 be the third derivative of z**5/360 - 17*z**4/36 + 289*z**3/9 + 95*z**2 + 2*z. Find k, given that v(k) = 0.
34
Determine t so that 27 - 63/4*t + 1/4*t**3 + 3/2*t**2 = 0.
-12, 3
Let i(b) be the second derivative of -13*b + 0 + 1/12*b**3 - 1/24*b**4 - 1/40*b**5 + 1/4*b**2. Factor i(d).
-(d - 1)*(d + 1)**2/2
Suppose 24/11 - 2/11*w - 2/11*w**2 = 0. Calculate w.
-4, 3
Let y(r) = -r**3 - 3*r**2 - r + 4. Let l be y(-2). Let d be (-7 + (4 - l))/((-8)/8). Let 0 - u**4 + 2/3*u + u**2 - 1/3*u**d - 1/3*u**3 = 0. Calculate u.
-2, -1, 0, 1
Let i = 30 - 24. Let c(d) be the third derivative of 0 + 1/2*d**4 + d**2 - 1/210*d**7 - 13/60*d**5 + 0*d - 2/3*d**3 + 1/20*d**i. Factor c(x).
-(x - 2)**2*(x - 1)**2
Let f = -171946 + 5159591/30. Let t = -235/6 + f. Factor -2/5 + 2/5*s**3 - t*s**2 + 6/5*s.
2*(s - 1)**3/5
Let o(x) = 16*x**3 - 24*x**2 - 52*x. Let w(v) = -v**3 + v**2 + v. Let s(h) = o(h) + 12*w(h). Factor s(f).
4*f*(f - 5)*(f + 2)
Suppose 0 = -3*i - 3*k - 1 + 4, -5*i + 3*k = 19. Let j be 2 - (-4 + i + 5). Factor 2/3*g**j + 0*g + 0 - 1/3*g**2 - 1/3*g**4.
-g**2*(g - 1)**2/3
Suppose 60*f = 8*f. Let z(r) be the second derivative of f*r**3 + 0 + 0*r**2 - 1/150*r**6 + 0*r**4 + 1/100*r**5 + 9*r. Suppose z(c) = 0. What is c?
0, 1
Let r(c) = 7*c + 6. Let s be r(4). Let p = 36 - s. Factor -2/9*v**p + 4/9 + 2/9*v.
-2*(v - 2)*(v + 1)/9
Suppose -y - q = -14 - 5, -3*y + 63 = 5*q. Suppose -d**3 + 3*d**3 + 7*d + 2*d**3 + 5*d - y*d**2 = 0. Calculate d.
0, 1, 3
Let o(c) be the third derivative of -2/33*c**3 + 0*c + 1/330*c**5 + 1/132*c**4 - 8*c**2 + 0. Find l, given that o(l) = 0.
-2, 1
Let m(l) be the third derivative of 0 + 37/36*l**4 + 4/3*l**3 - 38*l**2 + 0*l + 1/30*l**5. Factor m(b).
2*(b + 12)*(3*b + 1)/3
Let f(b) be the third derivative of -b**8/20160 - b**7/1260 + b**6/144 + b**5/2 + 50*b**2. Let i(q) be the third derivative of f(q). Let i(g) = 0. Calculate g.
-5, 1
Factor -98*q - 80*q**2 - 60 - 4*q**3 - 30*q + 120*q**2 + 188.
-4*(q - 4)**2*(q - 2)
Let o(f) = f**2 + 16*f + 40. Let v(q) = -5. Let p(b) = 4*o(b) + 20*v(b). Find z, given that p(z) = 0.
-15, -1
Let t(w) be the second derivative of -w**7/21 - 8*w**6/15 + 2*w**5/5 + 16*w**4/3 - w + 19. Find y, given that t(y) = 0.
-8, -2, 0, 2
Let h(m) = -2*m + 11. Let t be h(7). Let q be (-96)/180 - 4/t. Solve 2/5*a**4 + 0*a**2 - 2/5 - 4/5*a + q*a**3 = 0.
-1, 1
Let y = -41 + 46. Let i(s) = 13*s**2 - 5*s - 27. Let k(c) = 84*c**2 - 32*c - 176. Let f(p) = y*k(p) - 32*i(p). Factor f(u).
4*(u - 2)*(u + 2)
Let y(r) = 9*r**3 - 45*r**2 + 29*r + 72. Let i(j) = -3*j**3 + 15*j**2 - 10*j - 24. Let f(s) = -11*i(s) - 4*y(s). Factor f(p).
