Let i(y) be the second derivative of -13/120*y**4 - 1/300*y**6 - 1/5*y**3 + 19*y - 3/100*y**5 + 0 - 1/5*y**2. What is o in i(o) = 0?
-2, -1
Let s(t) be the second derivative of 125*t**7/84 + 245*t**6/3 + 10177*t**5/8 + 28219*t**4/12 + 5491*t**3/3 + 722*t**2 + 14*t + 5. Factor s(l).
(l + 19)**2*(5*l + 2)**3/2
Let q(a) be the third derivative of 1/4*a**5 + 5/6*a**3 + 0 + 5/8*a**4 - 15*a**2 + 1/24*a**6 + 0*a. Factor q(l).
5*(l + 1)**3
Factor 2*k**5 + 2993 - 4*k**4 - 2993 + 2*k**3.
2*k**3*(k - 1)**2
Let s(r) = 2*r - 2. Let y be s(4). Let a(w) = -w**4 + w**3. Let t(q) = -7*q**4 + 16*q**3 - 36*q**2 + 54*q - 27. Let c(b) = y*a(b) - t(b). What is k in c(k) = 0?
1, 3
Let w(t) = -3*t + 22. Let v be w(4). Factor 12 + 0*i + i**2 - i - 4 - v.
(i - 2)*(i + 1)
Let k(p) be the first derivative of -p**4/4 + p**3/2 + 3*p**2 - 12*p + 12. Let s(r) be the first derivative of k(r). Factor s(l).
-3*(l - 2)*(l + 1)
Let z(x) be the third derivative of -x**7/210 - 13*x**6/480 + x**5/240 + 13*x**4/96 + x**3/8 - 891*x**2. Let z(p) = 0. What is p?
-3, -1, -1/4, 1
Let r be (-1)/((35/(-7) - 5) + 5). Factor -2/5*s + 1/5*s**4 + 0 + 2/5*s**3 - r*s**2.
s*(s - 1)*(s + 1)*(s + 2)/5
Let o(p) be the first derivative of 2/3*p**6 - 16*p**2 + 7*p**4 - 31 + 4*p**5 - 4/3*p**3 - 16*p. Find m, given that o(m) = 0.
-2, -1, 1
Suppose 6*h**3 - 3/2 - 43/2*h**2 + 11*h = 0. Calculate h.
1/4, 1/3, 3
Let u(q) be the second derivative of -2/15*q**6 - 24*q**3 - 16*q**4 + 0 - 13/5*q**5 - 21*q + 0*q**2. Factor u(z).
-4*z*(z + 1)*(z + 6)**2
Let t(q) = -7*q**2 + 64*q - 3. Let l be t(9). Let d(b) be the first derivative of -6 - 1/3*b**4 - 4/15*b**5 + 0*b**2 + 2/9*b**l + 4/9*b**3 + 0*b. Factor d(u).
4*u**2*(u - 1)**2*(u + 1)/3
Factor -8/5*a**3 + 0 - 128/15*a + 2/15*a**4 + 32/5*a**2.
2*a*(a - 4)**3/15
Let t(l) = -l + 11. Let c be t(9). Suppose -3*v + 48 = 21. Factor -x - 8*x - x**3 - v*x**c + 3*x**2.
-x*(x + 3)**2
Factor 0*m + 0 + 1/5*m**2 - 2/5*m**3 + 1/5*m**4.
m**2*(m - 1)**2/5
Let u(b) = -262*b - 1307. Let o be u(-5). Let 16/13*z + 2/13*z**o - 32/13 + 14/13*z**2 = 0. What is z?
-4, 1
Let n(y) be the first derivative of y**3/3 - y**2/2 + y - 2. Let c be (1 + -2)/(-1 + 0). Let f(x) = -7*x**2 + x - 4. Let w(j) = c*f(j) + 4*n(j). Factor w(k).
-3*k*(k + 1)
Let r(m) be the second derivative of 0 - 5/4*m**4 - 3/2*m**3 + 17*m + 3*m**2. Factor r(f).
-3*(f + 1)*(5*f - 2)
Let x be 3 + 1 - (-15 + (-2)/(-1)). Let h be (-22)/(-20)*34/x - 2. What is z in -1/5*z**4 + 1/5*z**5 - h*z**3 + 0*z + 1/5*z**2 + 0 = 0?
-1, 0, 1
Let h = -7 - 3. Let g be 2*((-11)/h + -1). Determine v, given that 1/5 + 3/5*v**2 + g*v**3 + 3/5*v = 0.
-1
Let x(k) be the third derivative of k**5/72 + 5*k**4/48 + 12*k**2 + 3. Suppose x(l) = 0. Calculate l.
