Let f(w) be the first derivative of 1/5*w**2 + 0*w + 2/15*w**3 + 2. Find c, given that f(c) = 0.
-1, 0
Let b(t) = -3*t**4 - 23*t**3 - 52*t**2 - 47*t - 16. Let x(q) = -q**4 - q**3 - q. Let n(o) = -b(o) - x(o). Factor n(w).
4*(w + 1)**2*(w + 2)**2
Suppose 0 = -w + 4 - 1. Let o(d) be the second derivative of d + 0 + 0*d**2 - 1/60*d**6 + 0*d**w - 1/20*d**5 - 1/24*d**4. Factor o(s).
-s**2*(s + 1)**2/2
Let m = 2137/7 - 305. Factor -18/7*j**2 + 8/7*j**3 - m + 12/7*j.
2*(j - 1)**2*(4*j - 1)/7
Let h(x) be the first derivative of -x**5/3 + 3*x**4/2 - 4*x**3/3 - 4*x**2/3 + 11. Find w such that h(w) = 0.
-2/5, 0, 2
Let d(b) be the first derivative of -6 + 2*b**5 - 3*b**4 + 0*b + 8*b**2 - 8/3*b**3 - 1/3*b**6. Factor d(g).
-2*g*(g - 2)**3*(g + 1)
Let c(f) = f**2 + 5*f + 6. Let x be c(-4). Suppose 0 + 2/9*p**x + 4/9*p**3 - 4/9*p - 2/9*p**4 = 0. What is p?
-1, 0, 1, 2
Let c(o) be the first derivative of -1/10*o**4 + 0*o - 3 - 4/15*o**3 - 1/5*o**2. Find r, given that c(r) = 0.
-1, 0
Suppose -2*n - 2*o - 124 = -6*n, 4*n = -o + 112. Let g = -27 + n. Determine y so that 0 - 1/3*y**g - 1/3*y**4 + 0*y + 2/3*y**3 = 0.
0, 1
Factor j**2 - j**3 + j**2 + j**4 - j + j**2 - 2*j**3.
j*(j - 1)**3
Let z(m) be the second derivative of -m**5/70 - m**4/42 + m**3/21 + m**2/7 - 17*m. Solve z(h) = 0.
-1, 1
Factor -30*d**2 + 0*d**4 + 3*d**5 + 132*d**3 + 39*d**4 + 6*d**3 - 525*d + 375.
3*(d - 1)**2*(d + 5)**3
Let m be (-2 + 4)*(-1)/(-5). Solve -m*k + 0 - 4/5*k**2 - 2/5*k**3 = 0 for k.
-1, 0
Let g(x) = x + 8. Let y be g(-4). Let m(n) = n**3 - 5*n**2 + 4*n + 3. Let c be m(y). Solve 1/3*d**c - 1/3*d + 1/3*d**2 - 1/3 = 0 for d.
-1, 1
Let z = -4 + 6. Factor 6 - 5*t**z - 24*t - 15 + t**2 - 27.
-4*(t + 3)**2
Let u(p) be the first derivative of 4/5*p**6 + 9/2*p**4 - 3 + p - 7/2*p**3 - 3*p**5 + 3/2*p**2. Let n(x) be the first derivative of u(x). Factor n(l).
3*(l - 1)*(2*l - 1)**3
Let z(b) = -b**3 + 5*b**2 + b - 3. Let v = 17 + -12. Let m be z(v). Factor 34*y**3 - 8*y + 36*y**3 + 13*y**m - 5*y**2.
2*y*(5*y + 2)*(7*y - 2)
Let f(v) be the third derivative of -v**5/140 - v**4/56 + v**3/7 - 13*v**2. Factor f(w).
-3*(w - 1)*(w + 2)/7
Let k(r) = -r**3 + 2*r**2 + 5*r - 4. Let m be k(3). Let t(j) be the first derivative of -1/2*j**m + 0*j + 1/6*j**3 - 2. Factor t(y).
y*(y - 2)/2
Suppose -2*z - 3*z = 0. Factor 2/3*c**3 - 2/3*c + 0 + z*c**2.
2*c*(c - 1)*(c + 1)/3
Let q(d) be the first derivative of -d**3/3 + 21*d**2/2 + 21*d + 6. Let g(s) = -2*s**2 + 32*s + 32. Let l(h) = 5*g(h) - 8*q(h). Factor l(n).
-2*(n + 2)**2
Let h(q) = q**2 + 1. Let u(z) = z**4 + z**3 + z**2 + 1. Let r(a) = 3*h(a) - 3*u(a). Suppose r(j) = 0. What is j?
-1, 0
Solve 0 + 2/5*m + 1/10*m**2 = 0.
