 + u**3 - v*u**4 - 3/2*u + 1/2.
(u - 1)**4*(u + 1)/2
Factor 1/2*o**2 + 1/6*o**3 + 0 + 1/3*o.
o*(o + 1)*(o + 2)/6
Suppose 3*q - 1 = -h + 3, 2*h + 10 = 0. Let c(r) be the first derivative of -1 - 1/10*r**4 + 2/5*r + 7/15*r**q - 7/10*r**2. Determine l, given that c(l) = 0.
1/2, 1, 2
Let c(k) be the first derivative of -3*k**4/4 + 6*k**2 - 6. Suppose c(m) = 0. What is m?
-2, 0, 2
Let g(p) be the first derivative of p**5/20 - p**4/3 + 2*p**3/3 + 7*p - 8. Let d(o) be the first derivative of g(o). Find q such that d(q) = 0.
0, 2
Let y be -7*(1 + -2)/20. Let o(i) be the first derivative of -1/2*i - 9/16*i**4 - 1 + 9/8*i**2 + y*i**5 - 5/12*i**3. Factor o(n).
(n - 1)**2*(n + 1)*(7*n - 2)/4
Let u(z) be the second derivative of z**4/8 + z**3/2 + 3*z**2/4 + 4*z. Factor u(h).
3*(h + 1)**2/2
Let d(x) be the first derivative of 4/5*x**2 + 4 + 2/15*x**3 + 8/5*x. Factor d(b).
2*(b + 2)**2/5
Let s(g) = g**5 - g**3 - g**2. Let h(q) = -6*q**5 - q**4 + 2*q**3 + 2*q**2. Let r(j) = -5*h(j) - 10*s(j). Solve r(m) = 0.
-1/4, 0
Let a(n) = -3*n**4 - 12*n**3 - 12*n**2 + 3. Let s(b) = 5*b**4 + 23*b**3 + 24*b**2 - b - 7. Let l(f) = -11*a(f) - 6*s(f). Determine u, given that l(u) = 0.
-1, 1, 3
Let x(w) = -w - 1. Let t(l) = l**2 + l. Suppose -5*q = -4*q - 1. Let b(j) = q*t(j) + x(j). Factor b(i).
(i - 1)*(i + 1)
Let b(i) = -i**3 - 4*i**2 + 3*i - 7. Let x be b(-5). Let u be x*1/((-3)/(-2)). Factor 2/9*d**3 + 0 - 10/9*d**4 + 2/3*d**5 + 0*d + 2/9*d**u.
2*d**2*(d - 1)**2*(3*d + 1)/9
Solve -20/3*q**3 - 4/3*q**4 + 4/3*q**5 - 16/3 + 16/3*q + 20/3*q**2 = 0 for q.
-2, -1, 1, 2
Let p(b) = 0*b**2 - 4*b**2 - 1 + 9*b**2. Let c be p(-1). Factor 6*a**3 + 6*a**2 + 2*a**c + 2*a + 4*a**4 - 4*a**4.
2*a*(a + 1)**3
Let b(v) = -v**5 + v**4 - v**2 + v - 1. Let o(m) = 2*m**5 - 2*m**4 + 4*m**3 + 2*m**2 - 6*m + 6. Let n(u) = -6*b(u) - o(u). Factor n(x).
4*x**2*(x - 1)**2*(x + 1)
Solve -18/7*f**3 + 0*f - 32/7*f**5 + 48/7*f**4 + 2/7*f**2 + 0 = 0.
0, 1/4, 1
Let n be (1/18)/(21/112). Let s(u) be the first derivative of -7/9*u**2 + 2/9*u**4 - n*u**3 - 4/9*u + 2. Factor s(i).
2*(i - 2)*(2*i + 1)**2/9
Let r(n) be the third derivative of 1/105*n**7 - 3*n**2 - 2/3*n**3 + 1/30*n**5 + 1/4*n**4 - 1/20*n**6 + 0*n + 0. Factor r(m).
2*(m - 2)*(m - 1)**2*(m + 1)
Let u(m) be the third derivative of -2*m**7/945 + m**6/270 + 2*m**5/135 - m**2. Solve u(b) = 0.
