31/(-7) - -5)/((-6)/(-21)). Factor 0*a - 3/2*a**2 - 1/2*a**3 + w.
-(a - 1)*(a + 2)**2/2
Let y(t) = -20*t**2 + 8*t + 3. Let b(n) = 20*n**2 - 7*n - 2. Let m(a) = 3*b(a) + 2*y(a). Determine p, given that m(p) = 0.
0, 1/4
Let d(b) be the third derivative of 1/24*b**3 - 1/48*b**4 - 4*b**2 + 0*b + 1/240*b**5 + 0. Suppose d(o) = 0. Calculate o.
1
Let k(q) be the first derivative of -1/3*q**3 + 3 - 1/8*q**4 + q + 1/4*q**2. Find o such that k(o) = 0.
-2, -1, 1
Let q(p) be the second derivative of p**5/60 - p**4/24 - 5*p**2/2 + 3*p. Let c(l) be the first derivative of q(l). Factor c(h).
h*(h - 1)
Let q(p) = -p**3 + p**2 + 1. Let s(y) = -y**4 - 3*y**3 + 5*y**2 + 2. Let n(u) = 6*q(u) - 2*s(u). Find g, given that n(g) = 0.
-1, 1
Let h(y) be the first derivative of 1 - 1/12*y**2 + 0*y - 7/12*y**4 - 7/18*y**3 - 4/15*y**5. Determine l, given that h(l) = 0.
-1, -1/2, -1/4, 0
Let q be (-16)/(-6) - 10/15. Let k be 15/40*q/3. Factor 0 + 0*p**3 + 1/2*p**2 + 1/4*p - 1/2*p**4 - k*p**5.
-p*(p - 1)*(p + 1)**3/4
Let z = 85 - 339/4. Suppose o - 4*o = -6. Let 0 + 0*h**3 + 0*h + 1/4*h**o - z*h**4 = 0. What is h?
-1, 0, 1
Let m be (152/(-4))/(2*-1). Factor 27*n - m*n - 10*n**4 + 6*n**3 + n**2 + 23*n**2.
-2*n*(n - 2)*(n + 1)*(5*n + 2)
Suppose -5*t - 2*r = -16, 5*t + 5 = 3*r + 6. Factor -1/3 - 5/6*s - 2/3*s**t - 1/6*s**3.
-(s + 1)**2*(s + 2)/6
Let q = 823/15 + -164/3. Factor 0*t + 0 - q*t**2 + 4/5*t**3.
t**2*(4*t - 1)/5
Let b(w) = w**3 - 7*w**2 + 3. Let v be b(7). Suppose 6*t = 4*t + 5*d + 10, 4*t + 8 = -4*d. Solve 1/5*p**v + t*p + 0 + 2/5*p**2 = 0 for p.
-2, 0
Factor -8/17*c - 2/17*c**2 - 8/17.
-2*(c + 2)**2/17
Let q(a) be the third derivative of 0*a**3 - 3*a**2 + 0*a**4 - 1/360*a**6 + 1/90*a**5 + 0*a + 0. Factor q(u).
-u**2*(u - 2)/3
Let n be (-61)/(-5) - (-11)/(-55). Let z = 12 - n. Determine p, given that 11/2*p**4 + 1/2*p**2 - p + 3/2*p**5 + z + 11/2*p**3 = 0.
-2, -1, 0, 1/3
Factor 66/5*t**2 + 8/5 - 56/5*t + 112/5*t**3 + 32/5*t**4.
2*(t + 2)**2*(4*t - 1)**2/5
Let c = -79 + 81. Let t be 2/30 + 3/9. Factor 2/5 - 4/5*l + 0*l**c + 4/5*l**3 - t*l**4.
-2*(l - 1)**3*(l + 1)/5
Suppose 2*s = c - 1 + 2, 3*c = 4*s + 1. Factor -2*h + 6*h + 2*h**s + 2 - h**5 + h - 4*h**4 - 4*h**3.
-(h - 1)*(h + 1)**3*(h + 2)
Let j be 1 - (3 + 21/(-6)). Factor -7/2*u - j*u**2 - 1.
-(u + 2)*(3*u + 1)/2
Let i(f) = -f**2 - 21*f - 87. Let h be i(-15). Suppose -k + 12 = 2*y, 0*y + 15 = 3*y. Find m, given that h - 9/2*m + 3/2*m**k = 0.
1, 2
Let i = -4 - -29. Suppose i = u + 4*h, 3*u = -h + 7 + 13. Factor 2/5*t**3 + 0 + 0*t**2 + 2*t**4 + 0*t + 8/5*t**u.
2*t**3*(t + 1)*(4*t + 1)/5
Factor 1/3*k**4 - 1/3 + 0*k**2 + 2/3*k - 2/3*k**3.
