w = 85/4 + -21. Suppose -8 = 2*n + 4*s, 5*n - 5 = -2*s - 1. Find k such that 1/4*k**n + 0 - w*k = 0.
0, 1
Let d be (-8)/(192/40)*4/(-10). Solve 0 + d*j - 2/3*j**2 = 0.
0, 1
Let b(d) = d - 3. Let t be b(3). Let t*n - 3*n**3 + 3/5*n**2 + 0 + 12/5*n**4 = 0. Calculate n.
0, 1/4, 1
Let h be 87/4 - 9/12. Find u such that 0*u + 21*u**3 + 3*u**2 + h*u**5 - 6*u**4 - 37*u**4 - 2*u = 0.
-2/7, 0, 1/3, 1
Let g(v) be the first derivative of 0*v**3 + 0*v**5 + 3 + 0*v - 1/9*v**6 - 1/3*v**2 + 1/3*v**4. What is b in g(b) = 0?
-1, 0, 1
Let a be (-40)/10 + (-24)/(-3). Let w(i) be the second derivative of 4*i**2 + 1/6*i**a + 4/3*i**3 + 3*i + 0. Find p such that w(p) = 0.
-2
Let l = -367/6 + 185/3. Factor 1/2*o**3 - l*o**5 + 1/2*o**2 - 1/2*o**4 + 0 + 0*o.
-o**2*(o - 1)*(o + 1)**2/2
Let t(w) be the first derivative of 3/2*w**4 - 2*w**3 + 1/2*w**6 - 5 + 9/5*w**5 - 9/2*w**2 - 3*w. Factor t(y).
3*(y - 1)*(y + 1)**4
Let l = -16 - -22. Let 4 + 5*o - o - 2*o**2 - l = 0. What is o?
1
Let t(g) be the first derivative of g**4/24 - g**3/18 - g**2/12 + g/6 + 7. Solve t(x) = 0.
-1, 1
Let a(t) be the first derivative of -t**2 + 2/5*t**5 + 1/2*t**4 + 3 - 2/3*t**3 + 0*t. Factor a(m).
2*m*(m - 1)*(m + 1)**2
Let p(m) be the second derivative of 2*m + 0*m**3 + 0*m**4 + m**2 - 1/30*m**5 + 0. Let w(v) be the first derivative of p(v). What is a in w(a) = 0?
0
Factor -40*g**2 - 6*g - 10*g + 50 + 4*g**5 + 16*g**4 + 4*g**3 - 18.
4*(g - 1)**2*(g + 2)**3
Let b(z) be the second derivative of -z**8/3360 + z**7/1680 - 5*z**3/6 - z. Let h(n) be the second derivative of b(n). Suppose h(q) = 0. Calculate q.
0, 1
Let w = 660 - 39599/60. Let x(f) be the third derivative of 1/6*f**5 + 4/3*f**3 + 0 + 0*f - 2/3*f**4 - w*f**6 - 3*f**2. Factor x(g).
-2*(g - 2)**2*(g - 1)
Let o = 7346/27 - 272. Let n(t) be the first derivative of 0*t**2 - o*t**3 + 1 + 0*t - 1/6*t**4. Solve n(m) = 0.
-1/3, 0
Suppose 0*o - 2*n - 3 = -3*o, 3 = -o + 2*n. Factor 4*l**2 + 5*l**3 + 6*l - 2*l**5 - 3*l**3 - 6*l**o - 6*l**4 + 2.
-2*(l - 1)*(l + 1)**4
Let l(b) be the third derivative of 0*b + 1/90*b**5 - 3*b**2 + 0 + 2/9*b**3 - 1/12*b**4. Let l(f) = 0. What is f?
1, 2
Let w(m) be the third derivative of m**8/1848 - m**7/1155 - m**6/220 + m**5/66 - m**4/66 + 7*m**2. Factor w(y).
2*y*(y - 1)**3*(y + 2)/11
Let d = -2 - -4. Let q(t) = d + 0*t**5 + 7*t**5 + 4 + 3*t**4 - 1 + 5*t. Let o(r) = 3*r**5 + r**4 + 2*r + 2. Let l(h) = 5*o(h) - 2*q(h). Factor l(p).
p**4*(p - 1)
Let g(q) be the third derivative of -q**7/1260 - q**6/270 - q**5/180 - q**3/6 - q**2. Let b(m) be the first derivative of g(m). Suppose b(a) = 0. What is a?
-1, 0
Let h(m) be the first derivative of m**6/12 + m**5/10 - m**4/8 - m**3/6 - 11. Determine n so that h(n) = 0.
-1, 0, 1
Let d(k) be the second derivative of 361*k**4/3 - 152*k**3/3 + 8*k**2 - 3*k. Factor d(f).
