 8/7*r**3. What is b in t(b) = 0?
-2/7, 1
Let v be (-6)/(-12) - ((2 - -1) + -3). Find h such that v - 1/4*h**2 - 1/4*h = 0.
-2, 1
Let y(a) = 14*a**4 + 8*a**3 - 4*a**2 - 36*a + 30. Let b(i) = -i**4 + i - 1. Let n(q) = -12*b(q) - y(q). Factor n(k).
-2*(k - 1)**2*(k + 3)**2
Let d(y) be the third derivative of y**5/12 + 25*y**4/24 + 41*y**2. Factor d(l).
5*l*(l + 5)
Let -50/3*v**3 + 40/3*v**2 + 0 + 6*v**5 + 0*v**4 - 8/3*v = 0. What is v?
-2, 0, 1/3, 2/3, 1
Suppose 0 = x - i - 3, 5*i = -9*x + 4*x + 25. Factor 26*p**5 - 3*p**4 + p**x + 2*p**2 + p**3 - 27*p**5.
-p**2*(p - 1)*(p + 1)*(p + 2)
Let s = -43 - -43. Factor s + 0*p - 2/5*p**3 + 2/5*p**2.
-2*p**2*(p - 1)/5
Let z be 4/16 + (-1)/4. Suppose z = -x - v + 3 - 0, -x + 7 = -3*v. Solve 0 - 6/7*c**2 - 2/7*c**5 + 6/7*c**x + 4/7*c - 2/7*c**3 = 0.
-1, 0, 1, 2
Solve -2/11*l**2 - 8/11*l**3 + 6/11*l**4 + 0 + 4/11*l = 0.
-2/3, 0, 1
Suppose 18*b**2 + 27 - 4*b**3 + 1/3*b**4 - 36*b = 0. What is b?
3
Let t(x) be the first derivative of -x**4/4 + x**3 - x + 2. Let h(b) be the first derivative of t(b). Find d such that h(d) = 0.
0, 2
Let s be 7 - 5 - -1*3. Suppose 2*c - s*c = -9. Factor 0*f**2 + 1/2*f**c + 1/4 - 1/4*f**4 - 1/2*f.
-(f - 1)**3*(f + 1)/4
Let v(r) = -r**2 + 14*r + 1. Let i be v(14). Let w be (1/(-2))/i*0. Solve -2/3*j**2 + w*j + 0 = 0 for j.
0
Let n(s) be the second derivative of -s**9/7560 + s**8/1120 - s**7/420 + s**6/360 + s**4/6 - 9*s. Let o(z) be the third derivative of n(z). Factor o(h).
-2*h*(h - 1)**3
Suppose -3/4*o**2 - 3/4*o**3 + 3/4*o**5 + 3/4*o**4 + 0 + 0*o = 0. What is o?
-1, 0, 1
Let g be 4/(-10)*70/(-84). Let r(l) be the third derivative of -g*l**3 + 0*l - l**2 - 1/10*l**5 + 0 + 1/3*l**4. Suppose r(d) = 0. What is d?
1/3, 1
Let z(h) be the second derivative of -h**4/15 - 2*h**3/15 + 4*h**2/5 + 3*h. Factor z(p).
-4*(p - 1)*(p + 2)/5
Suppose 2 = 4*g - 26. Suppose 5*u - 13 = g. Suppose -2/5*i**u + 0 - 2/5*i**3 + 0*i + 0*i**2 = 0. Calculate i.
-1, 0
Let c(k) = -8*k**4 + 6*k**3 + 4*k**2 - 6*k. Let j(n) = 17*n**4 - 11*n**3 - 8*n**2 + 11*n + 1. Let x(t) = 5*c(t) + 2*j(t). Let x(b) = 0. Calculate b.
-1, 1/3, 1
Suppose w + 2*m = 6, 2*w - 3*m + 0*m + 16 = 0. Let k be w - (-2)/(-4) - -3. Factor 0 + k*p**2 + 7/4*p**5 + 0*p + 11/4*p**3 + 4*p**4.
p**2*(p + 1)**2*(7*p + 2)/4
Let s(y) = -6*y**2 + y - 11. Let a = 23 - 11. Suppose -4*d = -d - a. Let w(p) = -2*p**2 - 4. Let r(b) = d*s(b) - 11*w(b). Let r(g) = 0. What is g?
0, 2
Let d(x) = 8*x**5 - 2*x**3 + 4*x**2 + 2. Suppose 0 = 3*m + 2*m + 30. Let l(u) = 7*u**5 - 3*u**3 + 4*u**2 + u + 1. Let k(g) = m*l(g) + 5*d(g). Factor k(v).
