*p**3. Suppose h(z) = 0. What is z?
-1/4
Let k(v) = -6*v**3 + 2*v**3 + 5*v**3 + 2 + v**2. Let t be k(0). Factor -8/9*c**3 + 8/9*c + 2/9*c**4 + 2/3*c**t - 8/9.
2*(c - 2)**2*(c - 1)*(c + 1)/9
Suppose 4*i - 24 = -4, -2*s + i + 3 = 0. Let x(g) be the first derivative of -1/3*g**3 + 2*g**2 - s*g + 2. Suppose x(f) = 0. What is f?
2
Let o = 227/462 - -2/231. Let x(d) be the second derivative of 0*d**4 + 0 - 3*d + d**2 - o*d**3 + 1/20*d**5. Suppose x(z) = 0. What is z?
-2, 1
Let f = -11 - -13. Let x(i) be the first derivative of 0*i**f + 1/20*i**4 + 1/15*i**3 + 0*i + 2 - 1/30*i**6 - 1/25*i**5. Factor x(v).
-v**2*(v - 1)*(v + 1)**2/5
Let t(f) be the first derivative of f**5/35 - f**4/7 + 8*f**2/7 - 8*f + 2. Let c(z) be the first derivative of t(z). Factor c(l).
4*(l - 2)**2*(l + 1)/7
Let l(g) be the second derivative of g**6/150 - g**5/50 - g**4/20 + 4*g**3/15 - 2*g**2/5 - 20*g. Solve l(w) = 0 for w.
-2, 1, 2
Let z(a) be the first derivative of 4/65*a**5 + 0*a - 1 - 2/39*a**3 + 0*a**2 + 1/26*a**4. Factor z(h).
2*h**2*(h + 1)*(2*h - 1)/13
Suppose -4 = -2*u + t, 3*u - 3*t - 4 = 8. Let l = 151 + -149. Factor 1/3*c**3 - c**4 + 0*c + 2/3*c**l + u.
-c**2*(c - 1)*(3*c + 2)/3
Suppose 12 + 12 = 4*c - 3*l, -4*l - 7 = 3*c. Let s(h) be the second derivative of h + 0*h**2 + 0 + 1/9*h**c - 1/18*h**4. What is p in s(p) = 0?
0, 1
Let n(y) be the second derivative of y**6/15 - y**5/5 - y**4/6 + 2*y**3/3 - 14*y. Factor n(x).
2*x*(x - 2)*(x - 1)*(x + 1)
Let v(o) be the first derivative of 2*o**5/35 + 5*o**4/14 + 2*o**3/3 + 3*o**2/7 - 27. Factor v(r).
2*r*(r + 1)**2*(r + 3)/7
Let a(n) be the first derivative of n**5/5 - 5*n**4/4 + 3*n**3 - 7*n**2/2 + 2*n + 3. Factor a(b).
(b - 2)*(b - 1)**3
Let u(n) = 2*n**2 - 16*n - 7. Let y(t) = -t**2 + 8*t + 3. Let q(l) = 4*u(l) + 7*y(l). Let a be q(9). Factor -d**a - d + d.
-d**2
Let a(d) be the second derivative of 0 + 1/21*d**3 - 2*d - 1/42*d**4 + 0*d**2. Find r, given that a(r) = 0.
0, 1
Let s(r) be the third derivative of -r**7/28 + 4*r**6/45 - r**5/15 + r**3/3 - 2*r**2. Let f(g) be the first derivative of s(g). Suppose f(h) = 0. Calculate h.
0, 2/5, 2/3
Let h(l) be the first derivative of l**7/105 + l**6/60 - l**5/30 - l**4/12 + l**2 - 3. Let y(g) be the second derivative of h(g). Find t such that y(t) = 0.
-1, 0, 1
Factor 8/5*h + 0 - 4/5*h**2.
-4*h*(h - 2)/5
Let h(d) = d**2. Let y be h(-2). Factor -w**5 - 2*w**y + w**4 + 0*w**5 + 0*w**5.
-w**4*(w + 1)
Let y(g) be the second derivative of -g**5/20 - g**4/12 + 5*g**3/6 - 3*g**2/2 - 3*g. Factor y(n).
-(n - 1)**2*(n + 3)
Let d(i) be the second derivative of 1/42*i**4 - 2/21*i**3 + 0 - 3/7*i**2 + 3*i. Factor d(c).
2*(c - 3)*(c + 1)/7
Find x such that 0*x**5 + 2*x**2 + 11*x**4 + x**4 - 5*x**5 - 9*x**3 = 0.
0, 2/5, 1
Determine j, given that -2/5*j**2 + 0 - 4/5*j = 0.
-2, 0
Factor 2/9 + 0*s - 2/9*s**2.
