Let a(k) be the first derivative of h(k). Find x, given that a(x) = 0.
-2/3, 0, 1
Let l(q) be the first derivative of -q**4/4 - 4*q**3/3 + 3*q**2/2 + 18*q - 34. Factor l(w).
-(w - 2)*(w + 3)**2
Let i(o) be the second derivative of 1/18*o**4 + 1/27*o**3 + 0 + 2*o + 0*o**2. Factor i(v).
2*v*(3*v + 1)/9
Let t = 22 + -19. Suppose t*b + 15 = 4*m, 4*m - 10 = -0*m + 2*b. Solve 0 + m*d + 1/2*d**3 + 1/4*d**4 + 0*d**2 - 1/4*d**5 = 0 for d.
-1, 0, 2
Let g be ((-5157)/(-6))/(42/(-16)). Let c = g + 328. Solve c*o - 2/7*o**2 - 2/7 = 0 for o.
1
Suppose -2*z - z = -5*p + 56, 4*p - 37 = 5*z. Suppose -p = -5*a - 3. Factor -1/2*i**4 + 1/2 + a*i**2 + 1/2*i**3 + 7/4*i - 1/4*i**5.
-(i - 2)*(i + 1)**4/4
Let b(a) be the third derivative of a**5/30 + 5*a**4/24 + a**3/3 - 10*a**2. Factor b(f).
(f + 2)*(2*f + 1)
Let f(y) be the second derivative of y**8/168 + y**7/105 - y**6/20 - y**5/30 + y**4/6 + 3*y**2/2 - y. Let s(a) be the first derivative of f(a). Factor s(w).
2*w*(w - 1)**2*(w + 1)*(w + 2)
Suppose 11 = -5*g + 41. Let q(c) be the third derivative of 0*c**3 + 1/60*c**4 + 0*c + c**2 - 1/840*c**8 + 1/75*c**5 + 0 + 0*c**g - 2/525*c**7. Factor q(y).
-2*y*(y - 1)*(y + 1)**3/5
Let i(m) be the second derivative of m**6/165 + m**5/110 - m**4/22 - 5*m**3/33 - 2*m**2/11 + 6*m. What is y in i(y) = 0?
-1, 2
Let n(z) be the first derivative of -3/5*z**5 + 7/4*z**4 - 2 - 2*z**2 + 0*z**3 + 0*z. Factor n(k).
-k*(k - 2)*(k - 1)*(3*k + 2)
Let p(g) be the first derivative of -g**3/15 + g**2/2 - 6*g/5 + 9. Solve p(x) = 0.
2, 3
Let d be (-68)/(-7) + 2/7. Let i be (-6)/d*5/(-1). Factor -r**3 + r**2 - i*r**4 + 0*r**2 + 2*r**4 + r.
-r*(r - 1)*(r + 1)**2
Let n = 2/3697 - 417773/22182. Let i = 39/2 + n. Determine h so that 0 + i*h**2 - 2/3*h = 0.
0, 1
Suppose 4*b = -3*o + 5, -5*b + 4*o = 8 - 22. Let x be (9 - b) + 2*-1. Factor 4*k**3 - 3*k**3 - 3*k**x + 2*k**5.
-k**3*(k - 1)*(k + 1)
Let q be -1*(-7)/((-14)/(-4)). Let w be (q/(-16))/((-4)/16). Factor 1/2*v**3 - w*v**2 - 1/2*v + 0 + 1/2*v**4.
v*(v - 1)*(v + 1)**2/2
Let o be (-21)/3 + -2 + 1. Let c be o/(-14)*1/2. Factor 2/7 - 4/7*r**3 - c*r**4 + 4/7*r + 0*r**2.
-2*(r - 1)*(r + 1)**3/7
Let m(j) be the first derivative of -j**6/900 - j**5/50 - 3*j**4/20 + j**3/3 + 3. Let d(x) be the third derivative of m(x). Factor d(l).
-2*(l + 3)**2/5
Let u(l) be the first derivative of l**6/180 - l**5/18 + 2*l**4/9 - 4*l**3/9 + l**2 + 5. Let x(j) be the second derivative of u(j). Factor x(s).
2*(s - 2)**2*(s - 1)/3
Factor -2/11*g**4 - 4*g**2 - 16/11*g**3 - 18/11 - 48/11*g.
-2*(g + 1)**2*(g + 3)**2/11
Let y(l) be the first derivative of l**6/3 + 4*l**5/5 + l**4/2 - 7. Solve y(i) = 0 for i.
-1, 0
Let n = -5 - -8. Find a, given that n*a - 3/5 + 12/5*a**4 - 3*a**3 - 9/5*a**2 = 0.
-1, 1/4, 1
Let z = 9 + -9. Suppose z = -x + 1 + 2. Factor -1/2*f**x - 3/2*f**2 - f + 0.
