11*t**7/280 - 7*t**6/40 - 67*t**5/240 - t**4/8 - 7*t**2 + 18*t. Suppose d(k) = 0. Calculate k.
-4, -3, -1, -1/4, 0
Factor 28*m + 37*m**5 - 23*m**4 + 22*m + 165*m**3 - 29*m**5 + 155*m**2 - 3*m**5 + 88*m**4.
5*m*(m + 1)**3*(m + 10)
Let n = -8 - -4. Let w be 43/9 + n/(-18). Solve -w*y**4 - 3*y**3 - 2*y**5 + 7*y**3 - 2*y + 5*y**4 = 0.
-1, 0, 1
Let s(f) be the second derivative of -f**4/30 + 5*f**3/3 + 84*f**2/5 + 5*f - 4. Suppose s(b) = 0. Calculate b.
-3, 28
Let d(o) be the first derivative of -15/2*o**2 + 5/3*o**3 + 23 + 10*o. Suppose d(n) = 0. What is n?
1, 2
Suppose -44 = 2*x - 6*x. Let l be -1 + x/8 - (-13)/520. Find q such that -l + 2/5*q**2 + 0*q = 0.
-1, 1
Let m(a) be the second derivative of -11*a**6/200 + 9*a**5/100 + a**4/20 - 17*a**2/2 - 14*a. Let n(i) be the first derivative of m(i). Factor n(v).
-3*v*(v - 1)*(11*v + 2)/5
Factor -13/3*f**2 - 1/6 + 9/2*f.
-(f - 1)*(26*f - 1)/6
Let v(s) be the third derivative of -s**6/30 + 7*s**5/15 - 7*s**4/3 + 16*s**3/3 + 2*s**2 + 8*s. Find o, given that v(o) = 0.
1, 2, 4
Let m(j) = -8*j**2 - 5*j + 15. Let p(q) = -13*q**2 - 11*q + 29. Let v(x) = 5*m(x) - 3*p(x). Solve v(f) = 0 for f.
2, 6
What is u in 3/2*u**2 + 0 - 15/2*u = 0?
0, 5
Let i(l) = 17*l**2 + 416*l + 5417. Let n(c) = 4*c**2 + 104*c + 1354. Let v(y) = -4*i(y) + 18*n(y). Factor v(s).
4*(s + 26)**2
Factor 8/3*t**2 + 4/3*t**3 - 20/3*t - 8.
4*(t - 2)*(t + 1)*(t + 3)/3
Let q be 1 - (-17 + (-984)/(-60)). Factor 4/5 + q*j + 4/5*j**2.
4*(j + 1)**2/5
Factor 9 + 9/2*q + 1/2*q**2.
(q + 3)*(q + 6)/2
Let o(x) be the first derivative of -5 - 4*x**2 + 6*x + 2/3*x**3. Determine a, given that o(a) = 0.
1, 3
Let g be (4/(-6))/(5 + 61/(-12)). Suppose 0 = o - 2*q - 2, -g*q + 3*q - 10 = -5*o. Solve 2/7 - 4/7*y + 2/7*y**o = 0.
1
Let o be (4/(-1))/(3 + -11 + 6). Suppose 0 = -4*z + 15 + 1. Determine j, given that j**3 - 5*j**2 - 6*j**3 + 2 + 2*j**3 + o + z*j = 0.
-2, -2/3, 1
Let w(u) = u**2 + u + 1. Let c(q) be the second derivative of 0 + 4/3*q**3 + 4/3*q**4 + 5*q**2 - 6*q. Let m(v) = 2*c(v) - 20*w(v). Factor m(y).
4*y*(3*y - 1)
Let q = -41 - -48. Let p(s) = -645*s**2 + 485*s - 95. Let d(u) = 967*u**2 - 727*u + 142. Let y(k) = q*p(k) + 5*d(k). Determine x, given that y(x) = 0.
3/8
Determine w, given that 0 + 4/11*w**3 - 2/11*w**4 - 4/11*w + 2/11*w**2 = 0.
-1, 0, 1, 2
Let f(d) = 19*d**2 + 409*d - 750. Let q(v) = -9*v**2 - 194*v + 375. Let w(g) = 4*f(g) + 9*q(g). Find l such that w(l) = 0.
-25, 3
Let w(v) = v**3 - v**2 + 1. Let a(i) = 2*i**3 - 6*i**2 + i + 6. Let k(t) = a(t) - 3*w(t). Determine d, given that k(d) = 0.
-3, -1, 1
Let j(u) be the first derivative of u**8/2016 - 3*u**2/2 + 14. Let d(b) be the second derivative of j(b). Suppose d(i) = 0. Calculate i.
0
Suppose r = -d + 6, 0*d - 3*d = 2*r - 21. Suppose -d = -2*w + o, -4*w + 24 = w - 2*o. Factor w*k**2 - 6*k**3 + k + 3*k**4 - 3*k - k**4.