-4, 0
Let c be (-1)/4 + 15/36. Let k(f) be the second derivative of -c*f**3 - 1/6*f**6 - 3/4*f**4 - f + f**2 + 13/20*f**5 + 0. Determine g, given that k(g) = 0.
-2/5, 1
Factor -5/3*g + 5/3*g**3 - 5 + 5*g**2.
5*(g - 1)*(g + 1)*(g + 3)/3
Suppose k + 28 = 5*k. Suppose -u**2 - u - 4 + k - 1 = 0. What is u?
-2, 1
Let j(o) be the second derivative of o**7/1680 - o**6/480 - o**5/160 + o**4/48 - 5*o**3/6 + 2*o. Let l(c) be the second derivative of j(c). Factor l(r).
(r - 2)*(r + 1)*(2*r - 1)/4
Let z(p) be the first derivative of -p**7/490 + p**6/140 - p**5/140 - p**2 - 2. Let s(b) be the second derivative of z(b). Let s(v) = 0. Calculate v.
0, 1
Suppose 0 = -3*z - 7*b + 5*b + 10, -z + 12 = 5*b. Factor 0*n + 0 - 1/2*n**z + 1/2*n**3.
n**2*(n - 1)/2
Let l(p) = p**2 - 9*p - 2. Let v(y) = -y**2 + 18*y + 5. Let b(i) = 7*l(i) + 4*v(i). Factor b(s).
3*(s + 1)*(s + 2)
Let o be (-9 - -4) + 1 + 4 - -4. Factor -2/3*m**5 + 0*m**o + 0*m + 2*m**3 + 0 + 4/3*m**2.
-2*m**2*(m - 2)*(m + 1)**2/3
What is d in -4*d**3 + 22*d**4 + 4*d**2 - 24*d**4 + 2*d**2 = 0?
-3, 0, 1
Let d be (3/12)/(6/48). Determine v, given that 2*v**3 - 2*v**2 + 6*v**d - 6*v**3 - 4*v**4 + 4*v = 0.
-1, 0, 1
Determine n so that 0*n**2 + 2*n - 2/7*n**3 - 12/7 = 0.
-3, 1, 2
Let o(h) be the second derivative of 0*h**3 - 2*h + 1/150*h**5 - 3/2*h**2 + 0 - 1/60*h**4. Let j(i) be the first derivative of o(i). Solve j(y) = 0 for y.
0, 1
Let p = -207/4 - -52. Suppose 0 = -4*g + 5*y + 5, -3*g - 2 + 7 = -5*y. Let g + 1/2*c**3 - 1/4*c**2 - p*c**4 + 0*c = 0. Calculate c.
0, 1
Let a(r) = -r**3 + 6*r**2 - r + 8. Let q be a(6). Suppose 6 = k + q*g, 5*g = 2*k + 9 + 6. Suppose -1/4*s**2 + k*s**3 + 0 + 1/4*s**4 + 0*s = 0. What is s?
-1, 0, 1
Let l(t) = -4*t**2 - 5*t + 5. Let v(d) = -6*d**2 - 7*d + 7. Let i(u) = 7*l(u) - 5*v(u). Factor i(g).
2*g**2
Let d(c) be the first derivative of c**6/20 - 3*c**5/40 - c**4/4 + 2*c + 1. Let l(v) be the first derivative of d(v). Factor l(k).
3*k**2*(k - 2)*(k + 1)/2
Let z be -12 - 1 - (3 - 4). Let g = z - -12. Suppose 0 + 1/3*m**3 + 1/3*m**2 + g*m = 0. What is m?
-1, 0
Let s(g) be the second derivative of -4/3*g**3 - 1/6*g**4 + 0 - 2*g - 4*g**2. Determine v so that s(v) = 0.
-2
Suppose 0*t = -2*t. Let d be -2 - (-3 + t) - -2. Factor 2 + 0*r - 4*r**2 + d*r**2 + r.
-(r - 2)*(r + 1)
Factor 3*j**2 + 0 + 0*j - 3/4*j**3.
-3*j**2*(j - 4)/4
Let s(d) be the first derivative of 0*d**2 - 2/3*d**3 - 1/6*d**6 + 0*d**5 + 3/4*d**4 + 1 + 0*d. Let s(o) = 0. What is o?
-2, 0, 1
Let h = -21 + 29. Suppose 3*j = h - 2. Suppose -o**3 - 2*o**3 + o**4 + j*o**3 = 0. Calculate o.
0, 1
Let d(x) be the first derivative of 9*x**4 - 4*x**3 - 16*x**2 + 16*x - 1. Factor d(z).
4*(z + 1)*(3*z - 2)**2
Let k(j) be the third derivative of 0*j**3 - j**2 - 1/40*j**6 + 0*j + 1/8*j**4 + 0*j**5 + 0. Solve k(f) = 0.
