p(t) be the first derivative of -t**5/5 - 3*t**4/2 - 3*t**3 - 2*t**2 - 1. Find a such that p(a) = 0.
-4, -1, 0
Let z be -1*(-8)/28 - 0. Factor z*a**2 + 2/7 + 4/7*a.
2*(a + 1)**2/7
Let w(r) = 2*r + 9. Let k be w(-4). Let o(x) be the first derivative of 0*x**2 - 4/9*x**3 - k + 1/6*x**4 + 0*x. Let o(t) = 0. What is t?
0, 2
Let w(v) be the first derivative of 2 + v**2 + 4/3*v**3 + 0*v + 1/2*v**4. Factor w(d).
2*d*(d + 1)**2
Let j(v) be the second derivative of -v**6/15 + 2*v**5/5 - v**4 + 4*v**3/3 - v**2 + 3*v. Determine h so that j(h) = 0.
1
Let c(g) be the second derivative of 2*g + 1/30*g**5 + 0 + 0*g**2 - 1/9*g**3 + 1/18*g**4 - 1/45*g**6. Find h such that c(h) = 0.
-1, 0, 1
Let x(r) = 5*r**3 - 4*r**2 - 4. Let l(v) = -11*v**3 + 8*v**2 + v + 9. Let q(k) = 4*l(k) + 9*x(k). Let q(s) = 0. What is s?
0, 2
Let a(s) = 4*s**3 - 9*s**2 + 5*s + 5. Let k(d) = 2*d**3 - 4*d**2 + 2*d + 2. Let j(t) = -2*a(t) + 5*k(t). Determine p so that j(p) = 0.
0, 1
Factor 16*h**3 + 10/3*h**4 + 32/15 + 368/15*h**2 + 64/5*h.
2*(h + 2)**2*(5*h + 2)**2/15
Let f be (-10)/30*3*-1. Let w(z) be the first derivative of 3/2*z**4 - f + 0*z + 5/12*z**6 + 7/5*z**5 - 1/4*z**2 + 1/3*z**3. Suppose w(d) = 0. Calculate d.
-1, 0, 1/5
Let i(b) = -b**2 - 35*b + 38. Let n(s) = s**2 - s + 1. Let k(q) = i(q) - 2*n(q). Factor k(z).
-3*(z - 1)*(z + 12)
Let z(n) = -n**2 - 2. Let c be z(0). Let v be 2 - (c - (-1)/(-1)). Factor -s**2 - 3*s**3 + v*s**3 + 0*s**3.
s**2*(2*s - 1)
Let i(j) be the second derivative of -1/4*j**4 + 0 + 3/2*j**2 + 2/15*j**5 - 1/3*j**3 + j. Let f(u) be the first derivative of i(u). Factor f(b).
2*(b - 1)*(4*b + 1)
Let o(u) be the second derivative of -1/3*u**3 + 1/9*u**4 + 0*u**6 - 1/63*u**7 - 2/3*u**2 - 3*u + 2/15*u**5 + 0. Determine v, given that o(v) = 0.
-1, 1, 2
Find a, given that 9/4 + 3/4*a - 5/4*a**2 + 1/4*a**3 = 0.
-1, 3
Let w(o) be the third derivative of -o**8/84 + 2*o**7/105 - 7*o**2. Factor w(q).
-4*q**4*(q - 1)
Let c(x) be the third derivative of x**5/60 - x**4/6 + 2*x**3/3 - 9*x**2. Find h, given that c(h) = 0.
2
Let n(d) = 3*d**2 + 2. Let a(m) be the first derivative of m**3/3 - 3. Let t(w) = -5*a(w) + n(w). Find v, given that t(v) = 0.
-1, 1
Let m(d) = -d**2 - 6*d + 8. Let i be m(-6). Factor i*w**3 - 20*w**3 + 5*w**2 - 13*w**2 - 4*w**4.
-4*w**2*(w + 1)*(w + 2)
Suppose -8 = 5*k - 9*k. Let y = 11 + -11. Factor -2/3 + y*d + 2*d**k - 4/3*d**3.
-2*(d - 1)**2*(2*d + 1)/3
Let p(b) be the second derivative of 0 + 1/2*b**2 - 1/540*b**6 - 2/27*b**3 - 3*b + 1/36*b**4 + 0*b**5. Let s(r) be the first derivative of p(r). Factor s(k).
-2*(k - 1)**2*(k + 2)/9
Let d(y) be the second derivative of y**7/420 - 7*y**3/6 + 8*y. Let j(p) be the second derivative of d(p). Solve j(s) = 0.
0
Let g(b) be the second derivative of -b**7/42 - 4*b**6/15 - 5*b**5/4 - 19*b**4/6 - 14*b**3/3 - 4*b**2 - 6*b. Suppose g(l) = 0. Calculate l.
