- 1/12*s**4 - 4/15*s**3 - 2/5*s**2 + s + 0. Factor d(j).
-(j + 1)*(j + 2)**2/5
Suppose 0 = -3*g + 4*w + 4, 4*g - 2*w = -w + 14. Factor 2*n**2 - 8*n**2 - 4*n**4 - n + 6*n**g + 5*n.
2*n*(n - 1)**2*(n + 2)
Let f be 14/(-63) - 38/(-9). Let i(s) be the first derivative of 0*s + 0*s**2 + 1/16*s**f + 1 + 0*s**3. Let i(m) = 0. Calculate m.
0
Factor -h + 27 - 4*h**3 + 4*h**2 - 31 + 5*h**3.
(h - 1)*(h + 1)*(h + 4)
Factor -1/2 - 1/2*b**3 + 1/2*b + 1/2*b**2.
-(b - 1)**2*(b + 1)/2
Let b(w) = -w**3 + 5*w**2 - 2*w - 2. Let c be b(4). Find g such that -c*g**3 + 5*g**4 - 2*g**3 + g**2 + 3*g - g = 0.
-2/5, 0, 1
Let u(m) be the third derivative of -1/12*m**4 + 2/3*m**3 - 3*m**2 + 0*m + 0 - 1/30*m**5. Factor u(s).
-2*(s - 1)*(s + 2)
Let r(l) be the first derivative of 1/3*l - 1/15*l**5 - 5 + 1/3*l**2 - 1/6*l**4 + 0*l**3. Factor r(z).
-(z - 1)*(z + 1)**3/3
Let n(f) be the second derivative of -f**7/6300 + f**6/900 - f**5/300 - f**4/12 - 3*f. Let d(j) be the third derivative of n(j). Factor d(m).
-2*(m - 1)**2/5
Factor 0*l + 0*l**2 - 2/23*l**4 - 2/23*l**3 + 0.
-2*l**3*(l + 1)/23
Let v(j) be the first derivative of -j**4/18 + 2*j**3/27 + j**2/9 - 2*j/9 - 23. Suppose v(w) = 0. What is w?
-1, 1
Find s such that -4*s**2 + 0*s**2 - 8*s**4 + 5*s**2 + 7*s**4 = 0.
-1, 0, 1
Let g(j) = j**2 + j - 1. Let l(r) = 10*r**2 + 11*r - 8. Let v(o) = 36*g(o) - 4*l(o). Find q, given that v(q) = 0.
-1
Let z(m) be the first derivative of -9/5*m - 3/2*m**2 + 8 + 2/5*m**3. Factor z(i).
3*(i - 3)*(2*i + 1)/5
Factor -2*k + 3*k**3 + 3*k + k**4 + 4*k**2 - k**2.
k*(k + 1)**3
Let x(z) be the second derivative of -8*z - 3/5*z**3 - 1/20*z**4 + 0 - 27/10*z**2. Factor x(v).
-3*(v + 3)**2/5
Suppose -9*x + 8*x = 0. Let p(t) be the second derivative of 1/6*t**3 + t - 1/4*t**2 - 1/24*t**4 + x. Factor p(d).
-(d - 1)**2/2
Let d(v) be the third derivative of v**7/1260 + v**6/180 + v**5/60 - v**4/24 + v**2. Let n(j) be the second derivative of d(j). Solve n(r) = 0.
-1
Let t(i) be the second derivative of 2/21*i**3 + 0 - 1/42*i**4 - 1/7*i**2 + 2*i. Find h, given that t(h) = 0.
1
Find v, given that -35/4*v - 5 + 5/2*v**2 = 0.
-1/2, 4
Suppose -2957*h**2 - 3 - 2*h + 14*h**3 + 2973*h**2 + 3*h**4 + 4*h = 0. Calculate h.
-3, -1, 1/3
Let l(t) = -t**3 - t**2 + t + 1. Let u(n) = -2*n**3 + 7*n**2 + 14*n + 5. Let c(i) = 5*l(i) - u(i). Factor c(f).
-3*f*(f + 1)*(f + 3)
Suppose 0 = 4*j - 17 + 1. Let u(q) be the second derivative of q + 0 + 1/4*q**j + 1/2*q**2 + 1/2*q**3 + 1/20*q**5. Solve u(x) = 0 for x.
-1
Suppose 0*k = -2*k - 6. Let c be (3 - k)*1/21. Solve 4/7*v + 2/7 + c*v**2 = 0.
-1
Let y(v) be the third derivative of -v**7/525 + v**5/50 - v**4/30 - 2*v**2. Find q, given that y(q) = 0.
