 the third derivative of 1/588*k**8 + 1/210*k**6 + 0 + 0*k**4 + 4/735*k**7 - 10*k**2 + 0*k**3 + 0*k + 0*k**5. Factor a(d).
4*d**3*(d + 1)**2/7
Factor d**3 - 3*d**3 + d**4 + d**4 + 0*d**4 + 4*d**3.
2*d**3*(d + 1)
Let t(j) be the first derivative of 32 + 2*j**2 - 4/9*j**3 + 0*j. Factor t(c).
-4*c*(c - 3)/3
Let b = 19 + 309. Let p = -326 + b. Determine v, given that 1/2 + 5/4*v + v**p + 1/4*v**3 = 0.
-2, -1
Suppose -14 - 66 = -4*o. Factor 45*x + o - 5*x**2 - 45*x.
-5*(x - 2)*(x + 2)
Let g(z) be the second derivative of -z**7/147 + 3*z**6/35 - 3*z**5/7 + 22*z**4/21 - 8*z**3/7 - 161*z. Factor g(a).
-2*a*(a - 3)*(a - 2)**3/7
Let m(q) be the first derivative of -8/3*q**3 + 15/7*q**4 + 0*q + 125/21*q**6 - 8/7*q**2 + 10*q**5 - 17. Suppose m(f) = 0. What is f?
-1, -2/5, 0, 2/5
Let c(z) be the second derivative of -7*z**6/45 + 12*z**5/5 + 19*z**4/6 - 22*z**3/9 + 78*z. Solve c(i) = 0.
-1, 0, 2/7, 11
Let l(m) be the second derivative of 1/2*m**2 + 0 + 7*m - 2/9*m**3 + 1/36*m**4. Let l(p) = 0. What is p?
1, 3
Let a = -6 - -8. Suppose -4*v = -a*v - 2*g - 10, 10 = 3*v + 2*g. Find c such that -v*c**4 + 7*c**3 - c**3 - 4*c**2 + c**4 + c**4 = 0.
0, 1, 2
Let j = 29970 - 29966. Find t such that 1/2*t**j - 8*t + 4*t**2 + 0 + 7/2*t**3 = 0.
-4, 0, 1
Let f be (105/(-20))/((-9)/24). Suppose -f = -6*c - c. Factor 4*x**3 + 14*x**2 - c*x**2 - 4*x**2 + 0*x**3.
4*x**2*(x + 2)
Let z(w) = 10*w**2 + 116*w + 144. Let x(b) = 3*b**2 + 38*b + 47. Let f(v) = 19*x(v) - 6*z(v). Find r, given that f(r) = 0.
-1, 29/3
Let n = -179/22 - -391/44. Factor n*u - 3/2 + 3/4*u**2.
3*(u - 1)*(u + 2)/4
Let b(r) = -2 - r**2 - 2 + 13 + 0*r**2 + 3*r. Let s be b(4). Factor -2 - 4*u - u**2 + 3 - s + 0.
-(u + 2)**2
Let q(g) be the first derivative of -6 + 10/3*g**3 - 5/4*g**4 + 0*g**2 + 0*g. Factor q(r).
-5*r**2*(r - 2)
Let q(o) = o + 10. Let l be q(-7). What is k in 7*k + 5*k + 1 - 20*k**3 + 24*k**l - 12*k**2 - 5 = 0?
1
Suppose -4*z - 16 = -2*z + 2*f, -2*f = -2*z - 16. Let a be -5*(-3)/60 + 2/z. Factor a*d**2 + 0 - 2/7*d + 2/7*d**3.
2*d*(d - 1)*(d + 1)/7
Let a(b) be the first derivative of b**7/525 + b**6/300 - 6*b**2 - 9. Let m(q) be the second derivative of a(q). Solve m(k) = 0 for k.
-1, 0
Let b be 52 - 59 - (-322)/6. Suppose -56/3*w**2 - b*w**4 + 8/3*w + 0 + 50/3*w**5 + 46*w**3 = 0. Calculate w.
0, 2/5, 1
Solve -13/2*z + 37/2*z**3 + 11 - 3/2*z**4 - 43/2*z**2 = 0 for z.
-2/3, 1, 11
Suppose d - 10 = -2*r, 3*r + 0*r = d + 5. Factor 6*u**3 - u**r + 12*u**2 - 4*u**3 + 6 + 2*u**3 + 15*u.
3*(u + 1)**2*(u + 2)
Find b such that 88/5 - 432/5*b + 10*b**3 + 102*b**2 = 0.
-11, 2/5
Suppose -64/9 + 40/9*v - 10/9*v**4 - 14/9*v**3 + 16/3*v**2 = 0. Calculate v.
-2, 1, 8/5
Let z = -16 - -20. Let w(o) = 7*o**3 + o - 4. Let g(r) = 57*r**3 + 9*r - 33. Let k(b) = z*g(b) - 33*w(b). Determine u so that k(u) = 0.