(k - 1)**3*(k + 1)/3
Let d(w) be the second derivative of w**4/54 + 2*w**3/27 - w**2/3 + 3*w. Factor d(p).
2*(p - 1)*(p + 3)/9
Suppose 4*j**5 + 0*j**4 - 4*j**4 - 12*j**3 - 768*j**2 + 772*j**2 + 8*j = 0. Calculate j.
-1, 0, 1, 2
Let i(m) be the third derivative of -m**6/120 - m**5/30 - 4*m**2. Factor i(l).
-l**2*(l + 2)
Let n = 1459/1694 + -1/242. Find l such that -2/7*l**3 + 10/7*l + 2/7*l**4 - 4/7 - n*l**2 = 0.
-2, 1
Let r(v) = v**3 - 4*v**2 - 5*v + 2. Let a be r(5). Let c(y) be the second derivative of 1/30*y**4 + 0*y**a + 2*y + 0 + 1/15*y**3. Suppose c(t) = 0. What is t?
-1, 0
Let l be (3 - 4)/(0/(-2) + -7). Factor -l*q**2 - 6/7*q - 9/7.
-(q + 3)**2/7
Let s(k) = 6*k**5 + k**4 - 8*k**3 - 5*k**2 + 3*k. Let y(q) = 5*q**5 + q**4 - 7*q**3 - 5*q**2 + 2*q. Let u(f) = 4*s(f) - 5*y(f). Factor u(a).
-a*(a - 2)*(a + 1)**3
Factor 3/7*s**2 - 6/7*s + 0.
3*s*(s - 2)/7
Let f(c) be the third derivative of -1/165*c**5 + 0*c**3 - 2*c**2 + 1/1155*c**7 - 1/660*c**6 + 0*c + 0*c**4 + 0. Let f(q) = 0. Calculate q.
-1, 0, 2
Let y(v) = -v**2 - 1 - v + 1 + 2. Let i be y(0). Factor 8/5*t - 32/5*t**i + 42/5*t**3 - 18/5*t**4 + 0.
-2*t*(t - 1)*(3*t - 2)**2/5
Let m = -511 + 513. Let t be 2/(-4)*(0 - 0). Factor 2/3*o**3 - m*o + t*o**2 + 4/3.
2*(o - 1)**2*(o + 2)/3
Factor 10/3 + 2/3*u**2 - 4*u.
2*(u - 5)*(u - 1)/3
Let j(t) be the second derivative of t**4/3 + 8*t**3/3 + 44*t. Factor j(h).
4*h*(h + 4)
Suppose -4*g = -5*h - 18, -3*h + 3 - 1 = 4*g. Let u(a) be the second derivative of -2/3*a**3 + g*a - 9/20*a**5 + 0 - a**4 + 0*a**2. Factor u(r).
-r*(3*r + 2)**2
Solve 11/2*c - 7/2*c**5 + 8*c**4 - 2*c**3 - 7*c**2 - 1 = 0 for c.
-1, 2/7, 1
Let f(x) be the first derivative of -2/3*x**3 + 2*x + 0*x**2 - 5. Find k, given that f(k) = 0.
-1, 1
Let o = 2551/30 - 85. Let m(w) be the second derivative of 0 + 0*w**2 + 1/18*w**4 + w - o*w**5 + 2/9*w**3. Suppose m(r) = 0. What is r?
-1, 0, 2
Let s(w) = w - 4. Let a be s(7). Solve -7*q**2 + 2*q**3 + 17*q + a*q**2 - 15*q = 0 for q.
0, 1
Factor 16*v**2 + 1024/3 - 2/3*v**3 - 128*v.
-2*(v - 8)**3/3
Let l(s) = -s**3 + 9*s**2 - 8*s + 6. Let j be l(8). Suppose 0 = -2*p + 4*f + 22, 3*p + f = -p + 8. Factor 3*k + k + 16*k**p - j*k**3 - 14*k**2.
2*k*(k - 1)*(5*k - 2)
Let s(z) be the first derivative of z**4 + 4*z**3/3 - 3. What is w in s(w) = 0?
-1, 0
Let a = -4 - -4. Suppose 5*u - 10 = -a*u. Find f such that 2 + 1 - u*f + f**4 - 4 + 2*f**3 = 0.
-1, 1
Let u(b) = b + 1. Let r be u(3). Let y(v) be the first derivative of -2*v**3 + v**2 + 3/2*v**r - 1 - 2/5*v**5 + 0*v. Factor y(c).
-2*c*(c - 1)**3
Factor 2*y - 6*y**5 - 30*y**3 - 22*y**4 + 5 + 2*y**3 - 12*y**2 - 3.
-2*(y + 1)**4*(3*y - 1)
Let u be 6/(-12) - 2/(-1). Factor 0 + u*f**3 - 3/2*f**4 + 3/2*f**2 - 3/2*f.