-2, 0, 1
Suppose -3*a - 8 = 34. Let n(y) = -y**2 + y - 3. Let l(t) = 4*t**2 - 4*t + 14. Let g(d) = a*n(d) - 3*l(d). Let g(z) = 0. Calculate z.
0, 1
Let o(l) be the third derivative of l**8/30240 - l**5/15 + 5*l**2. Let c(z) be the third derivative of o(z). Factor c(y).
2*y**2/3
Let c = 404 + -401. Suppose 1/6*a**c - 1/2*a**2 - 1/6 + 1/2*a = 0. What is a?
1
Let l(x) be the second derivative of x**6/1440 - x**4/96 - x**3/6 - x. Let i(t) be the second derivative of l(t). Factor i(w).
(w - 1)*(w + 1)/4
Let x(k) be the third derivative of -3*k**2 + 0 + 1/120*k**5 + 1/24*k**4 + 0*k + 0*k**3. Factor x(g).
g*(g + 2)/2
Let m(q) = q**2 + 5*q - 5. Let k be m(-5). Let y(r) = r**4 + 7*r**2 - 2. Let p(a) = a**4 + 13*a**2 - 4. Let s(c) = k*y(c) + 3*p(c). Let s(d) = 0. Calculate d.
-1, 1
Suppose -2*g + 1 + 5 = 0. Suppose 0 = -2*n - 1 + 7. Suppose o**4 + o**3 + 1 + 4*o + g*o**n + 5*o**2 + o**2 = 0. Calculate o.
-1
Let k(w) be the second derivative of -1/30*w**4 + 0*w**2 + 0*w**3 + 1/100*w**5 + 0 - 6*w. Factor k(u).
u**2*(u - 2)/5
Suppose -2 = g, -4*a - g = -3*g - 4. Factor 2/5 - 2/5*o**2 + a*o.
-2*(o - 1)*(o + 1)/5
Let v(x) be the third derivative of x**7/1995 + x**6/1140 - x**5/190 - x**4/228 + 2*x**3/57 - 5*x**2. Let v(a) = 0. What is a?
-2, -1, 1
Let p be 78/(-24) + 5 + (-6)/4. Let v(o) be the first derivative of 1/10*o**5 - p*o**2 + 4 + 1/12*o**4 - 1/9*o**3 + 1/36*o**6 - 1/6*o. Factor v(j).
(j - 1)*(j + 1)**4/6
Let q(c) be the second derivative of c**7/98 - c**6/70 - 3*c**5/70 - 17*c. Factor q(i).
3*i**3*(i - 2)*(i + 1)/7
Let x be 2/5 + (-4)/35. Let l be 2/(-8) - 1/(-4). Determine b so that 4/7*b + x*b**4 + 0*b**3 - 6/7*b**2 + l = 0.
-2, 0, 1
Let x(n) be the second derivative of n**5/100 - n**4/30 - n**3/30 + n**2/5 - 4*n. Factor x(t).
(t - 2)*(t - 1)*(t + 1)/5
Let h(t) be the second derivative of t**10/7560 + t**9/1260 + t**8/560 + t**7/630 - 11*t**4/12 + 8*t. Let v(w) be the third derivative of h(w). Factor v(j).
4*j**2*(j + 1)**3
Let w(c) = 4*c**2 + c + 2*c - c**2 + 2*c**3. Let i(v) = -5*v**3 - 7*v**2 - 7*v. Let m(p) = -6*i(p) - 14*w(p). Let m(k) = 0. What is k?
0
Let o(c) be the first derivative of 4*c**3/3 - 6*c**2 + 8*c + 7. Factor o(z).
4*(z - 2)*(z - 1)
Let w be 4/15 - 22/(-165). Suppose 0 - 2/5*t**5 + 2/5*t**2 - w*t**4 + 0*t + 2/5*t**3 = 0. What is t?
-1, 0, 1
Let j = -364/5 - -74. Find k, given that 9/5 + 1/5*k**2 + j*k = 0.
-3
Let k = -259 - -262. Factor 4/3*v**k - 2/3*v**2 - 2/3 - 5/3*v + 1/3*v**5 + 4/3*v**4.
(v - 1)*(v + 1)**3*(v + 2)/3
Let k(g) be the first derivative of -1 + 2/7*g**2 + 2/5*g**5 + 2/7*g**3 - 6/7*g**4 + 0*g. Factor k(j).
2*j*(j - 1)**2*(7*j + 2)/7
Let z(i) be the first derivative of i**5/10 + i**4/3 - i + 5. Let j(d) be the first derivative of z(d). Solve j(o) = 0.
-2, 0
Let o(i) be the first derivative of -i**4/22 + 10*i**3/33 - 3*i**2/11 - 18*i/11 + 15. Factor o(t).