-f*(f + 1)*(f + 2)/2
Let b(z) be the first derivative of -z**6/18 + z**5/15 + 5*z**4/12 + z**3/3 + 67. Let b(u) = 0. Calculate u.
-1, 0, 3
Let c(w) be the third derivative of -3*w**8/112 - 2*w**7/21 - w**6/30 - 5*w**2. Suppose c(n) = 0. What is n?
-2, -2/9, 0
Let w(n) be the third derivative of -2*n**7/315 + n**6/360 - 22*n**2. Factor w(h).
-h**3*(4*h - 1)/3
Let q be (-466)/840 + (-3)/(-9). Let h = 1/35 - q. Factor 0 + 1/4*r**2 - 5/4*r**3 + h*r + 3/4*r**4.
r*(r - 1)**2*(3*r + 1)/4
Suppose -3*z - 12 = -21. Let t(v) be the first derivative of 1 - 6/5*v**2 + 2/15*v**z + 18/5*v. Find m, given that t(m) = 0.
3
Let q(m) = -8*m**3 - 14*m**2 - 6*m + 5. Let v(z) = 9*z**3 + 15*z**2 + 6*z - 6. Let h(c) = -6*q(c) - 5*v(c). Suppose h(j) = 0. Calculate j.
-2, -1, 0
Let o(q) be the second derivative of 3*q**5/20 + q**4 + 2*q**3 - 4*q. Factor o(x).
3*x*(x + 2)**2
Suppose 5 - 16 = -3*f + 5*x, -3*x = 2*f - 20. Factor 0 + 6*t + 4*t**2 - f*t**2 + 0.
-3*t*(t - 2)
Let w(d) be the first derivative of 2*d**5/5 + 7*d**4/6 + 10*d**3/9 + d**2/3 - 6. Factor w(s).
2*s*(s + 1)**2*(3*s + 1)/3
Let j(m) = -2*m**2 - 30*m + 2. Let k be j(-15). Factor 0 - 7/2*b**3 + 8*b**2 - k*b.
-b*(b - 2)*(7*b - 2)/2
Let x(q) be the first derivative of -q**3/3 - q**2/2 - 6. Suppose x(b) = 0. Calculate b.
-1, 0
Let d be 6/(-3*4/(-8)). Factor 9/2*w**3 + 5/2*w**2 + 7/2*w**d + w**5 + 0 + 1/2*w.
w*(w + 1)**3*(2*w + 1)/2
Let v(l) be the second derivative of l**4/42 + 4*l**3/21 + 4*l**2/7 + 29*l. Determine i, given that v(i) = 0.
-2
Let m(z) be the first derivative of -z**5/5 + z**4/4 + z**3/3 - z**2/2 + 6. What is a in m(a) = 0?
-1, 0, 1
Let p = 171/275 + -6/275. Solve 3/5*b**3 + 0 - 3/5*b + p*b**2 - 3/5*b**4 = 0.
-1, 0, 1
Let n(f) = 11*f**2 + 16*f - 4. Let u(g) be the third derivative of -g**5/5 - 17*g**4/24 + 2*g**3/3 + 2*g**2. Let s(d) = 5*n(d) + 4*u(d). Factor s(i).
(i + 2)*(7*i - 2)
Let 4/3 - 5/3*o**2 + o**3 - 4/3*o = 0. What is o?
-1, 2/3, 2
Let a be 0*(3 + -7)/4. Let d(w) be the third derivative of 0*w**4 + 0*w + 1/105*w**7 + 0 + a*w**6 - 1/15*w**5 + 1/3*w**3 - w**2. Factor d(j).
2*(j - 1)**2*(j + 1)**2
Suppose -6 = -3*s - 0. Suppose -12/11*l - 28/11*l**s - 18/11*l**4 - 2/11 - 4/11*l**5 - 32/11*l**3 = 0. What is l?
-1, -1/2
Let d = -20/69 + 22/23. Solve 6*l**2 + d*l**3 + 18 + 18*l = 0 for l.
-3
Let w(k) be the second derivative of 3*k**5/80 + 3*k**4/16 + 3*k**3/8 + 3*k**2/8 + 2*k. Factor w(g).
3*(g + 1)**3/4
Let h(m) be the third derivative of -m**8/2016 + m**7/315 - m**6/720 - m**5/60 - 17*m**2. Find l such that h(l) = 0.
-1, 0, 2, 3
Let k be (-2)/(5/(30/(-4))). Find t, given that -87*t**4 + 18*t**5 + 10*t**3 + k*t - 67*t**3 - 6 + 93*t**2 - 30*t**3 + 66*t**5 = 0.
