d derivative of -l**4/8 + 3*l**3/4 - 3*l**2/2 + 40*l. Factor n(k).
-3*(k - 2)*(k - 1)/2
Suppose 0 = -5*w - 22 + 2, -3*w - 4 = 4*u. Determine z, given that 5*z**2 + u*z**2 + 4 - 5*z**2 + 6*z = 0.
-2, -1
Let s(j) be the second derivative of j**5/60 - 2*j**3/9 - 4*j. Factor s(c).
c*(c - 2)*(c + 2)/3
Find m such that -1/2*m**4 + 4*m - m**3 + 0 + 2*m**2 = 0.
-2, 0, 2
Let i be (-21)/112*2/(-6). Let p(m) be the first derivative of 1/4*m - 1/8*m**2 + 2 - 1/12*m**3 + i*m**4. Factor p(c).
(c - 1)**2*(c + 1)/4
Let o(s) be the second derivative of 5/18*s**3 - 1/30*s**5 - 7/90*s**6 + 0 + 1/6*s**2 + 2*s + 1/6*s**4 - 1/42*s**7. Suppose o(p) = 0. What is p?
-1, -1/3, 1
Factor -9/5*s + 3/5*s**2 + 6/5.
3*(s - 2)*(s - 1)/5
Let s(a) = -11*a**3 + 24*a**2 + 20*a - 3. Let d(n) = 12*n**3 - 24*n**2 - 19*n + 2. Let h = 1 - -4. Let u(r) = h*d(r) + 4*s(r). Find c such that u(c) = 0.
-1/4, 2
Let o(g) be the second derivative of 2*g**7/21 - 4*g**6/15 + 2*g**4/3 - 2*g**3/3 + 2*g. Factor o(f).
4*f*(f - 1)**3*(f + 1)
Suppose 2*z = 6*z - 16. Find v such that 2*v**2 + 0*v**4 - v - 2*v**z + 3*v**5 - 2*v**5 = 0.
-1, 0, 1
Let r(y) be the second derivative of -y**6/45 + y**5/30 - 5*y. Solve r(x) = 0 for x.
0, 1
Factor -s**3 - 8 + 3*s**3 + 2*s**2 - 12*s**2 + 16*s.
2*(s - 2)**2*(s - 1)
Let x(p) be the second derivative of p**4/18 - 2*p**3/9 - 11*p. Suppose x(s) = 0. What is s?
0, 2
Suppose -40 = -4*v + 4*s, -v = 5*s - 10 - 6. Let l = v + -32/3. Factor p - 1/3 + p**4 - l*p**5 - 2/3*p**2 - 2/3*p**3.
-(p - 1)**4*(p + 1)/3
Suppose 9*l = 41 + 4. Solve 0 + 6/5*b**3 - 8/5*b + 27/5*b**l - 9*b**4 + 4*b**2 = 0.
-2/3, 0, 2/3, 1
Suppose -15/2*f**2 + 27 - 129/2*f = 0. Calculate f.
-9, 2/5
Let m(y) be the third derivative of -y**8/1008 + y**7/210 - y**6/120 + y**5/180 + 9*y**2. Suppose m(q) = 0. Calculate q.
0, 1
Let b = 1/49 - -289/245. Let u = b + -1. Let 1/5*j**2 + 0 + u*j = 0. What is j?
-1, 0
Suppose -2*o = -0*o - 4. Let z be (-5)/((-2 + -2)/o). Factor -2*s**2 - 1/2 + z*s.
-(s - 1)*(4*s - 1)/2
Let b be (-16)/(-42) - (-6)/(-105)*-5. What is h in -2/3*h**2 + 2/3*h**3 - 2/3*h + b = 0?
-1, 1
Factor -5*h**2 - 7*h**2 - 7*h**2 + 4*h**2 + 5*h.
-5*h*(3*h - 1)
Let f(v) be the second derivative of -2*v**7/63 - 2*v**6/15 + 4*v**4/9 - 6*v. Factor f(x).
-4*x**2*(x - 1)*(x + 2)**2/3
Let v be (-2)/9 + (-60)/(-27). Factor v*l - 2 - l**2 + 2.
-l*(l - 2)
Let p = -7 - -12. What is u in 8*u**2 - 4*u + 3*u**3 - 7*u**3 + 4*u**p - 8*u**4 + 4*u**3 = 0?
-1, 0, 1
Determine d so that -5*d**4 - 5 + 46*d**2 - 20*d + 31*d**2 - 47*d**2 - 35 + 5*d**3 = 0.
-2, -1, 2
Let s(d) be the second derivative of d**8/16800 - d**7/3150 + d**6/1800 + 7*d**4/12 + 6*d. Let y(z) be the third derivative of s(z). Solve y(u) = 0.
0, 1
Let o(k) be the first derivative of -k**4/2 + 4*k**3/3 + k**2 - 4*k + 11. Find y such that o(y) = 0.
