Let h(a) be the first derivative of -a**3 - 3*a**2 + 1. Factor h(g).
-3*g*(g + 2)
Let w(c) be the third derivative of c**10/151200 - c**9/60480 - c**5/20 + 2*c**2. Let r(v) be the third derivative of w(v). Determine y so that r(y) = 0.
0, 1
Let w(p) = -4*p**4 + 16*p**3 - 22*p**2 - 6*p. Let q(m) = 4*m**4 - 16*m**3 + 21*m**2 + 5*m. Let o(v) = 6*q(v) + 5*w(v). Let o(a) = 0. What is a?
0, 2
Let l be (-26)/(-6) - (-6)/9. Suppose -n + s = -1, -l*n + s = -3*s - 8. Solve -9*h**2 + 9*h**2 + 2*h**n - 4*h**3 + 4*h - 2 = 0 for h.
-1, 1
Let y be 7 - 11 - (0 + -1). Let u be (1/y)/(7 - 8). Factor -u*o**2 - 1/3 - 2/3*o.
-(o + 1)**2/3
Let n(y) be the second derivative of y**5/60 + y**4/12 + y**3/9 - 17*y. Determine i so that n(i) = 0.
-2, -1, 0
Let z(l) = l**3 - l**2 - l - 1. Suppose 5 = x + 17. Let c = x + 6. Let q(p) = 7*p**3 - 4*p**2 - 5*p - 6. Let m(n) = c*z(n) + q(n). Determine s so that m(s) = 0.
-1, 0
Factor -2/7*q**5 + 4/7*q**3 - 2/7*q + 0*q**2 + 0*q**4 + 0.
-2*q*(q - 1)**2*(q + 1)**2/7
Let r(i) be the second derivative of i**6/15 - i**5/10 - i**4/2 + 5*i**3/3 - 2*i**2 - 10*i. Factor r(d).
2*(d - 1)**3*(d + 2)
Let u be (6 - 5)/(1/3). Solve 0*n**u + 0 + 1/5*n - 1/5*n**5 + 2/5*n**2 - 2/5*n**4 = 0 for n.
-1, 0, 1
Let y = 2 + 0. Let m be (-6)/9*(5 + -8). Determine b, given that 2 - 4*b**m - y + 2 + 2*b**4 + 2*b + 2*b**5 - 4*b**3 = 0.
-1, 1
Factor -q**3 - 12*q**2 + 700 - 700 - 2*q**3 - 12*q.
-3*q*(q + 2)**2
Let x = 44/75 + 2/25. Suppose -4*d + c + 13 = 0, d + 3*c - 17 + 4 = 0. Find a such that 0 - 2/3*a**5 + 0*a + 2/3*a**3 - 2/3*a**2 + x*a**d = 0.
-1, 0, 1
Suppose b**2 - 3/2*b**4 - 1/2*b**3 + 0*b + 0 = 0. What is b?
-1, 0, 2/3
Let i be 10/(-24) - 48/(-64). Let -1/2*w - i - 1/6*w**2 = 0. What is w?
-2, -1
Let j = 55/24 + 457/24. Suppose -u - 3*u = -8. Solve -62*t**u - 14*t**5 - j*t - 166/3*t**4 - 254/3*t**3 - 8/3 = 0.
-1, -2/3, -2/7
Let b be ((-2)/(-27))/((-6)/(-9)). Let a(t) be the first derivative of 2/9*t - 2/9*t**2 + 0*t**3 + 3 - 2/45*t**5 + b*t**4. Determine l, given that a(l) = 0.
-1, 1
Let z be ((-1)/3)/((-2)/(-62)). Let f = -10 - z. Let 0*n + 1/3*n**3 - 1/3*n**2 - 1/3*n**5 + 0 + f*n**4 = 0. What is n?
-1, 0, 1
Let a(y) be the third derivative of 5*y**8/336 - y**7/42 + 8*y**2. Factor a(c).
5*c**4*(c - 1)
Let j(m) = -23*m**3 + 64*m**2 - 44*m + 13. Let a(b) = 24*b**3 - 64*b**2 + 44*b - 12. Let s(w) = -5*a(w) - 4*j(w). Find t such that s(t) = 0.
2/7, 1
Let k(l) be the first derivative of 4 - 3*l - 1/60*l**4 + 0*l**3 + 1/100*l**5 + 0*l**2. Let p(b) be the first derivative of k(b). Factor p(t).
t**2*(t - 1)/5
Suppose 7*r - 6 = 8. Let t(o) be the third derivative of -1/120*o**6 + 0 + 2*o**r + 1/12*o**3 + 0*o + 1/24*o**4 + 0*o**5 - 1/420*o**7. Solve t(m) = 0 for m.