2*k*(k - 1)**3
Let w(p) be the second derivative of 0*p**2 - 7/18*p**4 + 1/6*p**5 + 0 - 1/45*p**6 + 18*p + 1/3*p**3. Factor w(f).
-2*f*(f - 3)*(f - 1)**2/3
Let n be 1/6 - (-29)/174. Factor 0*w**3 + n*w**4 - 1/3*w**2 + 1/6*w**5 - 1/6*w + 0.
w*(w - 1)*(w + 1)**3/6
Let l(c) = 3*c + 9. Let s be -5*(24/15 + -1). Let k be l(s). Solve 2/5*r**3 + k*r + 0 - 2/5*r**2 = 0.
0, 1
Let l = -728 - -725. Let d(n) = -n**3 + 7*n**2 + 3*n - 3. Let t(a) = -5 - 3 + 24*a**2 - 4*a**3 - 4*a**2 + 8*a. Let p(v) = l*t(v) + 8*d(v). Factor p(m).
4*m**2*(m - 1)
Let a(j) be the third derivative of -4*j**2 + 5/336*j**8 - 5/24*j**6 + 0*j**3 - 1/42*j**7 + 0*j**4 + 0*j + 0 - 1/4*j**5. Factor a(f).
5*f**2*(f - 3)*(f + 1)**2
Let l(b) be the third derivative of -b**6/810 - 7*b**5/135 - 49*b**4/54 - 4*b**3 - 20*b**2. Let x(o) be the first derivative of l(o). What is z in x(z) = 0?
-7
Let l = 723 + -14457/20. Let u(j) be the third derivative of -1/8*j**4 + 0 + 5*j**2 - 3/40*j**6 + 0*j + l*j**5 + 0*j**3 + 1/70*j**7. Factor u(t).
3*t*(t - 1)**3
Let u be ((-154)/231)/((-7)/72). What is f in -24/7*f + u + 3/7*f**2 = 0?
4
Suppose 0*o - 2*o = -6. Determine i so that 5*i - i**4 + 5*i**4 + 0*i**4 + 2*i + 15*i**2 + 1 + 13*i**o = 0.
-1, -1/4
Let j(b) = -4*b - 9. Let a be j(-3). Factor -a*w - 3*w**2 + 27 - 15 - w**3 - 13.
-(w + 1)**3
Let l(d) be the first derivative of -d**6/3 + 10*d**5 - 125*d**4 + 2500*d**3/3 - 3125*d**2 + 6250*d - 101. Determine i, given that l(i) = 0.
5
Let h(q) = -5*q**2 - 4*q - 4. Let a(w) = 10*w**2 + 7*w + 7. Let b(g) = 4*a(g) + 7*h(g). Factor b(c).
5*c**2
Let x(h) = 5*h**3 - 5*h**2 + 13*h - 1. Let f(m) = -1 - 38*m**2 + 66*m**2 + 2*m**3 - 29*m**2 - 3*m**3 - m. Let o(z) = -3*f(z) - x(z). Factor o(v).
-2*(v - 2)*(v - 1)**2
Let g(u) be the second derivative of -u**4/3 - 6*u**3 - 28*u**2 + 2*u + 25. Factor g(y).
-4*(y + 2)*(y + 7)
Suppose -120*n - 331*n - 96*n + 1641 = 0. Factor -2/5 - 1/5*x**n + x - 3/5*x**2 + 1/5*x**4.
(x - 1)**3*(x + 2)/5
Let b(u) = -u**3 + 2*u**2 + u + 1. Let a(k) = -4*k**3 - 20*k**2 + 16*k - 4. Let d(z) = -a(z) - 4*b(z). Factor d(w).
4*w*(w - 1)*(2*w + 5)
Let h(o) be the second derivative of 0 + 1/15*o**6 - 3/10*o**5 - 1/6*o**4 + 0*o**2 + 14*o + 1/21*o**7 + 2/3*o**3. Factor h(x).
2*x*(x - 1)**2*(x + 1)*(x + 2)
Let v(h) be the third derivative of -h**5/240 + h**4/16 - 5*h**3/24 - 74*h**2. Determine b, given that v(b) = 0.
1, 5
Let t be (-1 + 56/6)/(19/(-285)). Let x = 127 + t. Factor 0*p - 1/2*p**x + 0.
-p**2/2
Let x(y) be the third derivative of 1/30*y**6 + 2*y**4 + 0*y - 2/5*y**5 + 9*y**2 - 16/3*y**3 + 0. Factor x(p).
4*(p - 2)**3
Suppose -17 = -2*c - 3*d, 0 = 4*c + 2*d - 0*d - 54. Factor -6*y**3 + 6*y**2 + 5*y**4 + c*y**3 - y**2.