-1, 0, 1
Let r be 1/(-3) + 4/6. Let j = 136/3 - 45. Suppose -j*n**2 + 1/3*n - r*n**3 + 1/3 = 0. Calculate n.
-1, 1
Solve 6/23*b - 4/23 - 2/23*b**3 + 0*b**2 = 0.
-2, 1
Let o(z) = 27*z**4 - 92*z**3 + 95*z**2 - 30*z. Let m(d) = 432*d**4 - 1473*d**3 + 1521*d**2 - 480*d. Let f(w) = -2*m(w) + 33*o(w). Suppose f(t) = 0. Calculate t.
0, 2/3, 1, 5/3
Let w = 423/455 + -12/13. Let m = 11381/910 - w. Factor -m*t**4 - 2 - 15*t**3 + 6*t + 11/2*t**2.
-(t + 1)**2*(5*t - 2)**2/2
Factor 11*v**3 - 15*v**3 - 4*v + v**2 - 9*v**2.
-4*v*(v + 1)**2
Suppose 5*s - 10 = u - 6*u, -2*s - u + 6 = 0. Let -s*v**2 + 18*v - 64 + 20*v - 6*v = 0. Calculate v.
4
Let n(c) be the first derivative of -4*c**3/3 - 8*c**2 - 12*c - 4. Suppose n(u) = 0. Calculate u.
-3, -1
Solve 0*q - 1/3 + 1/3*q**2 = 0.
-1, 1
Let q(j) be the third derivative of j**7/1470 + j**6/840 - j**5/210 + 3*j**2. Factor q(s).
s**2*(s - 1)*(s + 2)/7
Let z(q) be the first derivative of q**4/20 + q**3/5 + 3*q**2/10 + q/5 + 13. Factor z(a).
(a + 1)**3/5
Let u(l) be the first derivative of -l**5 - 5*l**4/4 + 5*l**3/3 + 5*l**2/2 - 25. Determine h so that u(h) = 0.
-1, 0, 1
Let x(p) = -p**2 - 10*p + 3*p**2 - 3*p**2 - p**3 + 6 - 6*p**2. Let v be x(-5). Factor -6 + v*i - 3/2*i**2.
-3*(i - 2)**2/2
Let l(b) = -b**2 + 2*b + 3. Let j(o) = -5*o**3 + 2*o + 1. Let f be j(-1). Let z(h) = 1 - 11*h - 8*h + 20*h. Let a(v) = f*z(v) - l(v). Solve a(m) = 0.
-1
Let b = 3889/18 - 216. Let z(d) be the second derivative of -1/15*d**5 + 0 + 0*d**2 + d - 1/9*d**4 - b*d**3. Solve z(t) = 0 for t.
-1/2, 0
Let v(j) = 92*j**2 - 62*j - 17. Let u(l) = -31*l**2 + 21*l + 6. Let g(b) = 17*u(b) + 6*v(b). Factor g(y).
5*y*(5*y - 3)
Let i(k) be the first derivative of -k**4/13 + 10*k**3/39 - 4*k**2/13 + 2*k/13 - 5. Find c, given that i(c) = 0.
1/2, 1
Suppose -6 = -t - v, 0 = 3*t - 3*v + 2 + 4. Suppose -2*d - 5*d**2 + d**3 + d + 4*d**t + 1 = 0. Calculate d.
-1, 1
Let n be (-6)/((-3)/(-6)*-4). Let a be -1*(2 - n) + 3. Suppose -2*z - 18/7*z**2 - 4/7 - 10/7*z**3 - 2/7*z**a = 0. Calculate z.
-2, -1
Factor 0 + 3/5*i**2 - 3/5*i.
3*i*(i - 1)/5
Let g(c) be the third derivative of -c**5/270 - c**4/27 + 8*c**2. Let g(y) = 0. Calculate y.
-4, 0
Factor 44*h - 22*h**2 + 54*h**2 - 36*h**2.
-4*h*(h - 11)
Let r be (-7)/(-4 + 4 - -1). Let h be 2/r - 4/(-14). Find o, given that -2/7*o**2 + 2/7*o**3 + h*o + 0 = 0.
0, 1
Let b(o) be the third derivative of -o**6/180 - o**5/360 + o**4/48 + 23*o**2. Factor b(k).
-k*(k + 1)*(4*k - 3)/6
Let u be 1*(-1)/(1/(-6)). Let m be 0 - -3 - (-12)/u. Factor 3*r**2 - 5*r - 4*r**2 + m*r.
-r**2
Factor -2/11*p**4 + 2/11*p**3 - 2/11*p + 2/11*p**2 + 0.
-2*p*(p - 1)**2*(p + 1)/11
Let h(q) be the third derivative of -2*q**7/105 - q**6/10 - q**5/5 - q**4/6 - q**2. Factor h(t).
-4*t*(t + 1)**3
Let q(r) = 4*r**5 - 2*r**4