-3*(p - 4)*(p - 2)*(p + 1)
Let m(v) be the third derivative of v**8/13440 - v**7/3360 + v**6/2880 + 7*v**3/2 - 22*v**2. Let x(o) be the first derivative of m(o). Factor x(r).
r**2*(r - 1)**2/8
Let h be (-4)/(-22) + (3808/(-385))/(-16). Suppose 8/5*x**2 + h - 2*x - 2/5*x**3 = 0. Calculate x.
1, 2
Let d(g) = -4*g - 4 + 0 - 3 + 3. Let q be d(-2). Find a such that 22*a + 3*a**2 + a**2 - 14*a - q*a**3 = 0.
-1, 0, 2
Suppose -5*q - o = -20, -4 = 2*o + 6. What is i in -12*i - 38*i**5 + 85*i**q + 8*i**3 - 8*i**2 + 12*i**4 - 43*i**5 - 4 = 0?
-1, 1
Let x(q) be the third derivative of q**5/240 - 5*q**4/32 - 17*q**3/12 - 144*q**2. Factor x(c).
(c - 17)*(c + 2)/4
Let v be 2/5 + 1657/(-20). Let m = -325/4 - v. Suppose -2/5*z**4 + 0 + 0*z**2 - m*z**3 + 8/5*z = 0. Calculate z.
-2, 0, 1
Let u = 3949/107625 + -9/287. Let p = u - -5978/4125. Suppose -30/11*j**3 + p*j - 2*j**2 + 8/11 = 0. What is j?
-1, -2/5, 2/3
Let o(x) be the third derivative of 0*x**3 + 0*x - 1/60*x**5 + 1/24*x**4 + 0 - 47*x**2. Factor o(m).
-m*(m - 1)
Let t(i) be the first derivative of -3*i**4/8 + 31*i**3/2 - 177*i**2/4 + 87*i/2 + 68. Factor t(h).
-3*(h - 29)*(h - 1)**2/2
Let k(a) be the second derivative of -a**6/60 + a**5/5 + 19*a**4/8 + 25*a**3/3 + 13*a**2 + 427*a. What is u in k(u) = 0?
-2, -1, 13
Let x be (3 - -1)/(13/182*35). Factor 0 - 4/5*w + 2/5*w**4 + 2*w**2 - x*w**3.
2*w*(w - 2)*(w - 1)**2/5
Suppose -3*i - 8 = -4*i. Let y = -6 + i. Determine p so that -23*p**2 + 23*p**y + 3*p**5 - 3*p**3 = 0.
-1, 0, 1
Let c = 7939/5961 - -3/1987. Factor 2/9*p**2 + 2 - c*p.
2*(p - 3)**2/9
Factor f**2 - 3*f**2 + 2*f - 411*f**3 - 7*f**2 - 2*f**2 - 7*f**4 + 427*f**3.
-f*(f - 1)**2*(7*f - 2)
Let d(x) be the first derivative of 2*x**3/21 + 2*x**2 + 66*x/7 - 95. Factor d(q).
2*(q + 3)*(q + 11)/7
Let b(n) be the first derivative of n**4 - 40*n**3/3 - 112*n**2 + 51. Factor b(m).
4*m*(m - 14)*(m + 4)
Let y = 39 - 27. Let t(m) = m - 14. Let v be t(16). Factor -y*c + 5*c**3 - v + 8*c + 2*c**4 - c**3.
2*(c - 1)*(c + 1)**3
Let w(u) = u**4 - 7*u**2 + 6*u. Let c(a) = -4*a**4 + 34*a**2 - 30*a. Let f be (-145)/(-15) + ((-8)/3)/(-2). Let s(o) = f*w(o) + 2*c(o). Let s(v) = 0. What is v?
-2, 0, 1
Let f(d) be the first derivative of -13/3*d**3 - 3*d - 56/5*d**5 - 10*d**4 - 1 - 64/15*d**6 - d**2. Let s(j) be the first derivative of f(j). Factor s(a).
-2*(a + 1)*(4*a + 1)**3
Factor -4693*r**3 - 32*r + 4690*r**3 - 27 - 33*r**2 - 25*r.
-3*(r + 1)**2*(r + 9)
Let n(q) be the second derivative of -3/4*q**5 + 14*q - 25/12*q**4 + 55/6*q**3 - 15/2*q**2 + 0. Factor n(u).
-5*(u - 1)*(u + 3)*(3*u - 1)
Let p be ((-44)/55 + 0)*(-10)/4. Let h(q) be the first derivative of -q**4 + 14 + 2*q**p - 8/3*q**3 + 8*q. Factor h(b).
-4*(b - 1)*(b + 1)*(b + 2)
Let z be 8/8 + 12 + -12 + 2. Solve 0*n - 2/13*n**2 - 4/13*n**z + 2/13*n**4 + 4/13*n**5 + 0 = 0 for n.