-1, 0, 1
Let -4/3*c**4 + 2/3*c**2 - 10/3*c**3 + 0 + 4*c = 0. What is c?
-2, -3/2, 0, 1
Let y(a) = 56*a**2 + 7*a. Let o be y(1). Let u = 65 - o. What is h in -4*h**3 + 4/3*h**u + 14/3*h - 2/3*h**5 + 2 - 10/3*h**4 = 0?
-3, -1, 1
Let s(x) be the second derivative of x**5/16 - 35*x**4/24 + 125*x**3/24 - 15*x**2/2 + 5*x - 6. Find u, given that s(u) = 0.
1, 12
Determine h so that 1/4*h**4 - 11/4*h - 3/4*h**2 + 3/4*h**3 - 3/2 = 0.
-3, -1, 2
Suppose -4*p + 32 = 0, k = p - 3 - 3. Factor 6/7*q**k - 18/7*q + 8/7*q**3 + 4/7.
2*(q - 1)*(q + 2)*(4*q - 1)/7
Let n(t) be the third derivative of -t**6/72 + 4*t**5/45 + 17*t**4/72 - 2*t**3/9 + 86*t**2. Factor n(k).
-(k - 4)*(k + 1)*(5*k - 1)/3
Let c(d) be the third derivative of -d**6/24 + d**5/2 - 5*d**4/8 - 25*d**3/3 - 92*d**2. Factor c(t).
-5*(t - 5)*(t - 2)*(t + 1)
Let l(a) = a**3 - 15*a**2 + 4. Let i be l(15). Let b(s) be the first derivative of -2/3*s**3 + 0*s**i + 1/5*s**5 + 0*s**2 + s + 4. Factor b(o).
(o - 1)**2*(o + 1)**2
Let h(t) = -t**2 + 19*t - 15. Let s be h(18). Find z such that 4*z - 16*z**2 + 0*z**s - 55*z**4 + 5*z**3 + 80*z**4 = 0.
-1, 0, 2/5
Let z be ((-16)/8)/((-9)/6 + 1). Find c, given that -113*c - 4*c**2 + 117*c - z*c**2 = 0.
0, 1/2
Let g be (-2)/5 - 2/(-5). Suppose -9*o**2 + 0 + g - 3*o**4 - 211*o - 9*o**3 + 208*o = 0. What is o?
-1, 0
Determine u, given that 196*u**2 - 61*u**2 + 39*u**3 + 10*u - 184*u**3 = 0.
-2/29, 0, 1
Let w be (-1)/((-18)/20 + (-4)/(-10)). Factor -23*k**2 + 18*k**w + 10*k**2.
5*k**2
Determine l so that 82/7*l + 12*l**2 + 2/7*l**3 + 0 = 0.
-41, -1, 0
Let u be 18 + -11 + -9 + (-57)/(-27). Let m(h) be the first derivative of 9 - 1/2*h**2 + u*h**3 + 2/3*h. Find o such that m(o) = 0.
1, 2
Let t = 1420 + -1418. Factor 2/9*l**t - 10/9*l + 0.
2*l*(l - 5)/9
Let c be 32/10 + 5/(-25). Suppose -m - c*m = -2*t - 48, -m + 34 = 5*t. Determine f, given that 15*f**3 + m*f**2 + 4 + 3*f**4 + 1 + 1 + 21*f + 13*f**2 = 0.
-2, -1
Let j(a) be the second derivative of -a**4/12 + 15*a**3/2 - 22*a**2 + 7*a - 5. Factor j(c).
-(c - 44)*(c - 1)
Let y(h) = -h**3 - 2*h**2 + h - 4. Let s be y(-3). Let l = 199 - 195. Factor b**2 + 3 + l*b + 0 - 9 + b**s.
2*(b - 1)*(b + 3)
Let w(n) = -5*n**3 + 107*n**2 - 200*n + 57. Let j(i) = 3*i**3 - 54*i**2 + 100*i - 28. Let v(r) = -9*j(r) - 4*w(r). What is x in v(x) = 0?
2/7, 2, 6
Let t(v) = -v**2 + 3*v + 12. Let c be t(5). Let -3/5 - 2/5*g + 4/5*g**c + 2/5*g**3 - 1/5*g**4 = 0. What is g?
-1, 1, 3
Factor -7*n**3 + 7/2*n**2 - 3/2*n**4 + 0 + 5*n.
-n*(n - 1)*(n + 5)*(3*n + 2)/2
Let v(j) be the third derivative of j**5/570 - j**4/114 - j**3/19 + 24*j**2 - 4*j. Factor v(c).
2*(c - 3)*(c + 1)/19
Suppose -2*c + 3*c = 14*c. Solve -4/3*r**2 + c + 2/3*r**3 + 2/3*r = 0.