4*(19*f - 2)**2
Let a(c) be the third derivative of c**6/120 + c**5/15 + c**4/8 + 9*c**2 - 4. Factor a(k).
k*(k + 1)*(k + 3)
Let u = 8293/6132 - -17/1022. Let a = -1/28 + u. Solve 0 - 2/3*g**3 - a*g**2 - 2/3*g = 0 for g.
-1, 0
Let k = 7 + -3. Let x = k - 3. Suppose -c - c**2 + x - c**3 + 2*c + 0*c**3 = 0. What is c?
-1, 1
Suppose 2 = 3*l - 2*l. Find m such that 2/7*m**3 + 2/7*m**4 - 2/7*m - 6/7*m**l + 4/7 = 0.
-2, -1, 1
Suppose -105 = -5*v + 4*g - 30, 4*g - 30 = -2*v. Solve -6*o - 21*o**5 + 27*o**3 + 15*o**2 - v*o**4 + 0*o**4 + 0*o**5 = 0 for o.
-1, 0, 2/7, 1
Factor v**4 - 16*v**2 + 16*v**2 + v**3.
v**3*(v + 1)
Solve 8*j + 8 + 8 + 14*j**2 - 13*j**2 = 0.
-4
Let g(r) = -r**3 + 6*r**2 + 3*r. Let b(z) = z**3 - 5*z**2 - 2*z. Let c(n) = 4*b(n) + 3*g(n). Factor c(f).
f*(f - 1)**2
Suppose 7*o - 2*o = -f + 2, -5*o + 2*f = 4. Find n, given that 0 + o*n + 2/3*n**2 = 0.
0
Let l(w) be the first derivative of w**5/5 + w**4/4 - w**3/3 - w**2/2 + 19. Let l(v) = 0. Calculate v.
-1, 0, 1
Suppose 5*y - 3*y = 6. Let -4/5*x**y + 2*x - 2/5*x**2 - 4/5 = 0. What is x?
-2, 1/2, 1
Let t(b) be the second derivative of -b**7/2100 + 7*b**6/1800 - b**5/150 - b**4/4 - 3*b. Let l(w) be the third derivative of t(w). Find j such that l(j) = 0.
1/3, 2
Determine m so that -4 - 3*m**2 + 98*m - 104*m + 1 = 0.
-1
Let i(c) = 9*c**2 - c + 5. Let l = 17 + -7. Let p(x) = x**3 - 9*x**2 - 11*x + 15. Let q be p(l). Let y(s) = 4*s**2 + 2. Let z(h) = q*y(h) - 2*i(h). Factor z(m).
2*m*(m + 1)
Let q(r) be the third derivative of -r**8/672 - r**7/120 - 3*r**6/160 - r**5/48 - r**4/96 - 3*r**2 - 2*r. Solve q(g) = 0 for g.
-1, -1/2, 0
Let w(n) = n**2 - 10*n + 9. Suppose -4*l = 4*d - 32, 0 = -3*l + 2*d - 0*d + 29. Let b be w(l). Solve -5*a**2 - 6*a + 4*a + b*a**2 = 0 for a.
-2/5, 0
Let i = 0 + 0. Let o be 8 + (2 - (2 + i)). Let -2*d**5 - 10*d + 2*d**2 + 2 + 10*d**2 - 20*d**3 + o*d**2 + 10*d**4 = 0. What is d?
1
Let i(a) be the second derivative of a**5/5 - 4*a**4/3 + 10*a**3/3 - 4*a**2 - 10*a. Determine l, given that i(l) = 0.
1, 2
Let x(v) be the second derivative of v**7/5040 + v**6/720 - v**5/80 + v**4/4 + 2*v. Let z(n) be the third derivative of x(n). Factor z(s).
(s - 1)*(s + 3)/2
Let k(r) be the third derivative of 0*r + 0 + r**2 - 1/24*r**3 + 1/80*r**5 + 1/48*r**4. Determine u so that k(u) = 0.
-1, 1/3
Let x(s) be the second derivative of -1/5*s**2 + 4/15*s**3 - 2/15*s**4 + 2*s + 0. Determine q, given that x(q) = 0.
1/2
Let j(m) be the first derivative of 3/4*m**4 + 0*m**3 + 1/2*m**6 + 0*m**2 + 6/5*m**5 + 0*m + 6. Determine k so that j(k) = 0.
-1, 0
Let c(y) = -7*y**3 + 6*y**2 + 4*y - 4. Let k(p) = -p**3 + p - 1. Let f(l) = -c(l) + 4*k(l). Factor f(h).
3*h**2*(h - 2)
Let s(g) be the second derivative of g**4/4 + g**3/5 - 38*g. Factor s(p).
