106134/5*s + 2/15*s**3 - 532/5*s**2.
2*s*(s - 399)**2/15
Let h(r) be the third derivative of -r**5/20 + r**4/8 - 1332*r**2. Suppose h(v) = 0. Calculate v.
0, 1
Let u(g) be the first derivative of 1/4*g**2 - 1/24*g**6 - 1/16*g**4 - 2*g + 13/12*g**3 - 1/4*g**5 - 71. What is s in u(s) = 0?
-4, -2, -1, 1
Let z(o) be the first derivative of -13/2*o**4 + 3/2*o**6 + 6*o**3 + 17/2*o**2 + 3*o - 79 - 21/5*o**5. Determine a so that z(a) = 0.
-1, -1/3, 1, 3
Let j(g) = g**3 + g. Let n(k) = 7*k**3 + 17*k**2 + 55*k - 41. Let p(q) = 6*j(q) - n(q). Let s be p(-13). Factor 0 + 1/4*r**3 + 3/4*r - r**s.
r*(r - 3)*(r - 1)/4
Let o(y) be the second derivative of y**7/2520 + y**6/72 + y**4/12 + 5*y**3/6 - 80*y. Let p(b) be the third derivative of o(b). Suppose p(g) = 0. Calculate g.
-10, 0
Let v(o) = 28*o + 36. Let i = -248 - -247. Let p(y) = -y**2 - 2*y + 1. Let q(b) = i*v(b) + 4*p(b). Determine z so that q(z) = 0.
-8, -1
Let b(x) be the first derivative of 0*x**2 - 2/15*x**3 - 1/10*x**4 + 0*x + 9. Find y, given that b(y) = 0.
-1, 0
Let c = -901 - -2261. Find t, given that 624*t**4 - 6*t**5 - c*t**4 + 541*t**4 + t**5 - 2535*t**3 - 10985*t**2 = 0.
-13, 0
Let d = 6031/30280 - -5/6056. Let r(n) be the second derivative of 4*n + d*n**5 - n**4 + 0 - 2/3*n**3 + 6*n**2. Factor r(h).
4*(h - 3)*(h - 1)*(h + 1)
Suppose -9*k + 72 = -13*k + 4*g, -78 = 4*k - g. Let t be ((-15)/k)/(25/(-40) - -1). Factor -5*h**3 + h - 8/3*h**t + 0 - 4/3*h**4.
-h*(h + 1)*(h + 3)*(4*h - 1)/3
Let g(r) be the third derivative of r**5/270 + 1291*r**4/54 + 2581*r**3/27 - 3202*r**2. Suppose g(n) = 0. What is n?
-2581, -1
Let o be (-4)/30*(-3 + 3/(-6) + -76 + 78). Factor -2/5*x**2 + o*x**3 + 0 - 3/5*x.
x*(x - 3)*(x + 1)/5
Let f(y) be the first derivative of y**5/5 - 5*y**4 - 23*y**3/3 + 21*y**2 + 419. Find j such that f(j) = 0.
-2, 0, 1, 21
Let f(c) = 15*c**4 + 585*c**3 + 1690*c**2 - 35*c - 2200. Let j(r) = -38*r**4 - 1463*r**3 - 4229*r**2 + 87*r + 5500. Let v(o) = -13*f(o) - 5*j(o). Factor v(w).
-5*(w - 1)*(w + 2)**2*(w + 55)
Let n(y) = 5*y**2 - y. Suppose -20*k = -4 - 16. Let j(h) = -2*h**2 - h. Let s(b) = k*n(b) + 2*j(b). Determine o, given that s(o) = 0.
0, 3
Let u(x) be the first derivative of 4*x**2 + 142 + 9/10*x**4 - 2/25*x**5 - 16/5*x**3 + 0*x. Factor u(r).
-2*r*(r - 5)*(r - 2)**2/5
Let u(l) be the first derivative of l**4/16 - 190*l**3/3 - 1523*l**2/8 - 381*l/2 + 3458. Factor u(f).
(f - 762)*(f + 1)**2/4
Let u = 57 + 199. Let m = u - 1009/4. Solve -15/4*x**2 - m*x**3 - 5/4*x**4 - 5/4*x + 0 = 0.
-1, 0
Let c(i) be the second derivative of -3/5*i**5 + 0*i**4 - 43*i + 0 - 1/10*i**6 + 24*i**2 + 8*i**3. Factor c(r).
-3*(r - 2)*(r + 2)**3
Determine f so that 1/5*f**4 - 22/5*f + 24/5 - 7/5*f**2 + 4/5*f**3 = 0.
