 1/4*a**3.
-a*(a - 1)*(a + 1)/4
Solve -17*s**2 - 7*s**2 - 17 + 10 - s**4 + 22*s + 10*s**3 = 0 for s.
1, 7
Let -y**4 - 21*y**3 - 4*y - 40*y**2 + 8*y**4 + 16*y**2 + 42*y**4 = 0. What is y?
-2/7, 0, 1
Let y(n) be the second derivative of -n**6/30 + 39*n**5/20 - 169*n**4/4 + 2197*n**3/6 - 57*n. Find a such that y(a) = 0.
0, 13
Let n(m) be the third derivative of m**5/75 + m**4/15 + 2*m**3/15 + 35*m**2. Factor n(r).
4*(r + 1)**2/5
Let w(q) be the third derivative of -q**8/2016 + q**7/252 - q**6/144 - q**5/72 + q**4/24 + 2*q**2 - 9*q. Suppose w(b) = 0. What is b?
-1, 0, 1, 2, 3
Let z be (-5)/((-20)/(-1)) + 9/4. Factor -1/6*v**z + 1/6 + 0*v.
-(v - 1)*(v + 1)/6
Suppose -2*j = 2, 14 = -3*v - j + 19. Determine l so that -5*l**3 + v - 21/2*l**2 + 0*l = 0.
-2, -1/2, 2/5
Let b be (-1)/6 - 1/(-4)*2. Solve 0*l + 3/2*l**2 - 2/3 - 1/2*l**4 + b*l**3 = 0 for l.
-1, 2/3, 2
Let q(c) be the third derivative of c**9/1134 + c**8/630 - c**7/420 - c**6/270 + c**5/180 + c**3 - c**2. Let m(o) be the first derivative of q(o). Factor m(h).
2*h*(h + 1)**2*(2*h - 1)**2/3
Let n(l) be the first derivative of l**8/112 + 3*l**7/70 - l**5/5 + l**2 - 3. Let t(u) be the second derivative of n(u). Suppose t(w) = 0. What is w?
-2, 0, 1
Suppose 0 = -3*l - 74 + 209. Let i = l + -32. Factor -67/3*t**3 - 19*t**2 - 3*t**5 - 4/3 - 8*t - i*t**4.
-(t + 1)**3*(3*t + 2)**2/3
Determine z so that 0 + 1/3*z**3 - 2/3*z**2 + 0*z = 0.
0, 2
Suppose -8*t = -11 - 5. What is x in -18/5*x - 4/5 - t*x**3 - 24/5*x**2 = 0?
-1, -2/5
Let r be 3*(-2 + 10/3). Let h = -3 + 6. Factor -3*q**3 - q**2 + r*q**h + 0*q**2.
q**2*(q - 1)
Let k be (-5)/(-1) + (63/9)/21. Let 2*c - 8*c**3 - 1/3 - k*c**4 - 1/3*c**2 = 0. Calculate c.
-1, 1/4
Suppose 0*h + 5*k - 10 = 5*h, -2*h - 2*k = -12. Let 0 - 3/2*d**h + 3/2*d = 0. What is d?
0, 1
Suppose 8 = -4*k, -k = -5*z + 1 + 16. Suppose -5*q**4 + 2*q - 2*q**2 + 7*q**2 - 6*q**z + 4*q**3 + 0*q**3 = 0. Calculate q.
-1, -2/5, 0, 1
Let u(w) be the first derivative of 19/3*w**3 - 2*w - 2 + 2*w**2 + 28/3*w**4 + 24/5*w**5. Let p(r) be the first derivative of u(r). Factor p(x).
2*(3*x + 2)*(4*x + 1)**2
Let d be ((-7)/294)/(2/(-8)). Let k(s) be the second derivative of -1/42*s**4 - d*s**3 - s + 0*s**2 + 1/105*s**6 + 0 + 1/35*s**5. Solve k(c) = 0 for c.
-2, -1, 0, 1
Let s(y) be the third derivative of y**6/30 + y**5/15 - 5*y**4/6 + 2*y**3 - 12*y**2. Determine j, given that s(j) = 0.
-3, 1
Let s(b) be the third derivative of 0*b + 1/24*b**4 - 4*b**2 - 1/30*b**5 + 0 + 1/6*b**3. Solve s(x) = 0 for x.
-1/2, 1
Let q be (1 + -1)*(-6)/(-6). Factor 0*h - 2/5*h**2 + 0*h**3 + 2/5*h**4 + q.
2*h**2*(h - 1)*(h + 1)/5
Factor 1/10*v**2 - 1/10*v - 1/10 + 1/10*v**3.
(v - 1)*(v + 1)**2/10
Let j(u) be the first derivative of -u**3/9 + u**2 - 3*u - 3. Determine o so that j(o) = 0.