-2*(s - 1)*(s + 1)/9
Suppose u + 3 = -4*s, -3*u + 2*s + 16 + 3 = 0. Suppose u + 5 = 5*d. Find m, given that 2*m - 2*m**d + 2*m**2 + 0*m**2 - m**2 = 0.
0, 2
Suppose -c = -j - 4, 5*j = -5*c + 8 + 12. Let q(n) be the first derivative of 3 + 0*n + j*n**2 + 2/3*n**3. Factor q(x).
2*x**2
Let i(b) be the first derivative of -b**6/540 + b**5/90 - b**4/36 + 7*b**3/3 - 8. Let d(f) be the third derivative of i(f). Suppose d(y) = 0. What is y?
1
Let y(i) = 3*i - 12. Let d be y(5). Find n such that 2*n**2 - 2*n**4 + n**5 + n**5 + n - d*n**5 = 0.
-1, 0, 1
Factor 26*k**2 - k**4 - 24 - 9*k**3 + 4*k - 4*k**2 - 3*k**4 + 2*k**4 + k**5.
(k - 2)**3*(k + 1)*(k + 3)
Let w = 251833/168 + -1499. Let q(u) be the third derivative of 1/15*u**5 + 0*u**4 + 0 + 0*u - 1/6*u**3 + 1/60*u**6 - 1/70*u**7 - w*u**8 - 2*u**2. Factor q(r).
-(r - 1)*(r + 1)**3*(2*r - 1)
Let u be 14/(-6) + (13 - 10). Determine d so that 4/3*d**2 + 0 + 0*d - u*d**3 = 0.
0, 2
Let c = -81/7 - -169/14. Factor c*x**2 + x + 0.
x*(x + 2)/2
Let u(w) = -10*w**3 + 14*w**2 - 4*w. Let d(b) = 9*b**3 - 13*b**2 + 4*b. Let n(r) = 6*d(r) + 5*u(r). Determine h so that n(h) = 0.
0, 1
Let a(d) be the second derivative of -2/3*d**2 - 1/30*d**5 + 0 + 1/6*d**4 - d - 1/45*d**6 + 1/9*d**3. What is n in a(n) = 0?
-2, -1, 1
Let b = 356 + -1403/4. Let -57/4*h**4 + 0 - b*h**5 - 45/4*h**3 + 3/2*h - 3/4*h**2 = 0. What is h?
-1, 0, 2/7
Let g = -737/3 + 246. Determine o so that 1/3*o + 1/3*o**4 + 1/3*o**5 - 2/3*o**2 + g - 2/3*o**3 = 0.
-1, 1
Let q(f) be the third derivative of -f**5/140 + 3*f**4/14 + 2*f**2. What is p in q(p) = 0?
0, 12
Let c(g) be the third derivative of -1/300*g**6 - 1/20*g**4 + 0 + 2*g**2 - 1/50*g**5 - 1/15*g**3 + 0*g. Factor c(t).
-2*(t + 1)**3/5
Let j be (-16)/(-32)*(44/18 - 2). Solve -j*l**2 + 4/9*l - 2/9 = 0 for l.
1
Factor 6/7*v**2 + 2/7*v**3 - 8/7 + 0*v.
2*(v - 1)*(v + 2)**2/7
Let p(t) be the second derivative of t**5/270 + t**4/108 - t**2 + t. Let j(w) be the first derivative of p(w). Let j(i) = 0. What is i?
-1, 0
Let o = 3/22 + 4/11. Factor -1 + o*m + 1/2*m**2.
(m - 1)*(m + 2)/2
Suppose 2*b - 10*o = -14*o + 4, 2*b - 2*o = 4. Factor 0*h + 1/3*h**3 + 0 + 1/6*h**4 + 0*h**b.
h**3*(h + 2)/6
Let o(r) be the second derivative of -r**5/90 + r**4/18 - r**3/9 + r**2/9 - 10*r. Let o(n) = 0. Calculate n.
1
Let m(g) be the first derivative of -g**6/3 - 3*g**5/10 + g**4/3 + 4*g + 4. Let y(f) be the first derivative of m(f). Factor y(u).
-2*u**2*(u + 1)*(5*u - 2)
Let n = 217 - 1082/5. Determine z, given that -3/5*z**2 - 3/5*z**3 + 0*z + 3/5*z**5 + 0 + n*z**4 = 0.
-1, 0, 1
Let x(z) be the first derivative of -z**2/2 - 11*z + 11. Let y be x(-13). Suppose 9/2*w**4 - y*w**5 - w**3 + 3*w - 1/2 - 4*w**2 = 0. What is w?
-1, 1/4, 1
Let u(n) be the second derivative of -1/4*n**5 + 1/30*n**6 - 2*n**2 - 1/12*n**4 + 1/42*n**7 - n + 0 + 4/3*n**3. Factor u(c).