-4, -3, 1, 2
Let j(y) be the third derivative of y**6/280 - 13*y**5/70 + 179*y**4/56 - 11*y**3 + 799*y**2. Factor j(b).
3*(b - 14)*(b - 11)*(b - 1)/7
Let u be (14/(-8) + (-32)/(-16))*8. Factor -7*f - 22*f + 32*f + 6*f**u - 6 - 3*f**3.
-3*(f - 2)*(f - 1)*(f + 1)
Let p(r) be the second derivative of r**6/30 + 19*r**5/20 + 15*r**4/2 + 316*r. Factor p(h).
h**2*(h + 9)*(h + 10)
Let r(u) be the first derivative of u**5/4 - 175*u**4/16 + 160*u**3/3 - 155*u**2/2 + 2641. Let r(q) = 0. Calculate q.
0, 2, 31
Let t(i) be the third derivative of i**6/360 - 7*i**5/36 - 17*i**4/8 - 13*i**3/2 - 351*i**2. Let t(z) = 0. Calculate z.
-3, -1, 39
Let w(v) = 38*v**3 + 2*v**2 + 7*v - 9. Let g be w(1). Let o be (1 + (0 - 6))*(-38)/g. Factor 1/7*z**4 - 2/7*z**3 + 1/7 - 2/7*z**2 + 1/7*z + 1/7*z**o.
(z - 1)**2*(z + 1)**3/7
Let z(s) be the first derivative of 16*s - 8*s**2 + 4/3*s**3 + 8. Let z(f) = 0. Calculate f.
2
Suppose 75*m = -61 + 361. Let b(n) be the first derivative of -1/10*n**5 - 3/2*n - 2*n**3 - 3/4*n**m + 2 - 5/2*n**2. Factor b(c).
-(c + 1)**3*(c + 3)/2
Let y(z) = -21*z**2 + 11*z + 21. Let u be 10/((-20)/6) + 5. Suppose -3*h = h + 44. Let n(k) = -4*k**2 + 2*k + 4. Let v(w) = h*n(w) + u*y(w). Factor v(b).
2*(b - 1)*(b + 1)
Let s be 1/(5 - (-196)/(-38)). Let x = s - -49/6. Factor -2/3 + x*a - 5/6*a**2 - 1/3*a**3.
-(a - 1)*(a + 4)*(2*a - 1)/6
Suppose 4*s + 24 = 9*a - 13*a, -3*a = -3*s + 30. Let h(v) be the first derivative of v**s - 12/7*v - 2/21*v**3 + 27. Factor h(j).
-2*(j - 6)*(j - 1)/7
Suppose c + 4 = 5*d + 33, -2*d = -4*c + 26. Let a be -18*c/16 - (-18)/3. Solve a*v**2 + 0 + 21/2*v = 0 for v.
-7, 0
Let u(m) = 4*m**2 - 18*m + 26. Let o be u(-13). Factor 4*s**2 - 948*s - 34 - 6 + o*s.
4*(s - 5)*(s + 2)
Let f(d) be the second derivative of -d**5/5 + 44*d**4/3 - 874*d**3/3 - 2116*d**2 + 831*d. Factor f(y).
-4*(y - 23)**2*(y + 2)
Suppose 50/7*l + 2/7*l**2 - 52/7 = 0. Calculate l.
-26, 1
Let h = -284859 + 1994016/7. Factor 9/7 - h*m**2 + 6/7*m.
-3*(m - 3)*(m + 1)/7
Let h(b) be the third derivative of b**5/20 + 1923*b**4/4 + 3697929*b**3/2 + 3508*b**2. Find y such that h(y) = 0.
-1923
Let x(m) be the second derivative of -m**6/180 - m**5/6 + 26*m**4/9 - 112*m**3/9 + 1762*m. Factor x(h).
-h*(h - 4)**2*(h + 28)/6
Let h(x) = 2*x**2 + 7*x - 24. Let o be h(-6). Factor 16*r - r**3 + 13*r + 27*r + 16*r + o - 61*r + 4*r**2.
-(r - 6)*(r + 1)**2
Let x(h) be the second derivative of -25/6*h**4 + 85/6*h**3 + 26 - 20*h**2 + 1/4*h**5 - h. Let x(u) = 0. What is u?
1, 8
Suppose 0 = f - 4*d - 78, 9 = f + d - 44. Let b = 61 - f. Factor 1/3*u**4 - 1 + 0*u**b - 8/3*u - 2*u**2.
(u - 3)*(u + 1)**3/3
Let a be (-3)/(-5) + (-501)/60 - -8. Factor 7/2 + a*r**2 + 9/4*r.