-1, 1, 2
Let g(r) be the first derivative of 2*r**3/15 - 2*r/5 + 2. Factor g(v).
2*(v - 1)*(v + 1)/5
Let d(g) be the first derivative of 3/2*g**2 + 0*g**3 - 2*g + 4 - 1/4*g**4. Factor d(j).
-(j - 1)**2*(j + 2)
Let t(q) be the first derivative of -3*q**4/2 - 2*q**3/3 - 4. Factor t(g).
-2*g**2*(3*g + 1)
Let q(x) be the first derivative of -x**5/5 - x**4/4 + 2*x**3/3 - 19. Factor q(w).
-w**2*(w - 1)*(w + 2)
Let m(l) be the third derivative of -5/6*l**5 - 4/3*l**4 - 4/3*l**3 - 1/168*l**8 + 0 - 19/60*l**6 - 1/15*l**7 + 0*l - 2*l**2. Solve m(g) = 0 for g.
-2, -1
Let b(u) be the second derivative of 1/8*u**4 + 1/4*u**3 + 1/40*u**5 + 2*u + 1/4*u**2 + 0. Suppose b(h) = 0. What is h?
-1
Factor 2/21*r**4 + 2/7*r**3 + 0 + 2/7*r**2 + 2/21*r.
2*r*(r + 1)**3/21
Let s(j) be the second derivative of -1/6*j**4 + 4*j - 1/3*j**3 + 0 + 2*j**2. Factor s(n).
-2*(n - 1)*(n + 2)
Let q(m) = 2*m**2 - 2*m - 2. Let k be q(2). Suppose -g**k + 2 - g**2 - g**2 + 4*g + 5*g**2 = 0. What is g?
-1
Factor 1/7*h**3 - 1/7*h + 1/7*h**2 - 1/7.
(h - 1)*(h + 1)**2/7
Factor -8 + 1 + 15*r**4 - 9*r + 3*r**2 + 9*r**3 + 1 - 12*r**4.
3*(r - 1)*(r + 1)**2*(r + 2)
Let y(d) be the second derivative of -9*d**5/40 - d**4/2 - d**3/4 - 8*d. Factor y(q).
-3*q*(q + 1)*(3*q + 1)/2
Let l(t) be the third derivative of -t**6/360 + t**5/36 - t**4/12 - 7*t**2 - 2. Factor l(s).
-s*(s - 3)*(s - 2)/3
Let p(v) be the third derivative of -1/30*v**5 + 0*v**4 + 1/120*v**6 + 0*v + 0 + 0*v**3 + 6*v**2. Factor p(l).
l**2*(l - 2)
Let u(o) be the third derivative of 7/40*o**5 + 0 + 1/28*o**7 + 1/8*o**4 + 0*o + 0*o**3 + 9/80*o**6 + 7*o**2 + 1/224*o**8. Factor u(i).
3*i*(i + 1)**3*(i + 2)/2
Let j = 571 - 566. Determine a, given that 0*a**3 + 1/3*a**j + 0*a**2 + 0 + 0*a - 1/3*a**4 = 0.
0, 1
Suppose 0 = 2*u - 2 - 2. Let q(r) be the first derivative of 1/4*r**4 + 0*r + 0*r**3 + 1 - 1/2*r**u. Factor q(z).
z*(z - 1)*(z + 1)
Let t = -577 + 579. Factor 0 - 2/7*b + 1/7*b**t + 1/7*b**3.
b*(b - 1)*(b + 2)/7
Let a(b) be the third derivative of b**8/168 + 3*b**7/35 + 2*b**6/5 + 8*b**5/15 - 14*b**2. Factor a(p).
2*p**2*(p + 1)*(p + 4)**2
Let l = -66 - -69. Let a(j) be the second derivative of -1/20*j**5 - 1/30*j**6 + 0*j**l - 2*j + 1/42*j**7 + 0*j**2 + 0 + 1/12*j**4. Let a(x) = 0. Calculate x.
-1, 0, 1
Suppose 0*c = -3*c. Let x(v) be the third derivative of 1/30*v**5 + 1/4*v**4 + 2/3*v**3 + v**2 + c + 0*v. Solve x(d) = 0 for d.
-2, -1
Solve 0*t**3 + 2*t**2 + 3*t**3 - t**2 - 2*t**3 = 0.
-1, 0
Let y(b) be the third derivative of -b**5/120 + b**4/48 + b**3/6 + 26*b**2. Let y(p) = 0. Calculate p.
-1, 2
Suppose 0 - 2/3*z + 1/3*z**2 = 0. Calculate z.
0, 2
Let v = 30 + -25. Let m(f) be the third derivative of 1/50*f**v + 0*f**3 + f**2 + 1/60*f**4 + 0 + 1/100*f**6 + 1/525*f**7 + 0*f. Factor m(j).
