i(s) be the third derivative of k(s). Suppose i(h) = 0. What is h?
-2, 0
Let q = 10 + -7. Let d(u) be the first derivative of 2/9*u**q + 0*u - 1/3*u**2 + 3. Factor d(j).
2*j*(j - 1)/3
Let l be (-5)/(-3) - (-2 - 0)/(-2). Let h(i) be the second derivative of -3*i + 2/9*i**3 + 1/36*i**4 + l*i**2 + 0. Let h(s) = 0. What is s?
-2
Let q(s) be the first derivative of s**3 - 3*s**2 - 9*s + 46. Factor q(m).
3*(m - 3)*(m + 1)
Factor -16 + 4 - 6*c - 69*c**2 - 54*c - 21*c**3.
-3*(c + 1)*(c + 2)*(7*c + 2)
Let y(s) be the second derivative of 3/20*s**5 + 3*s - 1/2*s**3 - 3/2*s**2 + 1/4*s**4 + 0. Factor y(p).
3*(p - 1)*(p + 1)**2
Solve 1 - w**3 - w**4 - 1 = 0 for w.
-1, 0
Let v(x) be the first derivative of -2 - 1/15*x**3 + 2/5*x + 1/10*x**2. Factor v(t).
-(t - 2)*(t + 1)/5
Suppose 0 = 2*z - 3*o + 1, 5*z = o + o + 3. Suppose -z + 18*p**4 + 18*p**4 - 33*p**2 - 6*p**3 + 24*p**5 - 18*p - 2 = 0. Calculate p.
-1, -1/2, 1
Let l be (6 - 1) + -3 + 1. What is r in -5*r**2 - 9 - l + 2*r**2 + 12*r = 0?
2
Let z be 2/(6/(-9)*6 + 8). Factor z*s**2 - 1/2*s**4 + 0 - 1/2*s**3 + 1/2*s.
-s*(s - 1)*(s + 1)**2/2
Factor -30*l + 0*l**2 + 6*l**2 - 35 - l**2.
5*(l - 7)*(l + 1)
Let a be (8/(-12))/((-5)/3). Let k = -3 + 6. Factor 2/5*c**2 - 2/5*c**4 + a*c**k + 0*c - 2/5*c**5 + 0.
-2*c**2*(c - 1)*(c + 1)**2/5
Let i be 2/(-5) + (-2)/(-5). Suppose i = -3*v - r + 7, 2 + 26 = 2*v - 4*r. Factor 0 + 0*h - 1/3*h**3 - 1/3*h**5 + 2/3*h**v + 0*h**2.
-h**3*(h - 1)**2/3
Let j be 0*(-4 + (-9)/(-2)). Suppose 0 - 2/3*r**2 + 1/3*r**3 + j*r = 0. Calculate r.
0, 2
Let g(m) = -4*m**3 + 8*m**2 - 6*m - 6. Let b be (-50)/(-4) - (-3)/(-2). Let p(y) = 7*y**3 - 15*y**2 + 11*y + 11. Let s(j) = b*g(j) + 6*p(j). Factor s(t).
-2*t**2*(t + 1)
Let x(j) be the first derivative of 5*j**4/8 + 5*j**3/2 + 15*j**2/4 + 5*j/2 + 13. Let x(m) = 0. Calculate m.
-1
Let r(g) = -g**3 - g**2 + 5. Let f(w) = -w**3 - w**2 + 6. Let t = -19 - -14. Let q(d) = t*f(d) + 6*r(d). Factor q(v).
-v**2*(v + 1)
Let g = -37 + 40. Let v = -51/2 - -27. Factor -3/2*n - 3/2*n**4 + 3/2*n**g + v*n**2 + 0.
-3*n*(n - 1)**2*(n + 1)/2
Suppose 0 = 4*p + 2*h + 22, -3*p - 7 - 3 = -5*h. Let z(k) = 28*k**2 - 3*k. Let j(w) = 42*w**2 - 4*w. Let y(c) = p*j(c) + 8*z(c). Factor y(r).
2*r*(7*r - 2)
Factor -640*b**2 + 662*b**4 - 2500*b**5 - 64*b - 1209*b**4 - 2400*b**3 - 3453*b**4.
-4*b*(5*b + 2)**4
Factor s**3 + 0*s**3 + 4*s - 4*s**2 + s - 2.
(s - 2)*(s - 1)**2
Let i be (1 + 5)*(-34)/6. Let j be 2/(-5) - i/10. Let 3*k - j*k + 2*k**4 - 4*k**3 + 2*k**2 = 0. What is k?
0, 1
Let w(a) = -a**2 + 8*a - 9. Let t be w(6). Find r such that 3*r**3 - 4*r**t - r**4 + 0*r**3 = 0.