3*p*(5*p + 2)/5
Determine o so that 0 - 2/17*o**4 + 0*o**2 + 6/17*o**3 - 8/17*o = 0.
-1, 0, 2
Let j be (-20)/(-3) + (-90)/15. Solve j*g**2 + 0*g - 2/3 = 0 for g.
-1, 1
Let h(z) be the third derivative of z**7/3780 - z**6/540 - z**4/24 + z**2. Let b(a) be the second derivative of h(a). Factor b(s).
2*s*(s - 2)/3
Suppose 5*g - 20 = 5. Let p be (-5)/((-100)/28) - -1. Suppose 16/5 + 2/5*d**g + 22/5*d**3 - 4/5*d**2 - p*d**4 - 24/5*d = 0. Calculate d.
-1, 1, 2
Let x(r) = -5*r**2 + 5*r + 7. Let a(h) = 29*h**2 - 29*h - 41. Let q(i) = 6*a(i) + 34*x(i). Factor q(g).
4*(g - 2)*(g + 1)
Factor 6*j**5 - 3*j**2 - 3*j**3 - 3*j**5 - 11*j**4 + 14*j**4 + 0*j**2.
3*j**2*(j - 1)*(j + 1)**2
Let x(m) = m + 4. Let h be x(-2). Suppose -5*k = -2*k - 9. Factor 0 + 1/5*u**4 - 1/5*u**h - 1/5*u + 1/5*u**k.
u*(u - 1)*(u + 1)**2/5
Let l(r) be the second derivative of -r**3/3 + r. Let q be l(-2). Factor 4*d**q - 6*d**3 - 3*d**2 - 2*d**5 - d + 7*d**2 + d**5.
-d*(d - 1)**4
Let g(j) be the third derivative of j**7/735 - j**6/420 - j**5/105 - 25*j**2. Factor g(h).
2*h**2*(h - 2)*(h + 1)/7
Let d(a) be the third derivative of -a**6/120 + a**5/210 + 9*a**2. Find z such that d(z) = 0.
0, 2/7
Let h(q) = 20*q**2 + 4*q + 6. Let j(l) = -l**2. Suppose -z - g = -1 + 3, -g + 6 = -3*z. Let b(i) = z*h(i) - 44*j(i). Find t, given that b(t) = 0.
-1, 3
Suppose -6*u + u = 2*f - 15, 5*f = -2*u + 6. Let s(z) be the first derivative of -2/21*z**u - 1 - 6/7*z**2 - 18/7*z. Factor s(d).
-2*(d + 3)**2/7
Let u(i) = -2*i**3 + 2*i**2 - 4. Let r(v) = -1. Let s = -2 + 1. Let z(d) = s*u(d) + 4*r(d). Solve z(y) = 0.
0, 1
Suppose -24 + 12 - 3*t**2 + 3 + 4*t + 8*t = 0. Calculate t.
1, 3
Let n(s) be the first derivative of -2*s**3/15 + s**2/2 - 3*s/5 - 15. Factor n(z).
-(z - 1)*(2*z - 3)/5
Solve 1/3*v**3 + 3 - 5/3*v**2 + v = 0 for v.
-1, 3
Solve 5*j**5 + 15*j**4 + 35*j**2 + 6*j + 7*j**3 - 2*j**5 + 20*j**3 - 14*j**2 = 0 for j.
-2, -1, 0
Let d(g) be the first derivative of -1/39*g**6 + 4/65*g**5 + 0*g + 0*g**3 + 0*g**2 - 1/26*g**4 - 6. Factor d(m).
-2*m**3*(m - 1)**2/13
Let d(k) be the first derivative of -k**4/2 + 4*k**3/9 - k**2/9 - 1. Solve d(n) = 0 for n.
0, 1/3
Let s = 117/4 - 29. Let x be 18/24*1/3. Solve -x*o**3 + 0 - s*o**2 + 0*o = 0.
-1, 0
Let d(u) be the third derivative of -u**8/240 + 3*u**7/350 + u**6/120 - 3*u**5/100 + u**4/60 + u**2. Solve d(l) = 0 for l.
-1, 0, 2/7, 1
Let -1/3*w**2 + 1/3 + 1/2*w = 0. Calculate w.
-1/2, 2
Suppose 0*c = 2*x + 5*c, -c - 22 = -4*x. Suppose -9 = t - 3*t - 5*k, 4*t - 3*k - x = 0. Solve 2*z - 6*z**3 + 4*z**3 + 0*z**3 - 2*z**4 + t*z**2 = 0.
-1, 0, 1
Let i be (-2)/6*0/(-3). Let a(h) be the third derivative of 0 + 1/30*h**5 + i*h**4 - 2*h**2 + 0*h + 0*