-3, 0
Let j(d) be the third derivative of d**5/140 - 65*d**4/56 - 33*d**3/7 - d**2 - 374*d. Factor j(y).
3*(y - 66)*(y + 1)/7
Determine o so that o**2 + 3/2*o**3 - 1/2*o + 0 = 0.
-1, 0, 1/3
Let s(c) = 365*c + 1825. Let u be s(-5). Factor -3/5*d**2 + u*d + 12/5.
-3*(d - 2)*(d + 2)/5
Let f be 0 + -2 - (-5 + 1). Let y = 310 + -1544/5. Solve 2/5 + 2/5*u + y*u**3 - f*u**2 = 0 for u.
-1/3, 1
Suppose -35701250/3 - 520/3*d**3 - 16900*d**2 - 2197000/3*d - 2/3*d**4 = 0. What is d?
-65
Suppose 5*q + 0*g + 5*g = 55, -4*q = 2*g - 34. Suppose 0 = -2*x - x + q. Let -4*d**3 + d**4 + d**3 + x*d**2 - 6*d**3 + 6*d**3 = 0. Calculate d.
0, 1, 2
Suppose 0 = -q + 89 - 89. Let w(f) be the first derivative of -4 + 4/3*f**3 + q*f + 0*f**2. Let w(k) = 0. Calculate k.
0
Let g(z) be the third derivative of -z**5/90 - 7*z**4/18 - 13*z**3/9 - z**2 - 7. Factor g(x).
-2*(x + 1)*(x + 13)/3
Let f(s) = s**2 - 47*s + 524. Let m be f(29). Let x(i) = -2*i - 6. Let g be x(-5). Solve -12*n**3 + 74/5*n**m + 8/5 + 18/5*n**g - 8*n = 0 for n.
2/3, 1
Let c(d) be the third derivative of d**8/16 - 13*d**7/70 - d**6/20 + 7*d**5/10 - 5*d**4/8 - d**3/2 - 286*d**2. Solve c(k) = 0 for k.
-1, -1/7, 1
Suppose -5*a + 4 = -11*y + 15*y, 2*y - 2 = 2*a. Factor a*z - 4/3 + 4/3*z**2.
4*(z - 1)*(z + 1)/3
Suppose -22*x = -41 - 41 + 16. Factor -22/7*a - 10/7 - 2/7*a**x - 2*a**2.
-2*(a + 1)**2*(a + 5)/7
Let w(p) be the first derivative of 48*p**5/25 - 342*p**4/5 - 1223*p**3/5 - 315*p**2/2 - 186*p/5 - 571. Solve w(y) = 0.
-2, -1/4, 31
Let w(g) = -g**3 - 10*g**2 + 9*g + 10. Let c be w(-11). Suppose 104*y**2 - 16*y + 16*y**4 - 180*y**3 + 250*y**5 - 34*y**4 - c*y**4 = 0. Calculate y.
-1, 0, 2/5
Let n be 0 - 1 - (-8)/4. Let u be n/3*(11 + -5). Factor -1 - i**2 + 3*i + 5 - 2*i**2 + u.
-3*(i - 2)*(i + 1)
Let x(y) = y**3 + y. Suppose c + 3*u = 1, 4*c + 3*u = 3 - 17. Let o(k) = -6*k**3 - k**2 - k + 4. Let q(r) = c*x(r) - o(r). Factor q(f).
(f - 2)*(f + 1)*(f + 2)
Let n(h) be the second derivative of -h**4/42 + 17*h**3/21 - 24*h. Solve n(l) = 0 for l.
0, 17
Let o be (-6)/(-15) - (-78)/5. Let z be (-3)/(-2)*o/12. Factor -6/7*x + 0 + 8/7*x**z - 2/7*x**3.
-2*x*(x - 3)*(x - 1)/7
Let v(a) be the first derivative of a**5/15 - 2*a**3/3 - 4*a**2/3 - a - 434. Find m, given that v(m) = 0.
-1, 3
Factor -2/3*k**3 + 0 + 32/3*k**2 + 0*k.
-2*k**2*(k - 16)/3
Suppose -12/7*w**3 - 6*w - 57/7*w**2 + 3/7*w**4 + 0 = 0. What is w?
-2, -1, 0, 7
Let p = -32 + 31. Let n(d) = 15*d**4 - 10*d**3 + 20*d**2 - 10*d + 5. Let i(m) = m**4 - m**3 + m**2. Let u(g) = p*n(g) + 20*i(g). Find a, given that u(a) = 0.
-1, 1
Let z(s) be the first derivative of -2*s**5 + 15/4*s**4 - 5/3*s**3 + 3 + 0*s + 0*s**2. Find d, given that z(d) = 0.