5*y**2*(y + 1)**2
Solve 12*k + 63/5*k**5 + 687/5*k**3 - 438/5*k**4 - 372/5*k**2 + 0 = 0 for k.
0, 2/7, 2/3, 1, 5
Let j = -938/3 - -313. Let r(g) be the second derivative of -g**2 + 1/3*g**4 - 1/5*g**5 - 3*g + 0 + 1/21*g**7 - 1/15*g**6 + j*g**3. Factor r(l).
2*(l - 1)**3*(l + 1)**2
Let l(k) = k**3 - 21*k**2 - 114*k - 194. Let d(o) = 5*o**3 - 85*o**2 - 457*o - 777. Let p(b) = 4*d(b) - 18*l(b). Factor p(t).
2*(t + 3)*(t + 8)**2
Let p be -10 + 117/12 - (-1)/4. Let l(d) be the third derivative of 0*d + 1/12*d**4 + 1/15*d**5 - 4*d**2 + 0*d**3 + 1/60*d**6 + p. Suppose l(k) = 0. What is k?
-1, 0
Let p(m) = m**3 - 8*m**2 - 33*m - 3. Let x be p(11). Let n be (-3*x/45)/(9/10). Factor -n*q**2 + 4/9 - 2/9*q.
-2*(q - 1)*(q + 2)/9
Suppose -4/5*i**2 - 1280 - 64*i = 0. Calculate i.
-40
Let p(l) be the third derivative of 3*l**6/40 + l**5 + 11*l**4/8 - 3*l**3 - 6*l**2 + 49*l. Determine y so that p(y) = 0.
-6, -1, 1/3
Let f = 10 - 5. Suppose f = i + 2*i - v, 5*v = i + 3. Determine c, given that -18*c**i - 9*c - 3*c**4 - 12*c**2 + 9*c**2 - 15*c**3 = 0.
-3, -1, 0
Find n, given that 49/3*n**5 + 56/3*n**2 - 65*n**3 - 14/3*n**4 + 0 - 4/3*n = 0.
-2, 0, 1/7, 2
Let j(f) = -4*f**4 - 18*f**3 - 14*f**2 + 2*f. Let v(y) = y**3 - y**2 - y. Let t(s) = -j(s) - 2*v(s). Find d such that t(d) = 0.
-2, 0
Let w(i) be the third derivative of 19/132*i**4 + 0 + 3/220*i**6 - 1/10*i**5 - 1/11*i**3 + 2*i**2 + 0*i. Factor w(f).
2*(f - 3)*(3*f - 1)**2/11
Let a = 63 + -67. Let z be (-13)/(-91)*(-14)/a. Solve -1/2*r**4 + z*r - 1/6*r**5 + 1/3*r**2 + 1/6 - 1/3*r**3 = 0 for r.
-1, 1
Suppose 0*j - 1/4*j**3 - 13/4*j**2 + 0 = 0. Calculate j.
-13, 0
Let y be 34/204 - 226/60. Let r = -116/35 - y. Factor -8/7*x**4 + r*x + 2/7*x**5 + 0 - 8/7*x**2 + 12/7*x**3.
2*x*(x - 1)**4/7
Let x(f) = f**2 + 9*f + 7. Let l be x(-7). Let q be (2/l)/(-1) - 270/(-819). Suppose -2/13 + q*j**2 - 6/13*j = 0. Calculate j.
-1/4, 1
Suppose 0 = 47*s - 110 + 110. Factor 0*u + s + 3/2*u**4 - 2*u**2 - 2*u**3.
u**2*(u - 2)*(3*u + 2)/2
Let m be (16/6)/(50/15) + 0. Let -m + 32/5*u**2 + 18/5*u**3 + 2*u = 0. What is u?
-1, 2/9
Factor 5*h**3 + 188160*h + 7024640 + 1174*h**2 - 254*h**2 + 130*h**2 + 630*h**2.
5*(h + 112)**3
Let f(r) be the second derivative of -r**4/30 + 3*r**3/5 - 5*r + 6. Factor f(d).
-2*d*(d - 9)/5
Suppose -6*r - 141 = -3*r. Let i = r + 237/5. Suppose 2*j**2 - 4/5*j + 0 + i*j**4 - 8/5*j**3 = 0. What is j?
0, 1, 2
Let w(k) be the first derivative of 47 + 4/5*k**5 + 19/4*k**4 + 0*k - 4/3*k**3 - 2*k**2 - 5/2*k**6. Solve w(h) = 0.
-1, -2/5, 0, 2/3, 1
Let x = -25 + 28. Factor 7 - 1 + x*m - 3*m**2 - 15*m - 3 + 12*m**3.
3*(m - 1)*(m + 1)*(4*m - 1)
Suppose -62*p = 20*p + 34*p - 348. Let -32/3*f**2 - 14/3*f**p - 22/3*f - 4/3 = 0. Wh