3*q**5/75 + 10609*q**4/60 + 3*q**2 + 83*q. Factor v(r).
2*r*(r + 103)**2/5
Let y(k) = -2*k**5 + k**4 - k**3 + 5*k**2 + 3*k - 6. Let x(i) = -i**5 - i**3 + 4*i**2 + 2*i - 4. Let d(b) = -3*x(b) + 2*y(b). Factor d(n).
-n**2*(n - 2)*(n - 1)*(n + 1)
Let h(b) be the second derivative of 0*b**2 + 0*b**3 - b + 1/3*b**4 + 0 - 2/15*b**6 + 0*b**5. Let h(c) = 0. What is c?
-1, 0, 1
Let u(f) be the third derivative of -1/1800*f**6 + 7*f**2 + 5/3*f**3 + 0*f**5 + 0 + 1/30*f**4 + 0*f. Let g(l) be the first derivative of u(l). Factor g(s).
-(s - 2)*(s + 2)/5
Let o(v) be the third derivative of v**10/211680 + v**9/52920 + v**8/47040 - 5*v**4/6 - 5*v**2. Let u(x) be the second derivative of o(x). Factor u(g).
g**3*(g + 1)**2/7
Let v(s) be the third derivative of 5/9*s**3 - 1/90*s**5 - 1/9*s**4 + 0*s + 0 - 12*s**2. Factor v(f).
-2*(f - 1)*(f + 5)/3
Let i(b) be the second derivative of -b**7/420 - b**6/12 - 5*b**5/4 - 125*b**4/12 - 7*b**3/6 - 14*b. Let d(f) be the second derivative of i(f). Factor d(x).
-2*(x + 5)**3
Suppose 68 = 3*x + 14*x. Let s(l) be the second derivative of 1/8*l**4 + 0 - x*l + 3/4*l**2 - 1/2*l**3. Factor s(o).
3*(o - 1)**2/2
Let l(t) be the second derivative of t**6/105 + 2*t**5/35 - 3*t**4/7 + 20*t**3/21 - t**2 + 165*t. Factor l(k).
2*(k - 1)**3*(k + 7)/7
Factor 400*f**3 + 12000 + 152*f**3 + 78*f**4 + 343*f**5 - 240*f**2 - 5522*f - 340*f**5 - 2878*f.
3*(f - 2)**2*(f + 10)**3
Let q = 108476/10129 - -7/1447. Suppose q*c + 18*c**2 + 12/7 + 27/7*c**3 = 0. Calculate c.
-4, -1/3
Let l(u) be the third derivative of u**8/1008 + u**7/315 - u**6/120 - u**5/45 + u**4/18 - 3*u**2 + 11*u. Suppose l(p) = 0. What is p?
-2, 0, 1
Let m(g) be the first derivative of -1/8*g**4 + 0*g**2 + 5/3*g**3 - 1/80*g**5 + 5 + 0*g + 1/240*g**6. Let n(q) be the third derivative of m(q). Factor n(s).
3*(s - 2)*(s + 1)/2
Let y(l) be the first derivative of -l**6/48 + l**4/8 - 59. Factor y(w).
-w**3*(w - 2)*(w + 2)/8
Let -57*n**3 + 4*n**2 + 3*n + 24*n**3 + 34*n**3 + 0 + 0 = 0. Calculate n.
-3, -1, 0
Let j(b) be the first derivative of -b**2 + 2/3*b**3 - 4*b - 14. Factor j(d).
2*(d - 2)*(d + 1)
Let i = 156 - 135. Find s, given that 0*s**3 + i*s**2 - 39*s**5 - 21*s**5 + 6*s - 111*s**4 - 36*s**3 = 0.
-1, -1/4, 0, 2/5
Let m(d) be the second derivative of -d**8/2016 + d**7/420 - d**6/360 - 7*d**2/2 - 12*d. Let x(r) be the first derivative of m(r). Factor x(j).
-j**3*(j - 2)*(j - 1)/6
Let p(b) be the first derivative of -2/5*b**2 + 0*b**4 + 2/5*b**3 + 11 + 0*b - 2/25*b**5. Determine m, given that p(m) = 0.
-2, 0, 1
Let y = 9 + -17/2. Factor y*q + 1 - 1/2*q**2.
-(q - 2)*(q + 1)/2
Let t = -24929/5 + 4986. Determine u so that -1/5*u**2 + t*u + 6/5 = 0.
-2, 3
Let c(z) be the third derivative of 1/40*z**4 + 2*z**2 + 0*z + 1/20*z**5 - 1/10*z**3 + 3/200*z**6 + 0. Suppose c(v) = 0. Calculate v.