(c - 1)**3*(c + 2)**2
Let y(o) = 2*o**4 + 2*o**3 - 4*o + 4. Let h(t) = -t**4 - 2*t**3 + 3*t - 3. Suppose 5*r + 20 = 3*q, 16 = -r - 3*r - q. Let u(v) = r*h(v) - 3*y(v). Factor u(n).
-2*n**3*(n - 1)
Suppose -2*a = -0*q + 2*q - 6, 4*q + 2*a = 10. Factor -2/3*t**q - 1/3*t + 0 - 1/3*t**3.
-t*(t + 1)**2/3
Let v(w) be the second derivative of w**7/84 + 7*w**6/60 + 9*w**5/20 + 5*w**4/6 + 2*w**3/3 + 30*w. What is k in v(k) = 0?
-2, -1, 0
Let j(y) = 35*y**5 - 140*y**4 + 155*y**3 - 70*y**2 - 20. Let i(p) = -5*p**5 + 20*p**4 - 22*p**3 + 10*p**2 + 3. Let q(d) = -20*i(d) - 3*j(d). Factor q(t).
-5*t**2*(t - 2)*(t - 1)**2
Let u be 3 + 2/(-6) + (-52)/24. Solve -3/4*i + 1/4*i**2 + u = 0.
1, 2
Let c(o) be the first derivative of -o**3/27 - o**2/3 - 8*o/9 + 32. Solve c(x) = 0 for x.
-4, -2
Let f(d) be the third derivative of -d**5/150 - d**4/15 - d**3/5 + 12*d**2. Factor f(i).
-2*(i + 1)*(i + 3)/5
Let q = -3639/11 + 331. Factor -2/11*z**4 + q*z**5 + 0 + 0*z + 0*z**2 + 0*z**3.
2*z**4*(z - 1)/11
Let h be (-85)/(-4) - 7/28. Let q be 20/h - (-2)/(-3). Factor 0 + 8/7*l + 8/7*l**2 + q*l**3.
2*l*(l + 2)**2/7
Factor 0*s**2 + 3/4*s**5 + 0 - 3/4*s**3 + 0*s + 0*s**4.
3*s**3*(s - 1)*(s + 1)/4
Let v(z) = -z**3 - 8*z**2. Let p be v(-8). Solve p - 2 - 4*a**2 - a**2 - 3*a + 4*a**2 = 0.
-2, -1
Let j be ((-3)/5)/((-2)/10). Suppose -4*t - 3*d + 12 = 0, j*t - 4*t + 2*d - 8 = 0. Factor t + 2/5*x**3 + 2/5*x + 4/5*x**2.
2*x*(x + 1)**2/5
Let m(n) be the first derivative of -n**6/15 - n**5/5 - n**4/6 - n + 1. Let w(z) be the first derivative of m(z). Factor w(o).
-2*o**2*(o + 1)**2
Let r(q) = 4*q**2 - 3*q - 2. Let j(n) = -n**2. Let c(m) = -15*j(m) - 3*r(m). What is o in c(o) = 0?
-2, -1
Let s be 4/5*(-5)/(-14). Factor 0 + 0*j**2 + 0*j**3 + 0*j - s*j**4.
-2*j**4/7
Let s(w) = 7*w**3 - 7*w - 4. Let k(l) = -2*l - 7*l**3 + 9 - 7*l**3 + 16*l + 4*l**2 - 3*l**2. Let c(x) = 2*k(x) + 5*s(x). Let c(t) = 0. What is t?
-1, -2/7, 1
Let u(j) be the second derivative of -j**5/75 - j**4/60 + j**3/15 + j**2 - 9*j. Let c(x) be the first derivative of u(x). Determine v, given that c(v) = 0.
-1, 1/2
Suppose -21 = -4*s + r, -s + 0*s - 5*r - 21 = 0. Solve d**4 + d**s + 2*d**5 - 2*d**4 - 2*d**3 = 0 for d.
-1, 0, 1
Solve -1 - 21*o - 4 + 2 - 18*o**4 - 51*o**2 - 51*o**3 = 0.
-1, -1/2, -1/3
Let w(q) be the second derivative of q**4/66 + 10*q**3/33 + 25*q**2/11 - 25*q. Find n, given that w(n) = 0.
-5
Let s = -11 + 17. Let w be 4/s - (-50)/60. Suppose w*g**4 + 0 + 1/2*g**2 - 3/2*g**3 + 0*g - 1/2*g**5 = 0. Calculate g.
0, 1
Suppose 6*a - 266 = -248. Suppose 8*o - 4*o**2 + 2/3*o**a - 16/3 = 0.