-2*(v - 1)**3*(v + 1)*(v + 2)
Let p(s) = -s**4 - 7*s**3 - 6*s**2 + 6*s. Let l = 1 - 0. Suppose -3*c - 17 = l. Let a(h) = -h**3 - h**2 + h. Let k(i) = c*a(i) + p(i). Factor k(m).
-m**3*(m + 1)
Suppose 20 = -4*l + 8*l. Let m = -3 + l. Factor -2/5*k**m + 4/5 + 2/5*k.
-2*(k - 2)*(k + 1)/5
Let a(g) = 9*g**3 - 7*g**2 + 5*g + 16. Let b(p) = -28*p**3 + 20*p**2 - 16*p - 48. Let d(u) = -16*a(u) - 5*b(u). Solve d(n) = 0.
-1, 2
Let b(v) = 3*v**2 - 4*v + 2. Let l be b(0). Factor -2*r**l + 18/7*r - 4/7.
-2*(r - 1)*(7*r - 2)/7
Let y(j) be the second derivative of j**7/945 - j**5/135 + j**3/27 + 2*j**2 - 3*j. Let n(d) be the first derivative of y(d). Factor n(s).
2*(s - 1)**2*(s + 1)**2/9
Let f(m) be the first derivative of m**4/2 - 4*m**3/3 - 3*m**2 - 12. Factor f(t).
2*t*(t - 3)*(t + 1)
Let m(o) = -o + 3. Let f(c) = c**2 - 2. Let d(k) = -3*f(k) - 2*m(k). What is l in d(l) = 0?
0, 2/3
Let v(u) be the first derivative of -4*u**6/9 + 22*u**5/15 - 3*u**4/2 + 2*u**3/9 + u**2/3 - 12. Factor v(g).
-2*g*(g - 1)**3*(4*g + 1)/3
Let r(h) be the first derivative of h**6/2 + 3*h**5/5 - 3*h**4/2 - 2*h**3 + 3*h**2/2 + 3*h - 9. Factor r(a).
3*(a - 1)**2*(a + 1)**3
Let n(t) be the second derivative of 0*t**3 + 0 + 1/20*t**5 + 0*t**4 - 3*t + 0*t**2. Factor n(f).
f**3
Factor 0*b + 0 - 3*b**2 - 3/2*b**4 + 9/2*b**3.
-3*b**2*(b - 2)*(b - 1)/2
Let t(s) = 8*s - 1 - 14*s + 4*s - s**2. Let k(z) be the second derivative of -z**3/6 - z**2/2 + 2*z. Let l(w) = 3*k(w) - t(w). Factor l(q).
(q - 2)*(q + 1)
Let c(y) be the third derivative of 1/63*y**7 - 1/30*y**6 - 3*y**2 - 1/336*y**8 + 0*y - 1/72*y**4 + 0*y**3 + 0 + 1/30*y**5. Factor c(g).
-g*(g - 1)**3*(3*g - 1)/3
Let x(w) = 4*w - 70. Let n be x(18). Factor 3/5*b**n - 3/5*b - 6/5.
3*(b - 2)*(b + 1)/5
Let n(c) = -c**5 - c**4 - c**3 + 3*c**2 - 2. Let l(f) = -5*f**5 - 4*f**4 - 5*f**3 + 15*f**2 - f - 11. Let h(x) = -2*l(x) + 11*n(x). What is v in h(v) = 0?
-2, -1, 0, 1
Let o(y) be the third derivative of y**9/15120 - y**8/3360 - y**7/2520 + y**6/360 - y**4/3 + 6*y**2. Let v(s) be the second derivative of o(s). Factor v(a).
a*(a - 2)*(a - 1)*(a + 1)
Let r(b) = b**2 + 5*b. Let d be r(-6). Let o(y) be the first derivative of 4/5*y**5 + 0*y**2 - 7/8*y**4 - 1/4*y**d + 0*y + 1/3*y**3 - 1. Factor o(h).
-h**2*(h - 1)**2*(3*h - 2)/2
Let g = -2615/2 - -1308. Let -g + 1/2*q**2 - 1/2*q + 1/2*q**3 = 0. Calculate q.
-1, 1
Let p = -418/3 + 140. Factor -2/3*w**2 + 1/3*w**3 + p - 1/3*w.
(w - 2)*(w - 1)*(w + 1)/3
Let z(u) = 6*u**4 - 11*u**3 + 17*u + 17. Let d(s) = -2*s**4 + 4*s**3 - 6*s - 6. Let v(x) = -17*d(x) - 6*z(x). Factor v(r).
-2*r**3*(r + 1)
Let l(h) be the first derivative of -2*h**5/25 - 2*h**4/5 - 2*h**3/3 - 2*h**2/5 - 7. Factor l(v).
-2*v*(v + 1)**2*(v + 2)/5
Let i(a) be the third derivative of -a**6/540 + a**5/270 + a**4/108 - a**3/27 + 2*a**2. Let i(y) = 0. What is y?