0, 1/2, 1
Let i be 159/5 - (-4)/20. Suppose -37*p + 20 = -i*p. Determine a so that -45/4*a**p - 9/4 + 3/2*a**2 + 39/4*a - 57/2*a**3 + 27/4*a**5 = 0.
-1, 1/3, 3
Let c be (-2 - (-35)/28) + 12/16. Let w(d) be the first derivative of 0*d**3 - 4 + 2/3*d**6 + d**4 + c*d - 8/5*d**5 + 0*d**2. Suppose w(y) = 0. What is y?
0, 1
Let x(a) be the first derivative of -3 + 1/12*a**4 - 2*a + 1/60*a**5 - 1/90*a**6 - 1/3*a**2 - 1/18*a**3. Let u(m) be the first derivative of x(m). Factor u(s).
-(s - 2)*(s - 1)*(s + 1)**2/3
Let a(z) be the third derivative of -z**7/315 - 11*z**6/18 - 971*z**5/30 + 1540*z**4/9 - 3136*z**3/9 - 333*z**2. Factor a(q).
-2*(q - 1)**2*(q + 56)**2/3
Let p(m) = -75*m - 73. Let f be p(-1). Let g(n) be the second derivative of -1/3*n**4 - 9*n + 0*n**2 + f*n**3 + 0. Find j such that g(j) = 0.
0, 3
Suppose 6*n = -n + 28. Suppose 5*b - 33*b + 93*b**3 + 24 - n*b**5 - 61*b**3 - 24*b**2 + 0*b**5 = 0. Calculate b.
-3, -1, 1, 2
Let s be ((-208)/520)/(16/(-10) + 1). Suppose 0 + s*v - v**3 + 1/3*v**5 + 1/3*v**4 - 1/3*v**2 = 0. Calculate v.
-2, -1, 0, 1
Suppose -10 - 5 = -5*b. Factor -2*t**3 - 2*t + 2 - b*t + 9*t - 2*t**3 - 2*t**4.
-2*(t - 1)*(t + 1)**3
Let m(x) be the third derivative of x**8/2352 + 11*x**7/1470 - 13*x**6/420 + x**5/210 + 25*x**4/168 - 13*x**3/42 + x**2 + 374. Let m(c) = 0. Calculate c.
-13, -1, 1
Suppose -8*r + 4*r = 52. Let l(u) = -2*u - 19. Let z be l(r). Solve -5*w**2 - z*w**2 + 56*w - 44*w + 4*w**3 - 4 = 0.
1
Suppose 0*j**5 + 4*j**5 + 19*j**2 + 240*j**3 - 500*j - 56*j**4 - 106*j**2 - 17*j**2 - 96*j**2 = 0. Calculate j.
-1, 0, 5
Let o be 6/(-5)*((-46)/4 + 4). Let n be -2 + (-66)/o*(-3)/10. Factor -1/5 + 0*g + n*g**2.
(g - 1)*(g + 1)/5
Let q(h) be the second derivative of 3*h**5/20 - 17*h**4/2 + 289*h**3/2 - 54*h + 2. Factor q(a).
3*a*(a - 17)**2
Let d(g) be the first derivative of -g**5/15 + g**4/12 + g**3 + 11*g**2/6 + 4*g/3 - 34. Determine n, given that d(n) = 0.
-1, 4
Let f be 303/(-45) + 2 - -1. Let q = -29/15 - f. Factor -9/5*o**2 - 3/5 + q*o + 3/5*o**3.
3*(o - 1)**3/5
Let c(p) be the first derivative of 27/4*p**4 - 6*p + 21/5*p**5 + 6 - 27/2*p**2 - 5*p**3. Determine b, given that c(b) = 0.
-1, -2/7, 1
Let d(c) be the third derivative of 0 + 1/126*c**7 - 4/9*c**3 + 1/6*c**5 - 13*c**2 + 0*c + 1/18*c**4 + 23/360*c**6. Factor d(s).
(s + 1)*(s + 2)**2*(5*s - 2)/3
Find g, given that 0 + 194/3*g**3 - 14/3*g**5 - 158/3*g**2 + 38/3*g**4 - 20*g = 0.
-3, -2/7, 0, 1, 5
Let h = 38824249/310 + -125239. Let v = h - 2/155. Factor -3/2*o**2 + 3/2*o - 1/2 + v*o**3.
(o - 1)**3/2
Let t(m) = 3*m**5 + 2*m**4 + 4*m. Let s(l) = -l**5 - l. Let q(k) = -4*s(k) - t(k). Factor q(i).
i**4*(i - 2)
Let q(z) be the third derivative of z**5/12 + 105*z**4/2 + 13230*z**3 + 324*z**2. Factor q(l).
5*(l + 126)**2
Let w(i) be the first derivative of i**6/72 + i**5/24 - 7*i**3 + 10. Let j(a) be t