2*j*(j + 1)**3/5
Suppose 24*u + 84 = 156. Let -8/3*d + 4/3*d**2 + 0 + 4/3*d**u = 0. What is d?
-2, 0, 1
What is z in -46*z**3 + 92*z**3 - 45*z**3 - z**5 = 0?
-1, 0, 1
Let a(p) be the second derivative of p**7/7 - p**6/3 - 7*p**5/10 + 7*p**4/2 - 16*p**3/3 + 4*p**2 - 27*p. Determine n, given that a(n) = 0.
-2, 2/3, 1
Let q(f) be the first derivative of 1/9*f**3 - 1/3*f**2 + 1/3*f + 9. Let q(o) = 0. Calculate o.
1
Let t be (-31)/(-3) + 1 + -4. Let i = -7 + t. Suppose -1/3*r - i*r**2 + 0 = 0. Calculate r.
-1, 0
Let b(o) be the second derivative of -27/7*o**2 - 3/14*o**4 + 9/7*o**3 + 1/70*o**5 + 0 + 6*o. Factor b(z).
2*(z - 3)**3/7
Let d(p) = 2 - 8*p**3 - 2 + 15*p**2 - 7*p. Let f(k) be the first derivative of k**3/3 - k**2/2 + 4. Let v(m) = -d(m) + 5*f(m). Suppose v(h) = 0. What is h?
0, 1/4, 1
Let m(w) be the third derivative of w**6/320 + w**5/16 + 3*w**4/16 - 9*w**3/2 - 2*w**2 + 31*w. Factor m(l).
3*(l - 2)*(l + 6)**2/8
Suppose -3*u = -5*i - 90, -4*i - 2*u - 40 = 2*u. Let r be 3/(-18) - i/18. Find n such that 1/3*n**3 + r - 1/3*n - 2/3*n**2 = 0.
-1, 1, 2
Let r be -5 - ((-38)/(-8) + -10). Find v, given that 0 + 1/2*v**2 - r*v - 1/4*v**3 = 0.
0, 1
Let n(x) be the third derivative of 7*x**6/120 + x**5/12 - x**4/12 - 7*x**2. Let n(c) = 0. Calculate c.
-1, 0, 2/7
Let p = 5 - -2. Let n be 2/p + 144/84. Solve 8/5 + 2/5*a**n - 8/5*a = 0 for a.
2
Find u such that -3 + 2 - 3*u + 3*u**2 + u = 0.
-1/3, 1
Factor -5/4*v**4 - 5*v**3 + 35/4 - 25*v + 45/2*v**2.
-5*(v - 1)**3*(v + 7)/4
Suppose 14 = 6*q + 2. Suppose 0 + 4/5*g + 2/5*g**q - 2/5*g**3 = 0. What is g?
-1, 0, 2
Suppose 0*f = f - 6. Let j(q) = 14*q**3 - 14*q**2 + 3*q - 3. Let m(c) = 5*c**3 - 5*c**2 + c - 1. Let t(s) = f*j(s) - 17*m(s). Solve t(w) = 0.
-1, 1
Let u(i) = i**3 + i**2 + i. Let w(z) = 2*z**3 - 10*z**2 + 2*z. Let k(q) = 2*u(q) + w(q). Factor k(x).
4*x*(x - 1)**2
Let 0 - 2/7*y**3 + 2/7*y**4 - 2/7*y**2 + 2/7*y**5 + 0*y = 0. What is y?
-1, 0, 1
Let s = 1/3 + 1/6. Factor -1/2*f**3 - f**2 + 0 - s*f.
-f*(f + 1)**2/2
Factor 0*a + 0 + 1/4*a**4 + 1/2*a**2 - 3/4*a**3.
a**2*(a - 2)*(a - 1)/4
Suppose -39*p + 44*p = 20. Let y(r) be the first derivative of 0*r**2 - 1 + 1/7*r**p + 0*r - 2/21*r**3. Factor y(c).
2*c**2*(2*c - 1)/7
Determine o so that -9/2*o**2 + 3 - 3/2*o = 0.
-1, 2/3
Let f = 40 - 29. Suppose -3*v + 32 = n + f, 0 = 4*n - v - 32. Let 3*m + 11*m - 1 + n*m**2 - m**2 - 3 = 0. What is m?
-2, 1/4
Factor -4/5*v**3 + 0*v + 2*v**5 - 6/5*v**4 + 0*v**2 + 0.
2*v**3*(v - 1)*(5*v + 2)/5
Let x = -291 + 2041/7. Factor 2/7*n**5 + 2/7*n**3 + 0 + x*n**4 + 0*n**2 + 0*n.
2*n**3*(n + 1)**2/7
Determine k so that 6*k - 26*k + 27 - 11 - 2*k**2 + 6*k**2 = 0.
1, 4
Let c(o) be the first deriv