -2*i(h) - 3*t(h). Factor v(z).
-3*(z - 12)*(z + 5)
Let k = 5357 - 5353. Solve 5/2*v**2 - 1/2*v**3 + 2 - k*v = 0 for v.
1, 2
Let f(h) be the first derivative of h**3/3 - h**2/2 - 4*h + 5. Let j be f(3). Factor 9*z**3 - 2*z**3 - 3*z - 3*z**j + 3*z**4 - 4*z**3.
3*z*(z - 1)*(z + 1)**2
Let u(j) be the first derivative of 8/9*j**2 - 4/45*j**5 + 4/9*j**3 - 16/9*j - 27 - 2/9*j**4. Factor u(s).
-4*(s - 1)**2*(s + 2)**2/9
Let -452/5*z + 51076/5 + 1/5*z**2 = 0. Calculate z.
226
Solve 12/5*m**4 - 4/5*m**2 + 24/5 + 76/5*m - 44/5*m**3 = 0.
-1, -1/3, 2, 3
Let o(r) be the first derivative of -r**6/2 - 18*r**5/5 - 9*r**4 - 10*r**3 - 9*r**2/2 - 382. Suppose o(b) = 0. What is b?
-3, -1, 0
Let j(o) = -o**3 - 3*o**2 + o + 5. Let t be j(-3). Factor 4*p**t + 4*p**3 + p**2 - 9*p**3.
-5*p**2*(p - 1)
Let h(l) be the first derivative of -1/4*l**4 + 1/3*l**6 + 0*l - 1/2*l**2 - l**3 - 23 + 3/5*l**5. Solve h(p) = 0.
-1, -1/2, 0, 1
Let y(t) be the third derivative of t**5/20 - 49*t**4/4 + 2401*t**3/2 - 79*t**2. Factor y(f).
3*(f - 49)**2
Let k(f) be the second derivative of f**5/35 - 2*f**4/21 - 8*f**3/21 + 16*f**2/7 + 9*f - 3. Determine g so that k(g) = 0.
-2, 2
Let x(j) be the third derivative of 1/112*j**8 + 0*j**3 + 3/70*j**7 + 0*j - 1/4*j**4 - 3/20*j**5 + 0 + 1/40*j**6 - 16*j**2. Let x(h) = 0. Calculate h.
-2, -1, 0, 1
Let y(o) = -o + 8. Let s be y(6). Suppose s*i + 2*i**2 + i**2 + 3*i**2 - i**2 = 0. What is i?
-2/5, 0
Let m be 4/3 + 1/(-3). Let x be ((-31 - m)/(-1))/1. Factor 16 - 80 + x*s - s**2 - 3*s**2.
-4*(s - 4)**2
Suppose 2/5*l**3 + 0 + 6*l - 32/5*l**2 = 0. Calculate l.
0, 1, 15
Let v(s) be the first derivative of s**4/4 - 46*s**3/3 + 44*s**2 + 665. Factor v(p).
p*(p - 44)*(p - 2)
Let j be (-7)/28*-4*4. Let k(i) be the second derivative of 1/12*i**j + 0 - 5*i + 0*i**2 + 1/6*i**3. Find a, given that k(a) = 0.
-1, 0
Let w(a) = -2*a**3 - a**2 - 3*a + 2. Let z be w(-2). Factor -z*i + 4*i**2 - 3*i**2 + 19*i**2 - 5*i**2.
5*i*(3*i - 4)
Suppose -4*m - 5*z + 5 = 3, m + 3*z + 3 = 0. Let b(i) be the first derivative of -1/8*i**2 + 1/2*i - 5 - 1/12*i**m. Solve b(r) = 0.
-2, 1
Let c(d) = d**3 + 8*d**2 - 4*d - 12. Let n be c(-8). Suppose -4*q = -5*g - 13 - 7, 0 = -q + 5*g + n. Factor q - 14/5*h**4 + 0*h + 24/5*h**3 + 8/5*h**2.
-2*h**2*(h - 2)*(7*h + 2)/5
Suppose 0 = -t - 0*t + 2. Let w(a) = -a - 17. Let r be w(-19). Factor -3*q**2 + 0*q**t + 2 + 4*q**r + q - 4*q.
(q - 2)*(q - 1)
Let n(l) = 4*l**3 + 3*l**2 + 2*l. Let p be -13 - -16 - (-1 + 2). Let t(d) = d**4 - d**3 - d. Let x(h) = p*n(h) + 2*t(h). Suppose x(s) = 0. Calculate s.
-1, 0
Suppose 30 = 2*s - 4*z - 10, -4*z = 5*s - 44. Suppose 0 = 4*y + 4 - s. Factor -27*m**4 - m**4 - 12*m**3 - 4*m - 4*m - 26*m**3 - 25*m**y - 1 - 8*m**5.
-(m + 1)**2*(2*m + 1)**3
Let o(q) be the second derivative of -q**5/30 - 4*q**4/9 - 16*q**3/9 + 8*q - 4. Let o(k) = 0. Calculate k.
-4, 0
Find w such that -3 - 12*w**2 - 24*w - 49*w**2 + 16*w**2 = 0.
-1/3, -1/5
Let v(k) be the second derivative of -k**5/60 - k**4/12 + k**3/18 + k**2/2 + 40*k. Determine f, given that v(f) = 0.
-3, -1, 1
Let b(y) be the first derivative of -2*y**5/15 - y**4/2 + 2*y**3/3 + 11*y**2/3 + 4*y + 8. Find v such that b(v) = 0.
-3, -1, 2
Let m(r) be the second derivative of -r**5/30 + 7*r**4/9 + r**3/9 - 14*r**2/3 - 31*r. Suppose m(w) = 0. Calculate w.
-1, 1, 14
Let r(v) = -2*v**3 - 113*v**2. Let u(l) = 8*l**3 + 453*l**2. Let q(b) = 22*r(b) + 6*u(b). Factor q(p).
4*p**2*(p + 58)
Let k(x) = 21*x**4 - 153*x**3 + 606*x**2 - 1152*x + 768. Let q(t) = -5*t**4 + 38*t**3 - 152*t**2 + 288*t - 192. Let n(c) = 2*k(c) + 9*q(c). Factor n(o).
-3*