5*g**2. Let i(k) be the second derivative of o(k). Solve i(v) = 0 for v.
0, 1
Let h(b) be the second derivative of -b**4/30 + b**3/15 - 2*b. Factor h(g).
-2*g*(g - 1)/5
Factor 0 - 8/3*n - 2/3*n**3 + 8/3*n**2.
-2*n*(n - 2)**2/3
Determine p, given that -1/11*p**3 - 3/11*p**2 - 2/11*p + 0 = 0.
-2, -1, 0
Let c(p) be the first derivative of -1/2*p**2 + 2/3*p**3 + 2 - p - 1/6*p**6 + 1/2*p**4 - 1/5*p**5. Suppose c(f) = 0. What is f?
-1, 1
Let c be (32/30)/1 + (-12)/30. Factor -7/3*h**2 - c + 3*h.
-(h - 1)*(7*h - 2)/3
Let a(q) be the third derivative of q**9/68040 - q**8/10080 + q**7/3780 - q**6/3240 + q**4/6 - q**2. Let o(t) be the second derivative of a(t). Factor o(p).
2*p*(p - 1)**3/9
Let l(a) be the second derivative of 9/20*a**5 + 7/2*a**3 + 0 - 2*a**4 + a - 3*a**2. Factor l(i).
3*(i - 1)**2*(3*i - 2)
Let o(p) be the first derivative of 3*p**4/2 - 8*p**3/3 - 5*p**2 + 4*p + 5. Suppose o(x) = 0. What is x?
-1, 1/3, 2
Let j(s) be the third derivative of s**5/330 - s**4/66 + s**3/33 + 9*s**2. Factor j(q).
2*(q - 1)**2/11
Let j(w) be the first derivative of -2*w**3/69 + 2*w**2/23 + 6*w/23 + 17. Factor j(b).
-2*(b - 3)*(b + 1)/23
Let m(b) be the first derivative of -b**6/720 - b**5/240 - 2*b**3 + 1. Let g(j) be the third derivative of m(j). Determine p, given that g(p) = 0.
-1, 0
Let g(i) = -i**2 + 6*i - 6. Let b be g(4). Factor 0*y**3 + 2*y**b - 2*y**3 + y - y.
-2*y**2*(y - 1)
Find l, given that 2*l**2 - 5*l**2 + 3*l**4 - 6*l**3 + 3*l**2 = 0.
0, 2
Let s(q) = -q + 3. Let m be s(3). Let m*h - h**4 + 4*h**3 - 5*h**2 - 3*h + 5*h = 0. Calculate h.
0, 1, 2
Factor -3 + 1/2*i**2 - 1/2*i.
(i - 3)*(i + 2)/2
Let 2/11 + 2/11*v**3 - 2/11*v - 2/11*v**2 = 0. What is v?
-1, 1
Let z(y) be the second derivative of 0*y**2 + 1/48*y**4 + 3*y - 1/24*y**3 + 0. Solve z(i) = 0.
0, 1
Factor 2*d**3 - 9*d + 54 - 8*d**3 + d**3 - 12*d**2 + 8*d**3.
3*(d - 3)**2*(d + 2)
Let k(l) be the second derivative of 0 - 1/12*l**4 + 3/2*l**2 + 1/3*l**3 + 3*l. Factor k(o).
-(o - 3)*(o + 1)
Let q(d) be the third derivative of -d**9/80640 + d**5/60 + 6*d**2. Let j(n) be the third derivative of q(n). Factor j(s).
-3*s**3/4
Let x(v) be the second derivative of -v**6/60 + v**2 + 3*v. Let o(j) be the first derivative of x(j). What is m in o(m) = 0?
0
Let m(j) be the second derivative of -j**4/42 + j**3/7 - 19*j. Solve m(h) = 0 for h.
0, 3
Let f be (-40)/(-6)*2/15. Let d = 618 - 616. Factor -8/9 - 2/9*c**d + f*c.
-2*(c - 2)**2/9
Let y(i) be the first derivative of -i**4 - 68*i**3/15 - 12*i**2/5 - 40. Determine w so that y(w) = 0.
-3, -2/5, 0
Factor -3/5 - 1/5*c**2 - 4/5*c.
-(c + 1)*(c + 3)/5
Let x(z) = -z**2 + 4*z + 2. Let d be x(4). Let v = 794/1773 - 2/591. Factor -8/3*a**d - 14/9*a**3 - 2/3*a + v.
-2*(a + 1)**2*(7*a - 2)/9
Let m(d) = -d**2 + d. Let w(b) = -3*b**2 - 1. Let q(c) = -2*m(c) + w(c). What is l in q(l) = 0?
