50 - k**4/15 - 4*k**3/5 + 17*k**2/2 - 2*k. Let x(q) be the first derivative of r(q). Factor x(u).
-2*(u + 6)**2/15
Let u(w) be the first derivative of 1/24*w**3 + 1/16*w**2 - 11 + 0*w. Factor u(n).
n*(n + 1)/8
Let o(w) = 2*w**3 + 49*w**2 - 25*w + 5. Let d be o(-25). Let z = 461/2 + -226. Determine l, given that -z*l**3 + 0 + 3*l**4 - 3/4*l**d - 3/4*l + 3*l**2 = 0.
0, 1
Suppose -y = 5*w - 179, -3*y - 2*w = -2*y - 185. Solve -12*o + 46*o**4 + y*o**2 - 33*o**3 - 7*o**4 - 273*o**2 = 0.
-1, -2/13, 0, 2
What is q in -115*q + 270*q**3 - 55 + 269*q**3 - 544*q**3 - 65*q**2 = 0?
-11, -1
Suppose i + 12 = 2*w + 3*i, -2*w + 5*i = 9. Factor -3*k**2 + k - 1 - w*k**2 - k**3 - 1 + 8*k**2.
-(k - 2)*(k - 1)*(k + 1)
Let n(j) = j**2 + 6*j - 10. Let i be n(-8). Let k = 2 + 2. What is q in k + 3 + 3*q**2 + 0*q - i*q - 4 = 0?
1
Let z(v) be the first derivative of v**6/30 + v**5/20 + 3*v + 3. Let y(o) be the first derivative of z(o). Factor y(c).
c**3*(c + 1)
Let q(w) = -10*w**2 - 5*w + 10. Let c(z) = -z**3 + 9*z**2 + 6*z - 8. Let d(f) = -5*c(f) - 4*q(f). Suppose d(x) = 0. Calculate x.
-1, 0, 2
Let l(i) = 25*i - 125. Let n be l(5). Let b(f) be the second derivative of 1/66*f**4 + 1/33*f**3 + 0*f**2 + n - 5*f. Factor b(j).
2*j*(j + 1)/11
Suppose -x + 11 = 5*m + 3, 2*x - 4*m = 30. Let c(d) = d**2 - 10*d + 10. Let w(u) = -2*u**2 + 21*u - 21. Let a(l) = x*c(l) + 6*w(l). Solve a(p) = 0 for p.
2
Let c(p) be the first derivative of 5*p**6/36 + 7*p**5/6 + 25*p**4/8 + 25*p**3/18 - 20*p**2/3 - 10*p + 337. Find h such that c(h) = 0.
-3, -2, -1, 1
Let d(n) be the first derivative of -2*n**2 + 2/45*n**3 - 7/150*n**5 + 0*n + 2 - 1/180*n**4. Let x(h) be the second derivative of d(h). What is g in x(g) = 0?
-1/3, 2/7
Suppose 20*i - 23*i = -42. Let y = 16 - i. Factor 71*o**2 + 15*o**3 - 3*o**4 - 81*o**y - 2*o**4.
-5*o**2*(o - 2)*(o - 1)
Suppose -7*o + 10 = -18. Determine b so that -7*b**2 + 359*b**o - b**2 - 311*b**4 + 28*b**5 + 12*b**3 = 0.
-1, 0, 2/7
Let n be (-2)/(-2*(-3)/(-9)). Let q = n + 15. Suppose q*h - 4*h**2 - 15*h + h**2 = 0. What is h?
0, 1
Solve 32*x + x**3 - 2*x**2 - 24 + 32*x - 127*x + 43*x = 0 for x.
-2, 6
Factor -c**4 - 5*c**3 - 2 + 2 - 1807*c**2 + 1801*c**2.
-c**2*(c + 2)*(c + 3)
Let c be ((-510)/(-126) + -4)/((-10)/(-7)). Let d(i) be the second derivative of 0 - 3*i - c*i**3 - 1/60*i**4 + 0*i**2. Factor d(h).
-h*(h + 1)/5
Let g(f) be the first derivative of 15*f**3 - 3/4*f**4 - 192*f + 16 - 72*f**2. Factor g(b).
-3*(b - 8)**2*(b + 1)
Suppose 3*k + t = -149, -3 = -k + 4*t - 44. Let w be ((-14)/k + (-4)/14)/(-1). Factor -3/2*h**4 - 4*h**3 - 3*h**2 + w*h + 1/2.
-(h + 1)**3*(3*h - 1)/2
Let f(x) be the third derivative of 11*x**5/20 - 5*x**4/8 + 9*x**2 - 6*x. Suppose f(i) = 0. What is i?
0, 5/11
Let k = -11013 - -77094/7. Solve -6/7 - k*w + 3/7*w**2 = 0.