-1, 0
Let u be ((-3)/(-7))/(6 - 40/7). Factor 3/2*j**3 + u*j**2 + 1/2*j**4 + 0 + 1/2*j.
j*(j + 1)**3/2
Let r(g) be the first derivative of 2*g**6/7 + 6*g**5/7 + 9*g**4/14 - 2*g**3/7 - 3*g**2/7 + 5. Suppose r(v) = 0. Calculate v.
-1, 0, 1/2
Let z(i) be the second derivative of 6*i + 1/120*i**5 + 0*i**2 + 0*i**3 + 0 + 1/36*i**4. Factor z(n).
n**2*(n + 2)/6
Let n(j) be the first derivative of j**3/12 - j**2 + 4*j - 8. Factor n(m).
(m - 4)**2/4
Let d be (-14)/(-3) - (-4)/12. Suppose 0 = 2*y - d - 15. Factor 6*z**4 - 3*z**4 + y*z**4 + 6*z**2 - 15*z**3 - 4*z**4.
3*z**2*(z - 1)*(3*z - 2)
What is g in -1/2*g**2 + 0 - 1/2*g = 0?
-1, 0
Let d(i) be the second derivative of 0 + 1/6*i**3 - 1/20*i**5 + 1/5*i**2 - 1/30*i**4 + i. Factor d(l).
-(l - 1)*(l + 1)*(5*l + 2)/5
Let d = 21 - 29. Let w(l) = 0*l - 3*l - 5*l + 5 + 11*l**2. Let t(r) = -7*r**2 + 5*r - 3. Let h(a) = d*t(a) - 5*w(a). Let h(q) = 0. What is q?
-1, 1
Let l(y) be the first derivative of -y**6/120 - y**5/20 - 2*y**3/3 + 4. Let n(z) be the third derivative of l(z). Factor n(t).
-3*t*(t + 2)
Let v(z) = -1 - 3*z**2 + 4*z**2 - 5*z**2 + 3*z**2. Let n(k) = -4*k**3 + 2*k**2 + 2. Let f(s) = -n(s) - 2*v(s). Let f(t) = 0. What is t?
0
Let o be ((-6)/8)/(2/(-8)). Find g such that -7*g**3 + 3*g**3 - 4*g**2 + 3*g**o + 5*g**2 = 0.
0, 1
Let x(j) be the second derivative of -49/20*j**5 + 2*j**2 + 0 + 7/4*j**4 + 4*j**3 - 4*j. Find q such that x(q) = 0.
-2/7, 1
Let -3*v**2 - 5 + 3 + 5*v**2 = 0. Calculate v.
-1, 1
Let z(n) be the first derivative of -2*n**3/21 - n**2/7 - 8. Factor z(i).
-2*i*(i + 1)/7
Let k = 139 - 136. Factor -3/2*w**2 - 1/4*w**4 - 1/4 + w**k + w.
-(w - 1)**4/4
Let j(i) be the first derivative of -3/2*i**2 + 0*i + i**3 - 3. Factor j(q).
3*q*(q - 1)
Factor 4/5*o**3 + 2/5*o**4 + 0 + 0*o + 0*o**2.
2*o**3*(o + 2)/5
Let c(d) = 2*d - 2*d - 2*d**3 - 2 + d**3 - d**2. Let k be c(-2). Solve -s**5 - 1/2*s**4 - 1/2 + k*s**3 - s + s**2 = 0.
-1, -1/2, 1
Let d(a) = 9*a**3 - 21*a**2 + 48*a - 21. Let u(w) = 2*w**3 - 5*w**2 + 12*w - 5. Let q(m) = 5*d(m) - 21*u(m). Let q(h) = 0. What is h?
-2, 0, 2
Let d(p) be the first derivative of -p**3/9 - p**2/6 - 16. Factor d(q).
-q*(q + 1)/3
Suppose -y = -4*u + 4, u = 3*y - y + 1. Let p(c) be the first derivative of 2 - 1/6*c**4 - 1/15*c**5 + y*c**2 - 1/9*c**3 + 0*c. What is z in p(z) = 0?
-1, 0
Let c(x) be the first derivative of -x**6/16 + 3*x**4/16 - 3*x**2/16 - 9. Factor c(s).
-3*s*(s - 1)**2*(s + 1)**2/8
Let h(g) = 3*g**4 - g**3 + 3*g**2 - g - 2. Let t = 8 + -10. Let d(a) = 10*a**4 - 2*a**3 + 9*a**2 - 3*a - 7. Let v(q) = t*d(q) + 7*h(q). Let v(s) = 0. What is s?
0, 1
Let k(u) be the second derivative of -5*u**4/24 + 13*u**3/12 + 3*u**2/2 + 23*u. Factor k(o).
-(o - 3)*(5*o + 2)/2
Let y(q) be the first derivative of 0*q + 0*q**3 + 0*q**2 + 1/24*q**6 + 0*q**5 - 1/16*q**4 - 2. Factor y(x).
x**3*(x - 1)*(x + 1)/4
Determine u, given that 0*u**2 + 0*u - 3/4*u**4 + 0 + 0*u**3 = 0.