-1, -1/2, 0, 1
Find z, given that -32*z + 0*z**2 + 0 - 1/2*z**5 + 0*z**4 + 65/2*z**3 = 0.
-8, -1, 0, 1, 8
Let q(b) be the first derivative of -b**4/22 + 2*b**3/33 + 2*b**2/11 - 27. Factor q(r).
-2*r*(r - 2)*(r + 1)/11
What is v in 70/13*v - 98/13 + 2/13*v**3 + 2*v**2 = 0?
-7, 1
Let s(i) be the second derivative of -5*i**4/12 - 190*i**3/3 - 3610*i**2 + 96*i. Factor s(n).
-5*(n + 38)**2
Let p(y) be the third derivative of -y**5/45 + 2*y**4 - 72*y**3 + 58*y**2. Factor p(n).
-4*(n - 18)**2/3
Let k = 145 - 39. Let x = k + -104. Factor 7/2*r**4 - 7/2*r**x + 0 - r**3 + r.
r*(r - 1)*(r + 1)*(7*r - 2)/2
Suppose 2*d + 4 = 0, 6 = -9*u + 5*u - 3*d. Solve -27/2*o**5 + u - 45/2*o**4 + 3*o + 33/2*o**3 + 33/2*o**2 = 0.
-2, -1/3, 0, 1
Let g(p) = -7*p - 12*p - 3 - 26*p**2 + 7 - 15. Let u(a) = 9*a**2 + 6*a + 4. Let x(q) = 4*g(q) + 11*u(q). Find o such that x(o) = 0.
-2, 0
Let d(k) be the third derivative of -17*k**6/780 - 2*k**5/39 - k**4/52 - 105*k**2. Factor d(x).
-2*x*(x + 1)*(17*x + 3)/13
Let y = -13154 - -13156. Factor -y*n**2 + 8/3 + 0*n - 2/3*n**3.
-2*(n - 1)*(n + 2)**2/3
Let h be 6*(-14)/21 + 6. Let r(i) be the first derivative of 8/27*i**3 + 2/9*i - 5/9*i**h - 4. What is k in r(k) = 0?
1/4, 1
Let d(v) be the second derivative of -1/21*v**3 - 11*v + 1/42*v**4 + 0*v**2 + 0. Factor d(q).
2*q*(q - 1)/7
Suppose -4*f = n - 11, -n - 136*f = -140*f + 5. Let b = -4/17 + 46/51. Determine k, given that -5/3*k**n + 1/3*k**2 + 2/3*k + b*k**4 + 0 = 0.
-1/2, 0, 1, 2
Let x(y) be the first derivative of 121*y**3 - y**2 - 130. Determine t so that x(t) = 0.
0, 2/363
Let q(k) be the third derivative of -1/945*k**7 - 1/45*k**5 + 0 + 2*k**2 + 0*k - 1/135*k**6 - 1/27*k**3 - 1/27*k**4. Factor q(u).
-2*(u + 1)**4/9
Let w(p) be the first derivative of p**3/27 - 26*p**2/9 + 676*p/9 - 40. Suppose w(o) = 0. What is o?
26
Let f(y) = -y - 12. Let m be f(-10). Let q be m + 8 + -1 - 3. Factor 5*n**4 + 3*n**3 + 0*n**4 - q*n**2 + 7*n - 7*n.
n**2*(n + 1)*(5*n - 2)
Let c(l) be the second derivative of l**9/3024 - l**8/1680 - l**7/420 + 11*l**3/6 - 12*l. Let o(p) be the second derivative of c(p). Factor o(k).
k**3*(k - 2)*(k + 1)
Suppose -204*u = -200*u - 16. Let t(j) be the first derivative of -1/4*j**3 - 4 + 1/16*j**u - 1/4*j + 3/8*j**2. Factor t(x).
(x - 1)**3/4
Let h(z) = -46*z**4 + 30*z**3 + 38*z**2 - 8*z + 30. Let t(n) = -2*n**4 + n**3 + 2*n**2 + 1. Let l(r) = 2*h(r) - 44*t(r). Let l(v) = 0. What is v?
-1, 1, 2
Suppose 3052*n - 8*n**5 + 4138*n**2 - 1444 + 118*n**4 - 412*n**4 + 1850*n - 2494*n**3 = 0. What is n?
-19, -1, 1/4, 2
Factor 8463/2*i**2 - 185/2*i**3 + 8649/2*i + 0 + 1/2*i**4.
i*(i - 93)**2*(i + 1)/2
Let t(w) = -2*w - 14. Let g be t(-8). Factor -6*f**4 + 18*f**5 - 10*f**3 + 4*f**2 - 10*f**g + 4*f**2.
2*f**2*(f - 1)*(3*f + 1)**2
Let j = 248 - 244. Let h(q) be the second derivative