-1, 2
Let f(k) be the first derivative of k**6/360 + k**5/90 + k**4/72 + 16*k**2 + 17. Let g(t) be the second derivative of f(t). Find x, given that g(x) = 0.
-1, 0
Let s(g) be the second derivative of -15/4*g**4 - 5/3*g**3 + 0*g**2 + 0 - 3*g**5 + 13*g - 5/6*g**6. Determine t so that s(t) = 0.
-1, -2/5, 0
Factor 24/5*b**3 + 5*b**5 + 16*b**4 + 16/5*b - 64/5*b**2 + 0.
b*(b + 2)**2*(5*b - 2)**2/5
Let n(s) = 38*s**3 + 309*s**2 + 41*s + 11. Let q be n(-8). Factor 3/2*u**q + 12*u + 15/2*u**2 + 6.
3*(u + 1)*(u + 2)**2/2
Let y(j) be the second derivative of 3*j**5/25 - 31*j**4/20 + 2*j**3 + 21*j**2/10 + 41*j. Factor y(u).
3*(u - 7)*(u - 1)*(4*u + 1)/5
Let a(j) be the second derivative of 2*j**6/15 + 2*j**5 - 28*j**4 + 368*j**3/3 - 256*j**2 + 65*j. What is d in a(d) = 0?
-16, 2
Let t(m) = 2*m**2 + 1. Let n(b) = -5*b**2 + 69*b - 76. Let v(k) = -n(k) - 4*t(k). Determine g, given that v(g) = 0.
-24, 1
Let n(z) be the second derivative of z**2 + 0*z**5 + 3*z - 1/12*z**4 - 2/9*z**3 + 0 + 1/180*z**6. Let q(d) be the first derivative of n(d). Factor q(l).
2*(l - 2)*(l + 1)**2/3
Let r be (-8)/14 + -2 + (-612)/(-42). Let f(d) be the second derivative of 0 - 1/30*d**4 + 0*d**2 + r*d + 1/15*d**3. Factor f(p).
-2*p*(p - 1)/5
Let k be (-2)/(-4) + (-14472472)/1232. Let l = 11757 + k. Let -18/11 - 370/11*j**3 - 62/11*j**2 + l*j - 208/11*j**4 - 32/11*j**5 = 0. Calculate j.
-3, -1, 1/4
Let p = 1210 + -2335/2. Let v = p - 42. Find y such that v*y**4 + 0 + 1/4*y + 5/4*y**3 + y**2 = 0.
-1, -1/2, 0
Factor -556*v - 26*v**3 + 173 - 188*v + v**4 + 56*v + 116*v + 213*v**2 + 311.
(v - 11)**2*(v - 2)**2
Determine g so that 27 + 13 - 71*g + 36*g + 2*g**2 - 7*g**2 = 0.
-8, 1
Let s(l) be the first derivative of -2*l**5/5 + 2*l**4 + 8*l**3 - 79. Factor s(t).
-2*t**2*(t - 6)*(t + 2)
Let c(u) = -u**3 - 10*u**2 - 9*u + 5. Let d be c(-9). Suppose -f - 4 = 0, -d*r - 3*f = -2*r + 3. Factor -9*z**r + 2*z**4 + 0*z**4 - 2*z**4 + 3*z**4 + 6*z**2.
3*z**2*(z - 2)*(z - 1)
Let v = 141 - -9. Let d be 1*(v/35 + -4). Factor 0*i**2 - 2/7*i**4 - d*i**5 + 4/7*i**3 + 0 + 0*i.
-2*i**3*(i - 1)*(i + 2)/7
Let t be (-4)/(-34) + (-133560)/(-17850). Let -t*r - 4/5 - 34/5*r**2 = 0. Calculate r.
-1, -2/17
Let d(h) = h + 3. Let b be d(-1). Suppose b*m + 0 = 5*o - 10, 5*m = -2*o - 25. Let -1/4*w + 1/4*w**2 + o = 0. Calculate w.
0, 1
Factor 6*o**2 + 0 - 16/3*o - 2/3*o**3.
-2*o*(o - 8)*(o - 1)/3
Let k(q) be the second derivative of 2*q**7/161 - q**6/345 - q**5/23 + 4*q**3/69 + q**2/23 + 397*q. Solve k(a) = 0 for a.
-1, -1/2, -1/3, 1
Let f(j) be the second derivative of 2*j**7/147 + 8*j**6/105 + 3*j**5/35 + 28*j + 2. Solve f(l) = 0 for l.
-3, -1, 0
Find c such that 2/5*c**2 + 4/5*c**3 - 4/5*c + 0 - 2/5*c**4 = 0.