0
Factor 15/2*z**5 + 33*z**4 + 57*z**3 + 3 + 39/2*z + 48*z**2.
3*(z + 1)**4*(5*z + 2)/2
Let w be 1/(-2) + (-2)/(-4). Suppose 0 = -g + 3 - w. Let -3*a**g + 4 + 5*a**4 - 6*a**2 + 3*a - 2 - a**2 = 0. What is a?
-1, -2/5, 1
Find h such that -131*h + 156*h + 5*h**2 - 1 + 1 = 0.
-5, 0
Let j(u) be the second derivative of u**6/10 - 9*u**5/20 + 3*u**4/4 - u**3/2 + 3*u. Factor j(f).
3*f*(f - 1)**3
Let g(f) = -f**4 + 1. Let l(u) = -3*u**5 - 9*u**4 + 6*u**3 - 6*u**2 - 3*u + 15. Let m(j) = -12*g(j) + l(j). Find w such that m(w) = 0.
-1, 1
Let g be 0 + 6 + 3/(-1). Let 6*j**3 - 2*j**3 - j - 4*j**3 - 2*j**2 - j**g = 0. Calculate j.
-1, 0
Let i(j) be the third derivative of j**9/34560 - j**8/16128 - j**7/10080 - j**5/30 + 3*j**2. Let x(n) be the third derivative of i(n). Factor x(q).
q*(q - 1)*(7*q + 2)/4
Let s(u) be the third derivative of -u**5/15 + u**4/6 - 3*u**2. Solve s(p) = 0 for p.
0, 1
Let z(h) be the first derivative of -h**4/10 - 2*h**3/5 - 2*h**2/5 + 13. Suppose z(f) = 0. Calculate f.
-2, -1, 0
Let t(v) = -5*v**2 - 6 + 5*v**4 - 2*v**3 + 1 - 2*v + 0 + v**2. Let z(u) = 6*u**4 - 3*u**3 - 5*u**2 - 2*u - 6. Let y(q) = -5*t(q) + 4*z(q). Factor y(k).
-(k - 1)*(k + 1)**3
Let q(p) be the third derivative of p**6/180 + p**5/90 - p**4/36 - p**3/9 - 8*p**2. Factor q(b).
2*(b - 1)*(b + 1)**2/3
Let m be 2/6*(8 + 1). Let c(y) = 9*y**2 + 3*y + 3. Let f(u) = -u**3 - 8*u**2 - 3*u - 2. Let z(k) = m*f(k) + 2*c(k). Factor z(v).
-3*v*(v + 1)**2
Let g(s) be the third derivative of -4*s**2 - 1/420*s**6 + 0 + 1/735*s**7 - 1/210*s**5 + 1/1176*s**8 + 0*s**4 + 0*s**3 + 0*s. Solve g(j) = 0 for j.
-1, 0, 1
Let a = -47 + 47. Let r(x) be the third derivative of a*x**4 + 0*x**3 + 0*x + x**2 - 1/240*x**5 + 1/480*x**6 + 0. Factor r(y).
y**2*(y - 1)/4
Let k(a) = -3*a**4 + 57*a**3 - 45*a**2 - 39*a + 48. Let f(g) = -g**4 + 14*g**3 - 11*g**2 - 10*g + 12. Let i(p) = -9*f(p) + 2*k(p). Let i(n) = 0. Calculate n.
-1, 1, 2
Suppose 5*b - 15 = -3*p + 2*b, 2*b - 10 = 2*p. Factor 1/4*s**3 + 0 + 0*s**2 - 1/4*s**4 + p*s.
-s**3*(s - 1)/4
Let x be 13/3 - (-8)/12. Determine k so that -3*k**2 - x*k**2 + 4*k + 2*k**2 = 0.
0, 2/3
Let j be 2 - (-1 + (-3 - -1) + 2). Let l(a) be the first derivative of a - a**2 + 1 + 1/3*a**j. Let l(p) = 0. What is p?
1
Let 3*y**5 + 30*y**2 - 59*y**3 - 14*y**2 + 27*y**4 + 140*y**3 + 65*y**2 = 0. What is y?
-3, 0
Let z be 0 + -5 - -5 - (-6)/100. Let g(d) be the second derivative of -1/75*d**6 - 1/15*d**3 + 0 - z*d**5 + d + 0*d**2 - 1/10*d**4. Factor g(w).
-2*w*(w + 1)**3/5
Let n = -40/11 + 4211/1155. Let z(h) be the second derivative of 0*h**6 - 1/25*h**5 + 0*h**4 - 3*h + 0 + n*h**7 + 0*h**2 + 1/15*h**3. Solve z(f) = 0.
-1, 0, 1
Factor 0*v + 6*v + 2*v**2 + 4 - 2*v**2 + 2*v**2.
2*(v + 1)