-2, -1
Let x = -37 + 37. Factor 0*g + x + 1/5*g**2.
g**2/5
Factor 1/5*k**2 - 1/5*k**4 + 2/5*k**3 - 2/5*k + 0.
-k*(k - 2)*(k - 1)*(k + 1)/5
Let j(z) be the first derivative of 1/6*z**4 + 0*z**3 + 4/15*z**5 + 0*z**2 + 0*z + 1/9*z**6 + 3. Let j(d) = 0. Calculate d.
-1, 0
Suppose 16*w - 13 = 35. Determine v so that -4/3*v**4 + 0*v**w + 4/3*v**2 - 2/3*v**5 + 0 + 2/3*v = 0.
-1, 0, 1
Find q, given that -2/5 + 2/5*q**2 + 0*q = 0.
-1, 1
Suppose -22*g - 9 = -24*g + 3*u, 2*u + 6 = g. Factor -s**3 + 5/3*s**2 + g + 2/3*s.
-s*(s - 2)*(3*s + 1)/3
Let g(o) be the second derivative of o**7/105 + o**6/25 - o**5/50 - 11*o**4/30 - 4*o**3/5 - 4*o**2/5 + 67*o. Factor g(v).
2*(v - 2)*(v + 1)**3*(v + 2)/5
Suppose 0 = -3*j - 5 + 26. Let d = j + -33/5. Solve -2/5*v**4 + 0 + 4/5*v**5 + d*v + 2/5*v**2 - 6/5*v**3 = 0.
-1, -1/2, 0, 1
Let q(t) be the third derivative of -t**6/1800 + t**4/120 - t**3/2 + t**2. Let r(w) be the first derivative of q(w). Let r(b) = 0. What is b?
-1, 1
Let h(a) be the second derivative of -a**4/30 - 4*a. Factor h(k).
-2*k**2/5
Let t be -2*4/(-2) - 4. Let t + 0*x**2 + 2/5*x**3 - 2/5*x = 0. What is x?
-1, 0, 1
Suppose 4*p = 5*i - 1, 0 = 3*p + i - 4 - 0. Let s = p + -1. Determine r so that s + 2/7*r**2 + 0*r - 2/7*r**3 = 0.
0, 1
Let d = 57 + -55. Let n(o) be the third derivative of -2*o**d - 1/18*o**4 + 0*o + 1/45*o**5 + 0 + 0*o**3 + 1/120*o**6. Factor n(u).
u*(u + 2)*(3*u - 2)/3
Let u(z) = 3*z**2 + z**4 + z + z**3 + 0*z**2 - 2*z**2. Let s be (4/8)/(2/4). Let g(o) = -o**4 - 5*o**3 - 5*o**2 - o. Let y(l) = s*g(l) + 3*u(l). Factor y(j).
2*j*(j - 1)**2*(j + 1)
Let z(g) be the second derivative of -g**4/66 - g**3/11 - 2*g**2/11 - 12*g. Suppose z(v) = 0. Calculate v.
-2, -1
Let y = -1/111 + -181/4551. Let j = 33/164 - y. Solve 1/4*k**2 + 1/2*k + j = 0 for k.
-1
Let l = 1141/40 - 225/8. Let -l - 4/5*t**3 + 4/5*t + 2/5*t**4 + 0*t**2 = 0. What is t?
-1, 1
Let g be 105/(-8)*16/12. Let b = -173/10 - g. Factor b*z**2 - 3/5 - 2/5*z.
(z - 3)*(z + 1)/5
Let n(x) = x**2 - 7*x + 6. Let f(g) = -4*g**2 + 34*g - 30. Let m(v) = -2*f(v) - 11*n(v). Factor m(r).
-3*(r - 2)*(r - 1)
Let r(m) be the second derivative of 1/105*m**7 - 1/25*m**5 + 3*m + 0 + 0*m**6 + 0*m**2 + 0*m**4 + 1/15*m**3. Find c such that r(c) = 0.
-1, 0, 1
Let j(q) be the first derivative of q**3/4 - 15*q**2/8 + 3*q + 21. Factor j(i).
3*(i - 4)*(i - 1)/4
Let v(i) = i**3 - 8*i**2 - 9*i + 3. Let o be v(9). Factor -1/4*l**o + 0 + 0*l**2 + 0*l.
-l**3/4
Let a(b) be the first derivative of b**4/14 + 10*b**3/21 + 8*b**2/7 + 8*b/7 + 13. Factor a(j).
2*(j + 1)*(j + 2)**2/7
Let r(g) be the second derivative of g**7/189 - g**6/135 - g**5/90 + g**4/54 - 5*g. Solve r(t) = 0 for t.