-1
Suppose -5*r = -3*p - 24, -6*r + 3*r = -p - 12. Let n(y) be the second derivative of 1/4*y**4 + 1/3*y**r - 1/30*y**6 + 0*y**2 + 0*y**5 + 0 + 2*y. Factor n(w).
-w*(w - 2)*(w + 1)**2
Let q be ((-3)/2)/(14/8). Let u = -11/21 - q. Factor 1/3*k + 0 - u*k**2.
-k*(k - 1)/3
Factor 2/3*a**5 + 0*a + 2/3*a**2 + 0 + 2*a**4 + 2*a**3.
2*a**2*(a + 1)**3/3
Let w(v) = 3*v**2 - 5*v + 2. Let y be w(0). Find u such that -1/3 - 2/3*u**y + u**4 - 1/3*u**5 - 2/3*u**3 + u = 0.
-1, 1
Factor 1/2*v**5 + 0*v**2 + 0*v + 0 + 0*v**3 + 1/2*v**4.
v**4*(v + 1)/2
Let x = 357 - 355. Solve 3/4*f**3 + 0*f**x - 3/4*f + 0 = 0 for f.
-1, 0, 1
Suppose 5*s + 153 = -l, -2*l = l + 2*s + 472. Let h = -627/4 - l. Factor -1 - h*i**2 - 1/4*i**3 - 2*i.
-(i + 1)*(i + 2)**2/4
Let c(k) be the second derivative of k**5/90 + k**4/54 - 2*k**3/27 + 12*k. Factor c(r).
2*r*(r - 1)*(r + 2)/9
Suppose 4 = 3*v + v, 4*f + 2*v = 10. What is x in 1/2 - 1/4*x - 1/4*x**f = 0?
-2, 1
Factor 0*g + 4/3 - 4/3*g**2.
-4*(g - 1)*(g + 1)/3
Let k(l) be the third derivative of l**7/210 - l**6/24 + 3*l**5/20 - 7*l**4/24 + l**3/3 + 4*l**2. Factor k(v).
(v - 2)*(v - 1)**3
Let u(r) be the second derivative of -r**6/105 + r**5/70 + r**4/42 - r**3/21 - 6*r. Factor u(z).
-2*z*(z - 1)**2*(z + 1)/7
Let h(w) be the second derivative of w**6/10 - w**5/7 - w**4/28 + w**3/21 - 3*w. Determine u so that h(u) = 0.
-1/3, 0, 2/7, 1
Suppose 4*v - 3*q = 40 - 14, -3*q = 4*v - 14. Let s(j) be the first derivative of 1/10*j**v + 1/4*j**4 - 1/2*j + 2 + 0*j**3 - 1/2*j**2. Factor s(w).
(w - 1)*(w + 1)**3/2
Suppose 0*o = 4*o - 4. Let q be 1 - o - (-3 + 3). What is t in 1/3*t - 2/3*t**3 + q*t**4 + 0 + 1/3*t**5 + 0*t**2 = 0?
-1, 0, 1
Let n(r) be the second derivative of r**8/30240 - r**7/5670 - r**6/3240 + r**5/270 + r**4/4 - 5*r. Let k(c) be the third derivative of n(c). Factor k(m).
2*(m - 2)*(m - 1)*(m + 1)/9
Let l(y) be the first derivative of -y**4/16 - 5*y**3/12 - 3*y**2/8 + 9*y/4 + 10. Suppose l(b) = 0. What is b?
-3, 1
Let m(p) be the second derivative of -p**4/30 - p**3/5 - 2*p**2/5 + 20*p. Find b such that m(b) = 0.
-2, -1
Let c(x) be the third derivative of x**9/24192 + x**8/13440 - x**7/5040 - 2*x**5/15 - 8*x**2. Let n(h) be the third derivative of c(h). Factor n(j).
j*(j + 1)*(5*j - 2)/2
Suppose -6 = 3*s + 3. Let y = 5 + s. Suppose -8*r**5 - 14*r**4 - 2 - 2*r + 2*r**y + 4*r**3 + 14*r**2 + 6*r + 0*r = 0. What is r?
-1, 1/4, 1
Factor -2/3*j**5 + 4/3*j**3 - 2/3*j + 0*j**4 + 0*j**2 + 0.
-2*j*(j - 1)**2*(j + 1)**2/3
Let r(a) be the second derivative of 39*a**5/20 - a**4/2 - 13*a**3/2 + 3*a**2 - 9*a. Let r(x) = 0. What is x?
-1, 2/13, 1
Let h = -9 + 11. Factor 2*a**3 - a**h + a**4 + 0*a**4 + a - 3*a**3.
a*(a - 1)**2*(a + 1)
Solve -49/3 - 14/3*w - 1/3*w**2 = 0 for w.