3
Let s(p) be the first derivative of p**7/700 - p**6/180 + p**5/150 - p**3 - 1. Let v(c) be the third derivative of s(c). Factor v(k).
2*k*(k - 1)*(3*k - 2)/5
Let a(p) = -p**2 - 7*p - 6. Let i be a(-6). Find n, given that i*n + n + 1 + 2*n + n**3 + 3*n**2 + 0*n = 0.
-1
Factor 55*v**3 - 6 + 0*v**2 - 30*v**3 - 28*v**3 + 6*v**2 + 3*v.
-3*(v - 2)*(v - 1)*(v + 1)
Factor 2/3*k**2 - 4/3*k - 2.
2*(k - 3)*(k + 1)/3
Find f, given that 2/9*f + 2/9*f**4 + 0 - 2/9*f**2 - 2/9*f**3 = 0.
-1, 0, 1
Let x(j) = -9*j**4 - 25*j**3 + 12*j**2 - 4*j + 13. Let p(v) = -2*v**4 - 6*v**3 + 3*v**2 - v + 3. Let i(f) = -26*p(f) + 6*x(f). Factor i(z).
-2*z*(z - 1)**3
Let i = 97 - 290/3. Suppose -4*k = 2*r - 6, 4*r + 0*r = 2*k - 8. Factor i*j**3 - j**k - 1/3 + j.
(j - 1)**3/3
Let i(w) be the first derivative of -w**4/30 + 2*w**3/15 - w**2/5 + 6*w - 4. Let l(u) be the first derivative of i(u). Factor l(x).
-2*(x - 1)**2/5
Let s(v) = -2*v**3 - 5*v**2 - 15*v - 23. Let d be s(-2). Suppose -4/7 + 18/7*h - 10/7*h**d + 12/7*h**2 = 0. Calculate h.
-1, 1/5, 2
Factor 7/3*r - 1/3*r**2 - 2.
-(r - 6)*(r - 1)/3
Let r = 1 - -4. Suppose 0 = -r*y, l - y = -4*y + 2. Suppose 0*q + 0 + 2/5*q**l = 0. Calculate q.
0
Suppose -28 = 2*h + a - 5*a, 4*h = -2*a - 46. Let t = h - -12. Factor t*p + 5/4*p**3 + 0 + 1/2*p**2 + 3/4*p**4.
p**2*(p + 1)*(3*p + 2)/4
Suppose 6*x**2 + 14/3*x + 4/3 + 2/3*x**4 + 10/3*x**3 = 0. What is x?
-2, -1
Let d = -196 + 2941/15. Let a(h) be the third derivative of 0*h**4 + 0 - d*h**3 + 1/150*h**5 + 0*h - 3*h**2. Factor a(f).
2*(f - 1)*(f + 1)/5
Let t = -4238/261 - -148/9. Let a = t + 98/87. Solve -14/3*m**4 + 0 + 6*m**3 + 0*m - a*m**2 = 0 for m.
0, 2/7, 1
Let t be (2/36)/(7/7). Let k(g) be the third derivative of 0*g - 2*g**2 + 1/18*g**3 + 1/60*g**5 + 0 + t*g**4. Factor k(a).
(a + 1)*(3*a + 1)/3
Let c = 52 - 48. Factor 1/5*u**c + 0 - 1/5*u - 1/5*u**2 + 1/5*u**3.
u*(u - 1)*(u + 1)**2/5
Determine w so that -22*w**3 + 11*w**2 - 5*w + 5*w**2 + 18*w**3 + 8 - 15*w = 0.
1, 2
Let j(l) = -2*l + 8. Let v be j(4). Let b(o) be the first derivative of 1/6*o**4 + 1/9*o**6 + 0*o**2 + 0*o - 1 + v*o**3 + 4/15*o**5. Let b(q) = 0. Calculate q.
-1, 0
What is s in -1 - 1/5*s**2 - 6/5*s = 0?
-5, -1
Factor 8*j**4 + 0 + 9/2*j**2 - 12*j**3 - 1/2*j.
j*(j - 1)*(4*j - 1)**2/2
Let w(p) be the first derivative of -p**4/36 + 5*p**3/27 + 23. Factor w(u).
-u**2*(u - 5)/9
Factor 30 - 17*o - 6 - 3*o - 4*o**2.
-4*(o - 1)*(o + 6)
Let o(m) be the first derivative of -2*m**5/35 - 5*m**4/14 - 2*m**3/3 - 3*m**2/7 + 9. Solve o(p) = 0 for p.
-3, -1, 0
Let g(c) be the first derivative of 8 - 7*c**3 + 3/2*c**2 + 0*c. Let g(q) = 0. What is q?
0, 1/7
Let i(s) be the second derivative of 3*s**5/20 + s**4/2 - 2*s**3 - 12*s**2 - 18*s. Factor i(q).