-3*f*(f - 1)**2*(f + 1)/2
Let v(z) be the first derivative of 1/5*z**3 + 2 - 3/20*z**4 + 0*z**2 + 0*z. Find i such that v(i) = 0.
0, 1
Suppose 4 = -w - 0. Let a(p) = -p**4 - 2*p**2 - 4*p + 7. Let z(c) = 6*c**4 + 9*c**2 + 21*c - 36. Let m(l) = w*z(l) - 21*a(l). Determine s so that m(s) = 0.
-1, 1
Let n(g) be the third derivative of g**8/336 - g**6/120 - 3*g**2. Let n(w) = 0. Calculate w.
-1, 0, 1
Factor -9*z**4 - 14*z**4 - 8*z + 30*z**3 + 68*z**2 + 5*z**5 - 72*z**2.
z*(z - 2)**2*(z - 1)*(5*z + 2)
Let h be (-12)/(-30) + 16/10. Let 4 - h*s**2 - 6*s - 3 + 2 + 5*s**2 = 0. What is s?
1
Let -20*p**2 + 10*p**2 + 10*p**2 - 4*p**3 + 4*p**4 = 0. What is p?
0, 1
Suppose 5*a + 3 = 13. Let z(n) be the second derivative of 0*n**6 + 0*n**4 + 0 + 1/63*n**7 + n + 0*n**a - 1/30*n**5 + 0*n**3. Let z(o) = 0. What is o?
-1, 0, 1
Let u(f) be the first derivative of -f**3/8 - 9*f**2/16 + 3*f/2 + 26. Solve u(y) = 0.
-4, 1
Let p(x) = x**3 - 5*x**2 + 7*x - 4. Let s be p(4). Let g be (s/(-10))/(4/(-10)). Factor -j**2 - 4*j + 3 - 5 - j**g.
-2*(j + 1)**2
Let z(u) be the second derivative of -u**7/3 - 26*u**6/15 - 27*u**5/10 - 2*u**4/3 + 4*u**3/3 - 15*u. Solve z(a) = 0.
-2, -1, 0, 2/7
Let a(d) = d**3 + 7*d**2 + 4*d - 8. Let f be a(-6). Suppose -5*h**3 + h**3 + f*h - 2*h**4 + 1 + 1 + 0*h**3 = 0. What is h?
-1, 1
Let z(t) be the third derivative of t**8/2520 - t**7/1260 - t**6/540 + t**5/180 + t**3/6 - 2*t**2. Let i(u) be the first derivative of z(u). Factor i(b).
2*b*(b - 1)**2*(b + 1)/3
Let y(u) be the third derivative of u**9/60480 - u**8/26880 + u**4/8 + 3*u**2. Let c(q) be the second derivative of y(q). Factor c(r).
r**3*(r - 1)/4
Suppose 0 = 4*n - 3*n - 6. Let u be (n/16)/(13/156). Determine b so that -u*b**3 - 3*b**4 - 3*b**2 - 3/4*b - 3/4*b**5 + 0 = 0.
-1, 0
Let t(s) be the first derivative of 4*s**5/15 - s**4/12 - 4*s**3/9 + s**2/6 - 16. Solve t(l) = 0.
-1, 0, 1/4, 1
Let k = -1448 + 75293/52. Let o = 95/156 - k. Factor -2/3*z + 4/3 - o*z**2.
-2*(z - 1)*(z + 2)/3
Let r(i) be the second derivative of i**4/12 + i**3/6 - 26*i. Determine o, given that r(o) = 0.
-1, 0
Let n(t) = 3*t**2 - 7*t. Let s(o) be the third derivative of -1/60*o**5 + 1/12*o**4 + 0*o**3 + 0*o + 0 + o**2. Let g(w) = -4*n(w) - 14*s(w). Factor g(k).
2*k**2
Factor 0 - 6/7*l + 33/7*l**2 - 27/7*l**3.
-3*l*(l - 1)*(9*l - 2)/7
Determine b so that -3 - 3/2*b**2 - 9/2*b = 0.
-2, -1
Find n, given that -13*n**2 - 2*n**2 - 751 + 771 + 5*n**3 = 0.
-1, 2
Suppose 3*l = 5*l - 38. Let i = l + -17. Factor 0*d - 2/3*d**4 - 4/3*d**i + 0 - 2*d**3.
-2*d**2*(d + 1)*(d + 2)/3
Let j(l) = -3*l**2 - 3*l - 1. Let u(z) = 3*z**2 + 3*z. Let d(k) = -6*j(k) - 7*u(k). Determine w so that d(w) = 0.
-2, 1
Suppose 2*x = -8 + 8. What is k in 2/11*k**4 + 0*k + 2/11*k**5 + x*k**3 + 0 + 0*k**2 = 0?
-1, 0
Let h(n) be the first derivative of n**3/9 + 6. Factor h(z).
z**2/3
Let q(y) = y + 8. Let l be q(-4). Determine b, given that