-1, 1/3
Let j = 37122 - 296965/8. Factor 1/8*o**3 + 35/8*o - 25/8 - j*o**2.
(o - 5)**2*(o - 1)/8
Let x(q) be the first derivative of -q**5/360 - q**4/72 + q**3/12 - 7*q**2/2 + 14. Let y(v) be the second derivative of x(v). Factor y(t).
-(t - 1)*(t + 3)/6
Let c = -15 - -22. Suppose -5*k + 105 = 5*u, -2*u - c = -k - 1. Suppose -k*a**3 - 5*a**2 + 4 + 2*a**2 + 15*a**3 = 0. What is a?
-2, 1
Let d(i) be the second derivative of i**4/78 - 11*i**3/39 + 10*i**2/13 - 95*i. Find z such that d(z) = 0.
1, 10
Let s(r) be the first derivative of -r**5 + 40 - 720*r + 10*r**4 - 240*r**2 + 40/3*r**3. Suppose s(p) = 0. Calculate p.
-2, 6
Let u(j) be the third derivative of j**10/4320 - j**9/6048 - j**8/576 + j**7/504 + 13*j**5/60 - 33*j**2. Let w(f) be the third derivative of u(f). Factor w(k).
5*k*(k - 1)*(k + 1)*(7*k - 2)
Let h(c) be the third derivative of 1/84*c**8 - 8/105*c**7 + 0 + 0*c**3 + 9*c**2 + 0*c + 4/15*c**5 - 2/3*c**4 + 1/10*c**6. Determine p, given that h(p) = 0.
-1, 0, 1, 2
Let b = 172 - 168. Suppose 6*j = b*j + 8*j. Factor 0*i**2 + 3/5*i**4 + 0*i + 6/5*i**3 + j.
3*i**3*(i + 2)/5
Let i(j) be the first derivative of j**5 + 5*j**4/2 - 35*j**3/3 + 10*j**2 - 242. Factor i(n).
5*n*(n - 1)**2*(n + 4)
Let q(f) = f**3 + f**2 - f - 1. Let v = -23 + 25. Let c = 7 + v. Let u(a) = -3*a**4 - 6*a**3 - 18*a**2 - 30*a - 15. Let i(l) = c*q(l) - u(l). Factor i(g).
3*(g + 1)**3*(g + 2)
Let p(r) = -r**3 - 12*r**2 - 13*r - 18. Let d be p(-11). Factor -1/8*b**2 + 0*b + 1/8*b**d + 0 + 0*b**3.
b**2*(b - 1)*(b + 1)/8
Suppose -5*d + 35*i + 32 = 34*i, 0 = d - i - 8. Let a be 5/2 + (-1)/(-2). Factor k - 4*k**a - 4*k**2 - d*k - k**3 - 6*k**2.
-5*k*(k + 1)**2
Let x(g) be the first derivative of 3*g**3 - 3*g**2 - 237. What is s in x(s) = 0?
0, 2/3
Let w(d) be the second derivative of -d**5/40 - 19*d**4/24 - 16*d**3/3 - 15*d**2 + 193*d. Find b such that w(b) = 0.
-15, -2
Let d(f) = -15*f - 26. Let l be d(-2). Factor -6*r**l + 7*r**5 + 18*r**4 + 0*r**5 - 33*r**3 - 4*r**5 + 18*r**2.
3*r**2*(r - 1)**2*(r + 6)
Let z be (-12)/27*9/(-2). Let l(y) be the third derivative of 0 - 1/12*y**5 + 1/40*y**6 - 1/18*y**3 + 7/72*y**4 + 0*y - 3*y**z. Factor l(a).
(a - 1)*(3*a - 1)**2/3
Let u be (68/12 - 5)*(-8)/(-16). Let a(p) be the second derivative of 0*p**2 - 1/10*p**5 + 0 - 1/3*p**3 - u*p**4 - 7*p. What is c in a(c) = 0?
-1, 0
Let w = 1245 + -1244. Find o, given that -1/2*o**2 - 3/2*o - w = 0.
-2, -1
Let m(f) be the first derivative of -f**3/24 - 5*f**2/16 + 3*f/4 - 484. Factor m(s).
-(s - 1)*(s + 6)/8
Let b be (99/165)/(4/64). Solve -b*m**4 - 144/5*m**3 + 6/5 + 9/5*m - 93/5*m**2 = 0.
-2, -1, -1/4, 1/4
Suppose 2*h = 3*h - 25. Suppose 5*c - 3*f - 3 = 0, 3*c + 5*f - h = 4. Suppose 1 - 4 - 4*k - c*k**2 - 2*k = 0. Calculate k.