-1, 1
Let j(i) = -i**2 + 2*i - 7. Let k(f) = f - 1. Let h(c) = j(c) - 5*k(c). Factor h(t).
-(t + 1)*(t + 2)
Suppose 6*b + 4*y - 10 = b, -b = 2*y - 2. Let n(z) = -2*z - 5. Let v be n(-4). Factor 2*s + s + s**5 - 2*s - b*s**v.
s*(s - 1)**2*(s + 1)**2
Let g(k) be the first derivative of 2/5*k**2 - 1/5*k**4 + 1/5*k - 1/15*k**3 + 7. Factor g(h).
-(h - 1)*(h + 1)*(4*h + 1)/5
Suppose -3*g = -3*w - 2*g + 6, 4*w + 2 = -2*g. Suppose -2*c = -w - 3. Factor -1/5*z**c - 2/5 + 3/5*z.
-(z - 2)*(z - 1)/5
Let l(h) be the second derivative of h**4/8 + 5*h**3/4 + 3*h**2 - 11*h. Factor l(q).
3*(q + 1)*(q + 4)/2
Let b(a) = -5*a**2 - 10*a + 25. Let q(p) = 5*p**2 + 9*p - 26. Let l(n) = 4*b(n) + 5*q(n). Find f, given that l(f) = 0.
-3, 2
Let v(j) be the first derivative of j**7/56 - 3*j**5/40 + j**3/8 + 6*j + 5. Let s(a) be the first derivative of v(a). Determine k, given that s(k) = 0.
-1, 0, 1
Let b(j) be the third derivative of -2/15*j**4 - 4/15*j**3 + 6*j**2 + 0 - 1/300*j**6 - 1/30*j**5 + 0*j. Solve b(d) = 0 for d.
-2, -1
Suppose m - 2*o - 15 = 0, -5 = -3*m - 0*m - 2*o. Suppose 8*q - 16 = 4*q. Let m*v + 3*v**2 - q*v - 2*v = 0. What is v?
0, 1/3
Let o(x) be the first derivative of -x**6/1080 - x**5/360 + x**3 + 1. Let l(m) be the third derivative of o(m). Suppose l(a) = 0. Calculate a.
-1, 0
Let h(s) be the second derivative of s**7/420 + s**6/180 - s**5/60 - s**4/12 - s**3/6 - 5*s. Let p(f) be the second derivative of h(f). Factor p(i).
2*(i - 1)*(i + 1)**2
Factor 3/2 - 3/2*o**2 - 3/2*o + 3/2*o**3.
3*(o - 1)**2*(o + 1)/2
Suppose -48 = 4*o + 2*l, 3*o + 5*l = o - 40. Let j = o - -10. Find w such that 0 - 2/11*w**2 - 6/11*w**3 + j*w - 6/11*w**4 - 2/11*w**5 = 0.
-1, 0
Let i(k) be the second derivative of k**7/462 + k**6/330 - k**5/44 - 5*k**4/132 + 2*k**3/33 + 2*k**2/11 - 3*k - 7. Find a such that i(a) = 0.
-2, -1, 1, 2
Let z = 8 + -6. Let y be 0*(7/35)/(4/10). Factor 10/7*v**z + 2/7*v**4 - 8/7*v**3 - 4/7*v + y.
2*v*(v - 2)*(v - 1)**2/7
Let f be 0*(-9)/18 + 0. Find l, given that f*l - 2/13*l**2 + 2/13*l**3 + 0 = 0.
0, 1
Suppose -11 + 1 = -2*k. Let s(x) be the second derivative of 2*x**k + 0*x**3 - x + 0 + 4/21*x**7 - x**2 + x**6 + 5/3*x**4. Find d such that s(d) = 0.
-1, 1/4
Let s(r) be the second derivative of -r**5/20 - r**4/6 + r**3/6 + r**2 - 4*r. Solve s(g) = 0 for g.
-2, -1, 1
Let w(g) = 2*g**2 - 9*g - 9. Let c = 5 + -2. Let z(t) = t**2 - t. Let v(n) = c*z(n) - w(n). Factor v(u).
(u + 3)**2
Let g(b) be the first derivative of -b**7/2520 + b**5/360 + 4*b**3/3 + 3. Let v(s) be the third derivative of g(s). Find o such that v(o) = 0.
-1, 0, 1
Suppose 0 = -b - i + 6, -3*i + 13 - 3 = -b. Let o be b/10 + (-234)/(-30). Factor -6*y**3 - 2 + 1 + y**4 - 2*y + o*y**3.
(y - 1)*(y + 1)**3
Let l = 13/15 - 2/3. Let z = 10 - 8. Factor -l*s + 0 - 1/5*s**z + 1/5*s**3 + 1/5*s**4.
s*(s - 1)*(s + 1)**2