(r + 2)*(r + 7)/4
Solve 3795*u**3 - 7588*u**3 + 3792*u**3 + u = 0.
-1, 0, 1
Factor 1254*z - 642*z**2 - 5*z**3 + 880 + 1512*z**2 + 501*z.
-5*(z - 176)*(z + 1)**2
Let h be (-4)/46 + 480/828*(-9)/(-60). Suppose 6/5*s**3 + 2/5*s**4 - 8/5*s**2 + h*s + 0 = 0. What is s?
-4, 0, 1
Let v(m) be the second derivative of 2*m**7/105 - m**6/15 + m**2 - 38*m. Let q(f) be the first derivative of v(f). What is i in q(i) = 0?
0, 2
Solve -1092/5*q - 218 - 2/5*q**2 = 0 for q.
-545, -1
Suppose 75*p = -5*q + 73*p - 74, 2*q - 2*p + 38 = 0. Let r be q/10*(-165)/198. Factor -2*o**2 - 1/3*o**4 - 1/3 + r*o**3 + 4/3*o.
-(o - 1)**4/3
Let k(t) be the second derivative of -2*t**7/21 - 18*t**6/5 + 262*t**5/5 - 210*t**4 + 18*t**3 + 1890*t**2 - 5013*t. Solve k(j) = 0.
-35, -1, 3
Let x = -36 + 46. Let r be (4/x + 0)/(6/120). Determine d, given that d**3 + 8*d**2 + 2*d**3 - 4*d**2 + r*d**2 = 0.
-4, 0
Let k = -40754 + 40756. Factor 9/2 + 1/2*c**k + 3*c.
(c + 3)**2/2
Let v(y) be the first derivative of y**6/2880 + y**5/120 + y**4/16 - 2*y**3/3 + 4*y**2 + 164. Let w(m) be the third derivative of v(m). Factor w(c).
(c + 2)*(c + 6)/8
Let j(f) be the first derivative of f**3 + 237*f**2/2 + 234*f + 89. Suppose j(z) = 0. Calculate z.
-78, -1
Let s(t) = -6493*t**2 - 6496*t + 30. Let w(x) = -1623*x**2 - 1624*x + 8. Let n(f) = 6*s(f) - 22*w(f). Suppose n(a) = 0. Calculate a.
-1, 1/813
Let r be (2457/(-315))/((-1)/(-165)). Let l = r + 21883/17. Determine q so that l*q**3 + 0*q**4 + 0*q**2 - 2/17*q**5 - 2/17*q + 0 = 0.
-1, 0, 1
Let x(g) be the first derivative of 4/5*g**3 + 162/5*g + 109 - 651/10*g**2. Determine v so that x(v) = 0.
1/4, 54
Let d be (32/(-160))/((-4)/(-20))*6/(-10). Determine n so that 0 - 3*n - d*n**3 + 18/5*n**2 = 0.
0, 1, 5
Let c(b) be the first derivative of -b**3/6 + 801*b**2/4 - 400*b - 9588. Suppose c(n) = 0. Calculate n.
1, 800
Let n(x) be the second derivative of x**5/40 + x**4/48 - 13*x**3/24 + 3*x**2/4 - 6034*x. Factor n(d).
(d - 2)*(d + 3)*(2*d - 1)/4
Let z(l) be the third derivative of -l**7/840 - 31*l**6/120 - 961*l**5/40 - 7*l**4/4 - 2*l**2 - 2*l. Let p(s) be the second derivative of z(s). Factor p(t).
-3*(t + 31)**2
Let p(x) = x**3 + 84*x**2 - 261*x + 4. Let b be p(-87). Let c(i) be the first derivative of -7 + 14*i**2 + 8*i + 5*i**b + 12*i**3 + 4/5*i**5. Factor c(n).
4*(n + 1)**3*(n + 2)
Suppose -3*y + 132*n = 131*n + 50, n - 5 = 0. Let v be (y + 18)/(3 - 1). What is t in -3/8*t**5 + 0 + 0*t**3 - 9/8*t**4 + v*t**2 + 0*t = 0?
-2, 0, 1
Determine m so that -4/7*m**2 - 36/7 - 74/7*m = 0.
-18, -1/2
Let n be -1 + 3 - (0/6 + -5). Let d(q) = -16*q**3 - 61*q**2 - 310*q - 192. Let o(g) = -18*g**3 - 60*g**2 - 311*g - 192. Let j(y) = n*d(y) - 6*o(y). Factor j(v).
-(v + 8)**2*(4*v + 3)
Let u(w) be the first derivative of w**6/2 + 9*w**5/5 - 171*w**4/2 - 982*w**3 - 8685*w**2/2 - 8775*w + 8135. Determi