-2*(t - 3)**2*(t + 1)/11
Let x(t) be the second derivative of 0*t**2 - 1/25*t**6 + 1/10*t**4 + 0 + 1/15*t**3 - 4*t - 1/50*t**5. Let x(j) = 0. Calculate j.
-1, -1/3, 0, 1
Find k such that 0 + 1/5*k**3 + 0*k**2 - 1/5*k = 0.
-1, 0, 1
Let z be 10/(4 - -1) - 0. Let p(o) be the third derivative of 1/240*o**5 + 0*o**4 + 0*o + 1/480*o**6 + 0 + 3*o**z + 0*o**3. Let p(h) = 0. Calculate h.
-1, 0
Factor -10/3*w**2 - 8/3*w**5 + 2/3 + 2/3*w + 16/3*w**4 - 2/3*w**3.
-2*(w - 1)**3*(2*w + 1)**2/3
Let v(k) = k**2 + 8*k - 9. Let b(h) = 4*h - 4. Let w(g) = 9*b(g) - 4*v(g). Suppose w(n) = 0. Calculate n.
0, 1
Let a(h) = -7*h**4 + 8*h**3 + 3*h**2 - 5*h + 7. Let k(q) = 8*q**4 - 8*q**3 - 4*q**2 + 4*q - 8. Let p(t) = 4*a(t) + 3*k(t). Factor p(g).
-4*(g - 1)**3*(g + 1)
Let j(w) be the third derivative of -w**5/330 - w**4/66 + 4*w**2. Determine v, given that j(v) = 0.
-2, 0
Factor -1/6*g**4 + 0*g**2 + 0 + 0*g**3 + 1/6*g**5 + 0*g.
g**4*(g - 1)/6
Let c be (-15)/(-2) + 2/(-4). Determine i so that -3*i + c*i**3 + 5*i + 8*i**2 + i**2 = 0.
-1, -2/7, 0
Let p be 40/18 + -3 - -1. Factor -2/9*y**2 - p*y + 2/9*y**3 + 2/9.
2*(y - 1)**2*(y + 1)/9
Let j(l) be the first derivative of l**4/36 - l**3/18 - l + 2. Let r(h) be the first derivative of j(h). Suppose r(m) = 0. Calculate m.
0, 1
Let g = -27 + 27. Let p(a) be the second derivative of g*a**2 + 0*a**5 + 1/24*a**3 - a - 1/24*a**4 + 1/60*a**6 + 0 - 1/168*a**7. Factor p(t).
-t*(t - 1)**3*(t + 1)/4
Suppose 5*g - g - 40 = 0. Let r = 13 - g. Let -2/5*w**2 + 14/5*w**r - 6*w**4 + 0 + 18/5*w**5 + 0*w = 0. What is w?
0, 1/3, 1
Let q(n) = n**4 + n**2. Let w(b) = -2*b**4 + 2*b**3 - 4*b**2 - 2*b. Let i(p) = -3*q(p) - w(p). Solve i(j) = 0 for j.
-2, -1, 0, 1
Suppose -6 = -4*j + j. Solve 5 - 181*a**3 + 167*a**j + 129*a**4 - 48*a**2 - 12*a**5 - 23*a**5 - 36*a - 1 = 0.
2/7, 2/5, 1
Let t = -39/8 - -387/40. Factor 0*o - 5*o**5 + 4/5*o**2 - t*o**3 + 9*o**4 + 0.
-o**2*(o - 1)*(5*o - 2)**2/5
Let t(s) be the second derivative of 0*s**2 - 2/21*s**7 - 2/15*s**6 + 1/5*s**5 - 5*s + 1/3*s**4 + 0 + 0*s**3. Solve t(a) = 0.
-1, 0, 1
Let -20 - 4*s**3 + 4*s + 72 - 18 - 22 - 12*s**2 = 0. What is s?
-3, -1, 1
Factor 1/4*q**2 + 9/4 + 3/2*q.
(q + 3)**2/4
Factor -1/3*u**5 - 5/3*u**4 - 1/3 - 10/3*u**3 - 10/3*u**2 - 5/3*u.
-(u + 1)**5/3
Let r(x) be the first derivative of x**5/5 - x**4/2 - 13*x**3/3 - 5*x**2 - 21. Find b such that r(b) = 0.
-2, -1, 0, 5
Let v(m) be the first derivative of -5*m**6/24 - 2*m**5/5 + m**4/4 + 13. Suppose v(i) = 0. Calculate i.
-2, 0, 2/5
Let l = -3/8 + 13/24. Let a(x) be the second derivative of 0 + 3*x - 1/12*x**4 + l*x**3 + x**2. Suppose a(q) = 0. Calculate q.
-1, 2
Let a(n) be the third derivative of n**6/480 - n**5/80 + n**3/6 - 2*n**2 + 9*n. 