-1
Let y(f) be the first derivative of f**4/9 + 5*f**3/9 - f**2 + 37*f - 8. Let t(i) be the first derivative of y(i). Factor t(s).
2*(s + 3)*(2*s - 1)/3
Let a(f) = -10*f**5 - 45*f**4 - 19*f**3 - 2*f**2 + 2*f - 4. Let c(x) = -12*x**5 - 45*x**4 - 18*x**3 - 3*x**2 + 3*x - 6. Let j(o) = 3*a(o) - 2*c(o). Factor j(l).
-3*l**3*(l + 7)*(2*l + 1)
Let v = -2922/17 - -172. Let y be (-184)/920*(-10)/17. What is b in -y*b + v*b**2 + 0 = 0?
0, 1
Let n(u) be the second derivative of -u**6/6 + 9*u**5/4 - 65*u**4/12 - 15*u**3/2 + 35*u**2 + 736*u. Suppose n(m) = 0. What is m?
-1, 1, 2, 7
Suppose -2*y = 4*z + 72, -4*y - 54 = 4*z + 14. Let n = z + 21. Find s such that 0*s**3 - 4*s**3 + s**4 + 4*s - 3*s**4 + 4*s**4 - 2*s**n = 0.
-1, 0, 1, 2
Let j(d) be the first derivative of -d**3 + 117*d**2/2 + 246*d - 124. Let j(q) = 0. What is q?
-2, 41
Let a be 154/(-66)*63/2. Let q = a - -221/3. Factor -q*j**2 + 2/3 + 1/2*j.
-(j - 4)*(j + 1)/6
Let s(t) = -t + 6. Let d be s(3). Suppose 14*x**d - x**4 - 6*x**3 + 10*x**2 + 4*x + 4*x**4 - x**4 = 0. What is x?
-2, -1, 0
Let k be (4/(-32))/((396/(-16))/9). Let g(w) be the third derivative of 0 + 0*w - 5*w**2 - 3/11*w**3 + k*w**4 - 1/330*w**5. Solve g(y) = 0 for y.
3
Let 4*h**3 + 1443 + 2*h**5 - 1443 - 6*h**5 + 0*h**5 = 0. What is h?
-1, 0, 1
Find h such that -2/15*h**3 + 32/15*h**2 + 0 + 24/5*h = 0.
-2, 0, 18
Let o be (0 + -1)*20/(-4). Let m(k) be the second derivative of 0 + 1/90*k**o + 0*k**4 - 3*k + 0*k**2 - 1/27*k**3. Factor m(n).
2*n*(n - 1)*(n + 1)/9
Let g(z) = -170 - 12*z - 16*z - 6*z**2 + 5*z + 84. Let s(t) = t**2 + t + 1. Let n(p) = -g(p) - 5*s(p). Factor n(d).
(d + 9)**2
Factor -x**2 + 32*x**3 + 16*x - 27*x**2 - 48 + 48*x - 28*x**3.
4*(x - 3)*(x - 2)**2
Let l(x) = -3*x + 20. Let n be l(8). Let z be (2/(-168)*n)/((-2)/(-6)). Let z*s**2 + 3/7*s**3 + 0 + 0*s = 0. What is s?
-1/3, 0
Let m be 2/(-3)*(-54)/12. Solve 24*w**2 + 8*w**4 - 15*w**5 - 5*w**3 + 27*w**m + 16*w**5 + 9*w = 0.
-3, -1, 0
Let y(x) be the third derivative of -x**5/12 + 15*x**4/2 + 190*x**3/3 + 6*x**2 + 29*x. Factor y(a).
-5*(a - 38)*(a + 2)
Let q(c) be the third derivative of -c**8/2016 + 19*c**7/1260 - 31*c**6/240 - 3*c**5/40 + 27*c**4/8 - 243*c**2. Suppose q(k) = 0. Calculate k.
-2, 0, 3, 9
Let f(r) = -6*r**2 + 129*r - 9. Let n(x) = x**2 + x + 3. Let p(i) = f(i) + 3*n(i). Let p(j) = 0. What is j?
0, 44
Suppose -3*w = -4*w + 6. Let u be ((-1)/10)/(w/(-12)). Find t, given that u + 2/5*t**2 + 3/5*t = 0.
-1, -1/2
Let b = -756920/10611 + 2/10611. Let j = 73 + b. What is v in -4/3 - 8/3*v - 1/3*v**3 - j*v**2 = 0?
-2, -1
Let b(p) = 5*p**3 + 15*p**2 + 10. Let a(u) = u - 1. Let v(n) = 3*n - 3. Let j(m) = -2*a(m) + v(m). Let t(x) = -b(x) - 10*j(x).