-1, 1
Let f(g) be the second derivative of g**8/168 - g**7/35 + g**6/20 - g**5/30 + 3*g**2 + 10*g. Let l(a) be the first derivative of f(a). Let l(s) = 0. What is s?
0, 1
Let n(h) be the third derivative of -h**5/180 - h**4/12 - h**3/2 + 13*h**2. Solve n(u) = 0.
-3
Let b(c) be the third derivative of -c**5/180 - 11*c**4/36 - 121*c**3/18 + 59*c**2. Let b(j) = 0. Calculate j.
-11
Suppose -3*l - 2*x = -0*x - 16, 3*l - 5*x + 19 = 0. What is g in -5*g + 2*g - g**3 + l*g - 2*g**2 = 0?
-1, 0
Let 5*r**3 - 22*r**2 - 3*r**3 + 4 + 10*r + 0*r**3 + 6*r**3 = 0. Calculate r.
-1/4, 1, 2
Let d(g) be the second derivative of 54*g**7/35 + 6*g**6/5 - 39*g**5/25 - g**4/15 + 4*g**3/15 - g. Find f, given that d(f) = 0.
-1, -2/9, 0, 1/3
Let v = -2 - -5. Suppose -3*b**2 - b - 5*b + b - b**v + 3*b = 0. What is b?
-2, -1, 0
Let i(d) be the third derivative of -1/48*d**5 - 1/160*d**6 + 0*d + 0 + 1/48*d**4 - 2*d**2 + 0*d**3. Solve i(n) = 0 for n.
-2, 0, 1/3
Let p(w) be the first derivative of w**3/3 + w**2 + w - 28. Determine q so that p(q) = 0.
-1
Let 10*h**5 - 5 - 50/3*h + 60*h**3 + 10*h**2 + 145/3*h**4 = 0. Calculate h.
-3, -1, -1/3, 1/2
Let u(i) be the second derivative of i**6/120 + i**5/15 + 5*i**4/24 + i**3/3 + i**2 + 4*i. Let z(b) be the first derivative of u(b). Factor z(h).
(h + 1)**2*(h + 2)
Let v = -14 - -14. Let k(p) be the second derivative of 2/15*p**5 + 1/126*p**7 + 0 + 0*p**3 + v*p**2 - 1/9*p**4 - 1/18*p**6 - p. Factor k(a).
a**2*(a - 2)**2*(a - 1)/3
Let c be 48/60 - 6/(-15). Solve -8/5 - 22/5*h**2 + c*h**3 + 24/5*h = 0 for h.
2/3, 1, 2
Let g be 0*(15/(-6))/5. Suppose 0 = -0*s - 2*s - 5*p + 24, g = 5*p - 20. Let 1/2*a - 1/2*a**3 + 1/2*a**4 + 0 - 1/2*a**s = 0. Calculate a.
-1, 0, 1
Suppose -3*l - 30 = 12. Let g = 17 + l. Factor 4/7*u**g - 2/7*u**4 + 2/7 - 4/7*u + 0*u**2.
-2*(u - 1)**3*(u + 1)/7
Let u be (2 - -5) + (-87)/15. Suppose 6/5*g - 9/5*g**4 + 12/5*g**2 - 3/5 - u*g**3 = 0. What is g?
-1, 1/3, 1
Let m(w) be the third derivative of w**7/735 - w**6/140 + w**5/105 + 17*w**2. Suppose m(k) = 0. What is k?
0, 1, 2
Let j be 1/((4/(-7))/4). Let s = j + 7. Factor 2/3*w**2 + s + 0*w.
2*w**2/3
Solve -38 + 16 - 3*u**2 + 22 - 3*u**3 + 6*u = 0.
-2, 0, 1
Suppose -2*y + 36 = 10*y. Factor -1/2*a**2 + 1/2*a**y + 0 - a.
a*(a - 2)*(a + 1)/2
Factor 2/7 - 2/7*p**3 - 2/7*p**2 + 2/7*p.
-2*(p - 1)*(p + 1)**2/7
Let m(t) = -6*t**5 + 34*t**4 - 14*t**3 - 2*t**2 - 6*t + 6. Let y(a) = -a**5 - a**4 - a**3 + a**2 + a - 1. Let d(r) = m(r) + 6*y(r). Factor d(f).
-4*f**2*(f - 1)**2*(3*f - 1)
Suppose -1/2*p**3 + 0 + 1/2*p + 0*p**2 = 0. Calculate p.
-1, 0, 1
Let q be 65/20 + (1 + -1 - 3). Suppose 1/2 - 1/4*b**2 + q*b = 0. Calculate b.
-1, 2
Let x(z) = -4*z**2 - 3*z + 3. Let q(h) = 8*h**2 + 7*h - 6. Let p(y) = -2*q(y) - 5*x(y). Let k(o) = 9*o**2 + 2*o - 7. Let s(n) = -3*k(n) + 7*p(n). Factor s(d).
d*(d + 1)
Let s(i) be the first derivative of i**3 - 3*i**2/2 + 2. Let s(o) = 0. Calculate o.