-1, -1/4, 2/7, 1
Let y(j) = -j**4 + j**3 + j**2 + j + 1. Let m(w) = -3*w**3 - 2*w**2 - w - 1. Let u = 5 + -3. Let z(v) = u*y(v) + 2*m(v). Determine b, given that z(b) = 0.
-1, 0
Suppose 2/3 - 5/3*u**2 + u = 0. Calculate u.
-2/5, 1
Let v(n) be the third derivative of 0*n**3 + 0*n + n**2 + 0*n**6 + 0 + 1/1260*n**7 - 1/120*n**5 - 1/72*n**4. Solve v(a) = 0 for a.
-1, 0, 2
Let -2*m - 5*m + 2*m**4 + 6*m**3 - 8*m**2 - 9*m - 2*m**3 = 0. What is m?
-2, 0, 2
Let i(k) be the third derivative of 23/60*k**6 + 1/30*k**5 + 5*k**2 - 13/42*k**7 - 1/6*k**3 + 0*k + 25/336*k**8 - 7/24*k**4 + 0. Factor i(w).
(w - 1)**3*(5*w + 1)**2
Let t(c) be the first derivative of c**6/9 + 2*c**5/15 - c**4/6 - 2*c**3/9 - 4. Factor t(p).
2*p**2*(p - 1)*(p + 1)**2/3
Let s(k) be the third derivative of 0*k**3 + 1/30*k**5 + 0*k + 1/6*k**4 + 2*k**2 + 0. Determine y, given that s(y) = 0.
-2, 0
Suppose 4*x + 3*k - 11 = 0, k = -2*x - 3*x + 11. Suppose -2*v**2 + 4*v**x + 0*v**2 = 0. Calculate v.
0
Let g(s) = -s**2 - 2*s - 3. Let d be g(-2). Let w be -2 - 6*(2 + d). Factor 0*t**3 - 4/5*t**w + 2/5*t**5 + 4/5*t**2 - 2/5*t + 0.
2*t*(t - 1)**3*(t + 1)/5
Let l = -7 - -8. Suppose -1 = f + 5*o + l, f + 3*o = 0. Factor -f*j**2 - 3*j**2 + 7*j**2 + j**2.
2*j**2
Let p(y) = -6*y**4 + 20*y**3 - 13*y**2 + 5*y. Let h(t) = -13*t**4 + 40*t**3 - 26*t**2 + 9*t. Let j(q) = 6*h(q) - 10*p(q). Factor j(n).
-2*n*(n - 1)**2*(9*n - 2)
Let c = -83/3 - -28. Let g be 2/(-8) + 1/4. Determine l so that 0*l + g + 1/3*l**2 - c*l**3 = 0.
0, 1
Let t = 0 + 6. Factor -34*p**2 + 10*p**3 + 2*p**2 + 2*p + 50*p**4 + t*p.
2*p*(p + 1)*(5*p - 2)**2
Let r(b) = 2*b**2 + 10*b + 16. Let d be r(-3). Solve -y**2 + 7/2*y**3 - 7/4*y + 1/2 - 7/4*y**5 + 1/2*y**d = 0.
-1, 2/7, 1
Suppose 3*u - 2*u - 6 = 0. Let z be (-1)/(((-3)/u)/1). Factor 0*i - 5/3*i**3 - 2/3*i**z - i**4 + 0.
-i**2*(i + 1)*(3*i + 2)/3
Let n(t) be the third derivative of t**8/1008 + t**7/315 - t**5/90 - t**4/72 - 7*t**2. Determine w so that n(w) = 0.
-1, 0, 1
Let z(d) be the first derivative of 3*d**4/4 + 2*d**3 + 3*d**2/2 - 2. Solve z(t) = 0.
-1, 0
Suppose -m**3 - 4*m**4 + 2*m**5 + m**4 - 2*m**3 - 3*m**5 - m**2 = 0. Calculate m.
-1, 0
Let r(t) be the second derivative of t**7/2520 - t**6/360 + t**5/120 - t**4/3 + 2*t. Let d(y) be the third derivative of r(y). What is v in d(v) = 0?
1
Let n(h) = 2*h - 5. Suppose 3*c = 6*c - 12. Let u be n(c). Factor -4*q**2 + u*q**4 + q**5 + 3*q**2 - q**3 - 2*q**4.
q**2*(q - 1)*(q + 1)**2
Let r(h) be the second derivative of -2*h + 1/18*h**3 + 1/360*h**6 - h**2 - 1/72*h**4 - 1/180*h**5 + 0. Let w(x) be the first derivative of r(x). Factor w(t).
(t - 1)**2*(t + 1)/3
Let u be -3 + -4 + 5 - -2. Let h(o) be the first derivative of -1/5*o**2 - 2/15*o**3 + u*o - 3. Factor h(k).
-2*k*(k + 