3*(q - 2)*(q + 2)**2
Let h(d) be the first derivative of d**4 + 4*d**3 - 16*d - 13. Solve h(f) = 0 for f.
-2, 1
Let r = -428956/137057 - 4/5959. Let t = -274/161 - r. Factor 4/7*f - 2/7*f**4 + 0 + 8/7*f**3 - t*f**2.
-2*f*(f - 2)*(f - 1)**2/7
Let c(s) be the third derivative of -s**7/168 - s**6/96 - 21*s**2. Suppose c(g) = 0. Calculate g.
-1, 0
Let c = -3/12547 + 2597439/878290. Let t = c + 9/14. Factor -t*p**3 + 0 + 0*p + 4/5*p**2.
-2*p**2*(9*p - 2)/5
Let v(t) be the second derivative of t**8/126 - 4*t**7/315 + t**6/180 + 3*t**2 - 7*t. Let o(a) be the first derivative of v(a). Let o(r) = 0. What is r?
0, 1/2
Let c = -3 - -4. Factor 5 + c - 2 - 2*o - 2*o**2.
-2*(o - 1)*(o + 2)
Suppose n = 2*k + 5, 0 = -2*n - 3*n - 4*k - 31. Let b(i) = 9*i**2 - 9*i - 6. Let r(c) = 10*c**2 - 9*c - 5. Let x(l) = n*r(l) + 2*b(l). Factor x(p).
-3*(p - 1)*(4*p + 1)
Let j(l) be the first derivative of 0*l**2 - 2/9*l**3 - 2/15*l**5 + 2 + 0*l + 1/3*l**4. What is k in j(k) = 0?
0, 1
Let q = -1/87 + 181/609. Let n be (6/7)/(3/4). Factor n + 8/7*m + q*m**2.
2*(m + 2)**2/7
Let n(g) be the first derivative of -2/9*g**3 + 0*g - 2 - 1/15*g**2 - 2/15*g**4. Solve n(x) = 0.
-1, -1/4, 0
Let n(j) be the second derivative of -j**5/45 - j**4/27 + 2*j**3/27 + 2*j**2/9 - 12*j. Find m, given that n(m) = 0.
-1, 1
Factor r - 2*r**2 - 9*r**4 + 8*r**2 - 2*r**5 - 6*r**3 + 3 - r**5 + 8*r.
-3*(r - 1)*(r + 1)**4
Let u be (8/6)/(3 - (4 - 3)). Factor -u*w - 1/3 - 1/3*w**2.
-(w + 1)**2/3
Suppose 0 = 8*i - 23*i + 45. Let s(x) be the second derivative of 0 + 1/4*x**i - 9/8*x**2 - 1/48*x**4 + 2*x. Factor s(z).
-(z - 3)**2/4
Let x(z) = -z**2 - 10*z - 5. Let f = -18 - -9. Let g be x(f). Factor 4/3*j**2 + 0*j**3 - 2/3*j**g - 2/3 + 0*j.
-2*(j - 1)**2*(j + 1)**2/3
Let b(l) be the third derivative of 0*l**5 - 1/60*l**6 + 0*l - 1/105*l**7 + l**2 + 0*l**3 + 0 + 0*l**4. Factor b(t).
-2*t**3*(t + 1)
Let m be (-76)/84 + -2 + 3. Let z(a) be the second derivative of 0 + a - m*a**3 + 1/42*a**4 + 0*a**2. Determine q, given that z(q) = 0.
0, 2
Factor 72/5*h**2 + 3456/5 + 864/5*h + 2/5*h**3.
2*(h + 12)**3/5
Let r(k) be the first derivative of -k**4/28 - k**3/21 + k**2/14 + k/7 - 6. What is x in r(x) = 0?
-1, 1
Suppose -3*b = 2*b + 13*b. Factor 0*s**4 - 1/2*s**5 + 3/2*s**3 + b*s + 0 - s**2.
-s**2*(s - 1)**2*(s + 2)/2
Suppose 5*m - 13 = 7. Solve -1/4 + 0*h - 1/4*h**m + 0*h**3 + 1/2*h**2 = 0 for h.
-1, 1
Let r = 9 + -5. Suppose -5*u + 10 = r*d, -2*d - 6 = d - 3*u. What is b in -4/7*b + 8/7*b**3 + 6/7*b**4 - 2/7*b**2 + d = 0?
-1, 0, 2/3
Let p(v) be the first derivative of v**6/6 - v**5 + 2*v**4 - 4*v**3/3 + 17. Suppose p(s) = 0. What is s?
0, 1, 2
Let c(j) = -2*j - 46. Let i be c(-23). Find q, given that 1/3*q**3 + i*q + q**2 - 4/3 = 0.
-2, 1
Suppose 