-1, 0, 1
Let j(d) be the first derivative of d**3/4 + 9*d**2/4 - 21*d/4 + 21. Determine s, given that j(s) = 0.
-7, 1
Suppose v = -2*v + 6. Factor 3*i**3 - i**2 + 3*i**3 - 7*i**3 - 2*i - 2*i**v.
-i*(i + 1)*(i + 2)
Let d be (1 + -5)*((-37)/18 + 2). Let j(q) be the first derivative of q**2 - 1 - d*q**3 - 4/3*q. Suppose j(h) = 0. What is h?
1, 2
Suppose -18 = -3*o - 3*k, 4*o + o + k - 14 = 0. Suppose -y = -r - 0*y, o = y. Let 1/2*m**3 - 1/2*m + 1/2*m**r - 1/2 = 0. Calculate m.
-1, 1
Let f be 80/(-50)*(-15)/6. Let s(c) be the first derivative of 3 + 8/7*c**3 - 9/14*c**f - 4/7*c**2 + 0*c. Factor s(u).
-2*u*(3*u - 2)**2/7
Let k = -16 + 16. Determine i so that -1/3*i**2 + 1/3 + k*i = 0.
-1, 1
Suppose -2*o - 4 = h, o - 4 = -3*h + 4*h. Let q(t) be the third derivative of 1/300*t**6 + 0*t**3 + 0*t - t**2 + 1/150*t**5 + o*t**4 + 0. Factor q(x).
2*x**2*(x + 1)/5
Let m = 110 + -62. Let b be 4/(-10) + m/20. Factor -2*x**3 + 0*x**2 + 0*x**2 - b*x**4 + 0*x**4.
-2*x**3*(x + 1)
Suppose -4*q - 2*y + 5*y + 3 = 0, -2*q + 4*y = 6. Let j(a) be the third derivative of 0*a**4 + 0 + 0*a - 3*a**2 - 1/21*a**q + 1/210*a**5. Factor j(o).
2*(o - 1)*(o + 1)/7
Factor 0*p**2 + 0*p**3 + 0*p + 0 - 2/9*p**4.
-2*p**4/9
Factor 0 + 1/5*g**5 + 0*g - 1/5*g**4 - 1/5*g**3 + 1/5*g**2.
g**2*(g - 1)**2*(g + 1)/5
Suppose -2*r**4 + 0*r + 0 + 0*r**2 + 1/2*r**5 + 2*r**3 = 0. What is r?
0, 2
Let c(h) be the first derivative of h**2 - 1 + 0*h - 2/3*h**3. Find l, given that c(l) = 0.
0, 1
Let d(p) be the first derivative of p**4/4 - 4*p**3/3 - 3*p**2/2 + 18*p - 61. Factor d(a).
(a - 3)**2*(a + 2)
Let w(i) be the third derivative of -i**7/1050 - i**6/300 + i**4/60 + i**3/30 + 9*i**2. Let w(k) = 0. What is k?
-1, 1
Suppose 0 = -4*n + n + 15. Suppose -12 = -w - 2*j, -4*w + n*j - 5 = -1. What is h in 0*h + 1/3*h**w + 0 - 1/3*h**2 + 0*h**3 = 0?
-1, 0, 1
Factor 5*y**4 + 12 + 2 - 10*y**2 + 5*y - 10*y**3 - 9 + 5*y**5.
5*(y - 1)**2*(y + 1)**3
Let l(k) be the third derivative of k**6/20 - 7*k**5/30 - k**4/2 + 10*k**2. Factor l(v).
2*v*(v - 3)*(3*v + 2)
Let q(u) = 6*u + 2. Let k be q(1). Suppose 0 = -r - 0*f + 5*f + 20, 2*r - 2*f - k = 0. Determine x so that r + 2/3*x**2 - 1/3*x - 1/3*x**3 = 0.
0, 1
Let h(w) be the second derivative of -w**6/20 - w**5/4 - w**4/2 - w**3/2 - w**2/4 + 11*w. Factor h(b).
-(b + 1)**3*(3*b + 1)/2
Let u(b) = -7*b**2 - 9*b + 5. Let v = -1 - -5. Suppose -v*t = t - 30. Let y(g) = -8*g**2 - 10*g + 6. Let r(j) = t*u(j) - 5*y(j). Factor r(q).
-2*q*(q + 2)
Let r(t) be the third derivative of -t**6/40 + 3*t**5/10 - 3*t**4/2 + 4*t**3 + 29*t**2. Factor r(b).
-3*(b - 2)**3
Let p(x) = -2*x - 7. Let o be p(-6). Let f(l) = l**3 - 4*l**2 + 3*l - 4. Let b be f(4). Factor 3*c**3 + 12*c**3 - 2*c**2 - b*c**4 -