-1, 0, 1, 2
Let t(m) be the second derivative of m**7/63 - 8*m**6/5 + 7*m**5 - 104*m**4/9 + 23*m**3/3 - 298*m + 1. Find i, given that t(i) = 0.
0, 1, 69
Let m(p) be the third derivative of 0*p + 1/15*p**5 - 2/105*p**7 + 1/6*p**4 + 0*p**3 + 3*p**2 - 1/30*p**6 + 0. What is o in m(o) = 0?
-1, 0, 1
Let w be (0/4)/(-3 - -1). Let i = 33 + -31. Factor w*n + 0 + 2/5*n**i.
2*n**2/5
Factor -3*f**3 + 3/4*f**5 + 0*f**4 - 3/2 + 9/4*f + 3/2*f**2.
3*(f - 1)**3*(f + 1)*(f + 2)/4
Suppose 118 - 4*o**4 - 243 + 109 + 3*o - 4*o**5 + 20*o**2 - 19*o + 20*o**3 = 0. What is o?
-2, -1, 1, 2
Let z(y) be the first derivative of -y**3/9 - y**2/3 + 11. Let z(j) = 0. What is j?
-2, 0
Let v(j) be the third derivative of -1/90*j**5 + 2/315*j**7 + 0 + 0*j + 1/90*j**6 - 5/72*j**4 + 1/1008*j**8 - 25*j**2 - 1/9*j**3. Factor v(c).
(c - 1)*(c + 1)**3*(c + 2)/3
Let w(v) = -8*v**2 - 37*v - 18. Let t(m) = m**2 + 4*m + 2. Let a(h) = 18*t(h) + 2*w(h). Factor a(c).
2*c*(c - 1)
Suppose -21 = 5*s + 2*c + 38, 3*s + 54 = 5*c. Let u be 2/s*99/(-33). Solve -u*i**2 + 14/13*i - 4/13 = 0.
1/3, 2
Let g(w) = -4*w**2 + 22*w - 10. Let k be g(5). Factor -3/5*d**2 + k - 3/5*d**3 + 0*d.
-3*d**2*(d + 1)/5
Suppose -8*a = -18*a - 60. Let j be (2/(-3))/(a/27). Factor -8/3*z**2 - 1/3*z - 5/3*z**j + 2/3.
-(z + 1)**2*(5*z - 2)/3
Let v(r) = -12*r**4 - 5*r**3 - 24*r**2 + 12*r + 7. Let t(i) = i**4 + i**3 + i**2 - 1. Let a(l) = -44*t(l) - 4*v(l). Let a(q) = 0. Calculate q.
1, 2
Let y(o) = 4*o - 6. Let w be y(3). Factor -10*b + 22 - w*b**2 + 14 + 10*b**2 - 14*b.
4*(b - 3)**2
Let n = -48 + 50. Let c(y) be the third derivative of 0*y**3 + 0*y + 1/210*y**7 - 3*y**n + 0*y**4 + 0*y**5 + 1/120*y**6 + 0. Factor c(o).
o**3*(o + 1)
Let t(w) be the second derivative of w**7/98 - w**6/10 + 3*w**5/14 + w**4/14 - 11*w**3/14 + 15*w**2/14 + 31*w - 3. Factor t(l).
3*(l - 5)*(l - 1)**3*(l + 1)/7
Let u(j) be the second derivative of -1/6*j**4 + 0 + j + 1/9*j**3 + 1/10*j**5 + 0*j**2 - 1/45*j**6. Factor u(v).
-2*v*(v - 1)**3/3
Let n(i) be the first derivative of -3*i**3/5 + 6*i**2/5 + 12*i/5 - 273. Solve n(q) = 0.
-2/3, 2
Solve 9/2*t - 3/2*t**3 - 3*t**2 + 0 = 0 for t.
-3, 0, 1
Let j be 2/10*(66 + -65). Let m(g) be the first derivative of -1/15*g**6 + 0*g**5 + 0*g**3 + 1/5*g**4 - j*g**2 + 7 + 0*g. Determine x, given that m(x) = 0.
-1, 0, 1
Let f(g) be the third derivative of -2*g**7/105 - g**6/10 - 3*g**2 - 6. Factor f(m).
-4*m**3*(m + 3)
Let x(c) = 2*c**3 - 12*c**2 + 28*c - 47. Let q be x(4). Factor -3*v - q - 9/4*v**2.
-(3*v + 2)**2/4
Let n = -1627 - -1630. Factor 1/2*w**n + 1/4*w**4 - 3/4*w**2 - 1 - 2*w.
(w - 2)*(w + 1)**2*(w + 2)/4
Let n(o) be the first derivative of 1/4*o**3 + o - 22 + o**2 - 1/20*o**5 - 1/8*o**4. Suppose n(x) = 0. Calculate x.
-2, -1, 2
Suppose f = 5*