-7
Let k be (44/6)/(1/3). Suppose 0 = y + 4*t - k, -3*y - 12 = y - 4*t. Solve 2*x**y - 5 - 1 + 4 = 0.
-1, 1
Let v(t) = t**3 - 2*t - 2. Let w(j) = -5*j**3 + 11*j + 11. Let r be (9/(-2) + -1)*-4. Let f = -2 + 6. Let g(c) = f*w(c) + r*v(c). Factor g(d).
2*d**3
Let d = -341 - -2389/7. Suppose d + 8/7*b**2 + 10/7*b = 0. What is b?
-1, -1/4
Let y(z) = z**5 - z**3 - z. Let f(q) = -6*q**5 - 3*q**4 + 3*q**3 + 5*q. Let b(u) = -f(u) - 5*y(u). Factor b(s).
s**3*(s + 1)*(s + 2)
Suppose 2 = -2*p - 2. Let j be (0/p - -2)/6. Factor -1/3*s - j + 1/3*s**2 + 1/3*s**3.
(s - 1)*(s + 1)**2/3
Let r = -40 + 40. Factor 2/9*o + 2/3*o**3 - 2/3*o**2 + r - 2/9*o**4.
-2*o*(o - 1)**3/9
Let r(z) be the first derivative of z**4/2 - z**2 + 11. Factor r(c).
2*c*(c - 1)*(c + 1)
What is d in -8*d**2 + 5*d**4 + 3*d**2 - 5*d**3 + 0*d**2 + 5*d = 0?
-1, 0, 1
Suppose 2*f**5 - 41*f**3 + 41*f**3 = 0. What is f?
0
Let c(n) be the third derivative of 0 + 0*n**7 + 0*n - 1/504*n**8 + 0*n**5 + 0*n**4 + 0*n**3 + 3*n**2 + 1/180*n**6. Suppose c(h) = 0. What is h?
-1, 0, 1
Let z(u) be the third derivative of u**6/260 + u**5/195 - u**4/52 - 2*u**3/39 - 4*u**2. Factor z(w).
2*(w - 1)*(w + 1)*(3*w + 2)/13
Let s(a) = a + 12. Let z be s(-10). Suppose 4*v - 3 = c, 2*v - z*c + 2 - 8 = 0. Determine o, given that 2/7*o**3 + 4/7*o + 6/7*o**2 + v = 0.
-2, -1, 0
Let w = -2 - -5. Suppose 3*l**4 + 8*l**w + l**4 + 36*l**2 + 30*l + 12*l**3 + 8 - 2*l = 0. Calculate l.
-2, -1
Factor 4/5*f**3 + 4/5*f**4 + 0 + 0*f - 8/5*f**2.
4*f**2*(f - 1)*(f + 2)/5
Let a(c) be the second derivative of -c**6/75 - 2*c**5/25 + 6*c. Factor a(l).
-2*l**3*(l + 4)/5
Let c(t) be the second derivative of -2*t - 1/10*t**5 - 4/45*t**6 + 0*t**3 + 0 - 1/27*t**4 - 5/189*t**7 + 0*t**2. Determine q so that c(q) = 0.
-1, -2/5, 0
Let u be (-3)/(-600)*(-1 + 7). Let w(m) be the second derivative of -1/20*m**4 + u*m**5 + 2*m + 0*m**2 - 1/150*m**6 + 1/30*m**3 + 0. Find b such that w(b) = 0.
0, 1
Let l(u) be the second derivative of u**4/48 - u**3/8 - u**2/2 + 13*u. Find i, given that l(i) = 0.
-1, 4
Let r = 9 + -19. Let f(k) = -2*k**5 - 12*k**4 - 6*k**3 + 14*k**2 - 2*k + 8. Let q(s) = s**4 + s**3 - s**2 - 1. Let j(a) = r*q(a) - f(a). Factor j(l).
2*(l - 1)**2*(l + 1)**3
Let q(t) = -t**2 + 1. Let d be q(-2). Let b be -3 - (d + 6 + -6). Factor 0 + 0*r**2 + 0*r**3 + 2/3*r**5 - 2/3*r**4 + b*r.
2*r**4*(r - 1)/3
Let z be 63/27*2/63. Let o(i) be the second derivative of z*i**4 + 0 + 0*i**2 + 1/27*i**3 - 2*i. Determine b so that o(b) = 0.
-1/4, 0
Let -5/4*j**2 + 25/4*j - 5 = 0. Calculate j.
1, 4
Find r, given that 0 + 0*r + 0*r**2 - 3/2*r**3 = 0.
0
Let y(n) be the second derivative of -n**5/150 - n**4/90 + 8*n**3/45 + 4*n**2/5 - 