0, 1
Suppose 341 = -3*r - 100. Let j = r + 1031/7. Factor 2/7*i**2 + 0 - j*i.
2*i*(i - 1)/7
Factor 6*u**2 - 8*u**2 - 75 + 30*u - 5*u**2 + 4*u**2.
-3*(u - 5)**2
Let j(u) = -u**2 + 2*u + 1. Let y(x) = 28*x - 4. Let t(q) = 4*j(q) + y(q). Factor t(c).
-4*c*(c - 9)
Let n(v) = 2*v**2 - 3*v - 2. Let f be n(-2). Factor 7*b**3 + 4*b**4 - 19*b**3 - 19*b**2 + f*b + 15*b**2.
4*b*(b - 3)*(b - 1)*(b + 1)
Find v such that -32/7*v - 8 - 2/7*v**2 = 0.
-14, -2
Let v(g) = g**4 + g**3 + 2*g**2 - 2. Let l(t) = 71*t**4 - 184*t**3 + 100*t**2 + 8. Let s(i) = -l(i) - 4*v(i). Factor s(j).
-3*j**2*(5*j - 6)**2
Let v(g) be the third derivative of -g**5/12 - 55*g**4/12 - 100*g**3/3 - 874*g**2. Factor v(d).
-5*(d + 2)*(d + 20)
What is k in 0*k**5 + 416*k - 41*k**4 - k**5 + 37*k**2 - 128 - 48*k**2 + 206*k**3 + 4*k**5 - 445*k**2 = 0?
2/3, 1, 4
Let g(x) be the first derivative of 49*x**5 - 945*x**4/4 - 305*x**3/3 + 705*x**2/2 - 180*x - 417. Suppose g(t) = 0. Calculate t.
-1, 3/7, 4
Let q(a) be the first derivative of -13 - a**2 + 0*a - 2/9*a**3. Factor q(z).
-2*z*(z + 3)/3
Suppose -5*j = 2*c - j - 8, -2*c - 5*j + 9 = 0. Factor -108 + 36*s + 7*s**2 - 16*s**c + 6*s**2.
-3*(s - 6)**2
Let y be (-1)/(-7) + (-102)/(-21). Let v = y - 0. Factor 12*t**3 + t**4 + t**5 - 5*t**3 + 5*t**4 + 8*t**2 + v*t**3.
t**2*(t + 2)**3
Let f be (3 - (-20)/(-8))*18. Suppose 5*c = c + 100. What is v in f*v**4 - 3*v**3 + 3*v**5 - c*v**2 - 3 + 4*v**2 + 15 = 0?
-2, -1, 1
Let p be (24/7)/(1050/(-196) + 6). Factor -32/3 - p*w - 2/3*w**2.
-2*(w + 4)**2/3
Let v(u) = -u**3 + 13*u**2 + 14*u + 2. Let w = 9 - -5. Let z be v(w). Factor 1/2*k**3 + 0 - 1/2*k + 0*k**z.
k*(k - 1)*(k + 1)/2
Let x = -24 - 7. Let w be 2 + -5 + x/(-9). Factor 0*f**2 + w + 2/9*f**3 - 2/3*f.
2*(f - 1)**2*(f + 2)/9
Let p(v) = -5*v + 33. Suppose 2*y - 5*y + 5*o = 2, 0 = 2*y - 2*o - 4. Let g be p(y). Find m, given that 1/3 + 0*m**2 + m - 4/3*m**g = 0.
-1/2, 1
Let x(k) be the first derivative of -10 - 10*k + 7/30*k**5 + 29/9*k**3 - 5/3*k**4 - 2*k**2. Let i(p) be the first derivative of x(p). What is s in i(s) = 0?
2/7, 1, 3
Let l = -32 + 34. Solve 21*v**5 - 142*v**2 - 121*v**5 + 47*v**l + 85*v**4 - 5 - 25*v + 125*v**3 + 15 = 0 for v.
-1, -2/5, 1/4, 1
Let d(w) be the second derivative of -w**6/6 + 29*w**5/4 - 280*w**4/3 + 490*w**3/3 - 122*w. Suppose d(g) = 0. Calculate g.
0, 1, 14
Factor 57*u**2 - 4*u + 4*u**3 - 41 - 59 + 16*u**2 + 27*u**2.
4*(u - 1)*(u + 1)*(u + 25)
Let d(c) be the third derivative of -c**8/2016 + c**7/180 - c**6/48 + c**5/40 - 30*c**2 + 2*c. Find u, given that d(u) = 0.
0, 1, 3
Let t(v) be the second derivative of -v**6/6 - v**5/2 - 5*v**4/12 + 12*v. Factor t(w).
-5*w**2*(w + 1)**2
Suppose -2*l + 12 = 2*l, 2*l + 27 = 3*s. Let a(p) be the second derivative of -8