0, 1
Let b(p) be the first derivative of p**6/3 - 16*p**5/25 + p**4/10 + 4*p**3/15 + 4. Find u such that b(u) = 0.
-2/5, 0, 1
Let k(f) be the second derivative of -1/90*f**6 + 0 - 1/30*f**5 + 0*f**2 + 1/126*f**7 + 2*f + 0*f**4 + 0*f**3. Solve k(m) = 0 for m.
-1, 0, 2
Let s(l) be the third derivative of -l**7/42 + 2*l**6/3 - 8*l**5 + 160*l**4/3 - 640*l**3/3 + 10*l**2. Factor s(c).
-5*(c - 4)**4
Suppose -2*l + 6 = l. Let q = -1837/7 - -263. Factor 2/7*r**4 + q - 2*r + 18/7*r**l - 10/7*r**3.
2*(r - 2)*(r - 1)**3/7
Factor -2*y + 2*y**5 - y**2 + 2*y**2 + 4*y**4 + 0*y**5 - 5*y**2.
2*y*(y - 1)*(y + 1)**3
Suppose 18/11*p**3 - 12/11*p**2 - 42/11*p - 12/11 = 0. What is p?
-1, -1/3, 2
Let p(f) = 51*f**3 + 9*f**2 - 99*f - 99. Let g(o) = o**2 + 10 - 5*o**3 + 8*o + 2*o - 2*o**2. Let x(c) = -21*g(c) - 2*p(c). Suppose x(n) = 0. What is n?
-2, -1, 2
Let h(a) be the third derivative of 243*a**7/280 + 261*a**6/80 + 949*a**5/240 + 29*a**4/24 + a**3/6 + 29*a**2. Factor h(f).
(f + 1)**2*(27*f + 2)**2/4
Suppose -12 + 6 = -3*c. Let v(i) be the first derivative of -1/2*i + 1/8*i**c - 1/16*i**4 + 1/6*i**3 + 2. Suppose v(g) = 0. Calculate g.
-1, 1, 2
Suppose -3*i + 0*i = -0*i. Let f(s) be the second derivative of s + i + 0*s**3 - 1/3*s**4 + 1/2*s**5 + 0*s**2. Solve f(v) = 0 for v.
0, 2/5
Let d(a) = a**2 + 6*a - 25. Let s be d(3). Factor 0 + c + 3/2*c**3 + 5/2*c**s.
c*(c + 1)*(3*c + 2)/2
Suppose -2*r = -0*r - 6. Let s(g) be the second derivative of 1/2*g**4 + 0*g**2 - 3/10*g**5 + 0 + 1/15*g**6 - 1/3*g**r - g. Factor s(q).
2*q*(q - 1)**3
Let s(t) be the second derivative of -3*t**5/80 + 3*t**4/16 + t**3/2 - 23*t. Let s(n) = 0. Calculate n.
-1, 0, 4
Suppose 0 = 2*h + 5*m + 2, 4*m + 0*m - 8 = -4*h. Factor 0*u**3 + 0*u**2 + 0 - 1/7*u**h + 0*u.
-u**4/7
Let z(m) = 24*m**2 + 12*m - 20. Suppose 5*u - 3*y = -5, 2*u - 4 = 6*u + 4*y. Let f(p) = p**2 + p - 1. Let c(d) = u*z(d) + 8*f(d). Solve c(q) = 0 for q.
-1, 3/4
Let m be 3*147/135 + -3. Let f = 23/30 - m. What is l in 0*l**2 + l - 1/2*l**4 - l**3 + f = 0?
-1, 1
Let k(w) be the third derivative of w**5/40 + 15*w**4/64 - w**3/4 - 27*w**2. Factor k(a).
3*(a + 4)*(4*a - 1)/8
Factor 6*a - 4*a**3 + a + 9*a - 8*a + 4*a**2.
-4*a*(a - 2)*(a + 1)
Find m, given that -3/4*m**5 + 3*m**2 + 3*m**4 - 9/2*m**3 - 3/4*m + 0 = 0.
0, 1
Suppose 4 = 2*j - 0. Suppose 0 = 5*u - 2*w - 195, u + 4*w - 39 = w. Let u*i**4 - 37*i**4 + 2*i**2 - 2*i**3 - 2*i**j = 0. What is i?
0, 1
Let c = -10 + 14. Let x(r) be the third derivative of 0*r - 4/15*r**3 - 121/150*r**5 - 4*r**2 + 11/15*r**c + 0. Suppose x(f) = 0. What is f?
2/11
Let b(q) be the third derivative of q**6/96 +