-1, 0, 2
Let g(u) = 2*u + 5. Let i be g(0). Solve 22*f**5 + 8*f**4 - 3*f**3 - 16*f**5 + i*f**3 = 0.
-1, -1/3, 0
Factor -8/5 - 4/5*m**2 - 12/5*m.
-4*(m + 1)*(m + 2)/5
Suppose -5*m + 2 = -3*m. Suppose -3*t = 2 - 8. Let y(n) = -n**4 + n + 1. Let f(h) = 2*h**5 + 4*h**4 - 4*h**3 - 4*h**2. Let i(a) = m*f(a) + t*y(a). Factor i(q).
2*(q - 1)**2*(q + 1)**3
Factor 5*j**3 - 8*j**2 + j**3 + 6*j**3 + 2*j**5 + 49*j - 8*j**4 - 47*j.
2*j*(j - 1)**4
What is r in 4/5*r - 2/5 - 2/5*r**2 = 0?
1
Let d(r) = 2*r**2 - 6*r + 3. Let u(m) = -4*m**2 + 12*m - 5. Let i(w) = -5*d(w) - 3*u(w). Factor i(v).
2*v*(v - 3)
Let h(l) = -l**2 - 10*l - 1. Let b(t) = t**2 + 15*t + 2. Let f(o) = 5*b(o) + 8*h(o). Determine q, given that f(q) = 0.
-2, 1/3
Let m(r) = -65*r**3 + 330*r**2 - 1085*r + 750. Let d(j) = -11*j**3 + 55*j**2 - 181*j + 125. Let o(c) = 35*d(c) - 6*m(c). Factor o(p).
5*(p - 5)**2*(p - 1)
Factor -3/7*l**4 + 6/7*l - 3/7*l**5 + 15/7*l**2 + 9/7*l**3 + 0.
-3*l*(l - 2)*(l + 1)**3/7
Let s(d) be the third derivative of 1/3*d**3 + 0 - 1/24*d**4 + 0*d - 1/60*d**5 - d**2. Determine t so that s(t) = 0.
-2, 1
Let t be 12/(-30)*10/242. Let n = 248/363 + t. Factor n*a**2 + 0 + 2/3*a.
2*a*(a + 1)/3
Let t(v) be the second derivative of -1/40*v**5 + 1/40*v**6 + 0 - v - 1/8*v**2 - 1/24*v**4 - 1/168*v**7 + 1/8*v**3. Factor t(f).
-(f - 1)**4*(f + 1)/4
Let i(d) be the first derivative of -1/18*d**6 - 2/9*d**3 + 0*d + 0*d**4 + 2/15*d**5 + 1/6*d**2 - 3. Factor i(f).
-f*(f - 1)**3*(f + 1)/3
Let o = 47482 - 665367/14. Let z = o + 89/2. Find w, given that 2/7*w**4 + 6/7*w**2 + 0 - z*w - 6/7*w**3 = 0.
0, 1
Let r be -2*(5 + 1 - 7). Factor 3/2*c - r*c**2 + 1/2.
-(c - 1)*(4*c + 1)/2
Let r be 3*1/1 + 1. Suppose 4*p = g - 14, -r*g + 10 = -3*p - 7. Find h such that h + 21/2*h**3 + 11/2*h**g + 5/2*h**5 + 0 + 17/2*h**4 = 0.
-1, -2/5, 0
Let m(x) be the third derivative of 0*x - 1/840*x**8 + 1/60*x**5 - 3/200*x**6 + 1/150*x**7 + 7*x**2 - 1/120*x**4 + 0 + 0*x**3. Factor m(s).
-s*(s - 1)**3*(2*s - 1)/5
Suppose i + 1 = -2. Let q(k) = -k**2 - 3*k + 4. Let m be q(i). Find h such that -4/7*h + 0 - 10/7*h**3 + 2*h**5 - 18/7*h**2 + 18/7*h**m = 0.
-1, -2/7, 0, 1
Let t(y) be the second derivative of -8*y**2 - 2/15*y**6 + 2/5*y**5 + y**4 + 0 - 8/3*y**3 + 8*y. Factor t(q).
-4*(q - 2)**2*(q + 1)**2
Let p = -1 - 11. Let r be (-4)/p - 1/(-3). Factor 0 - 1/3*z**2 - r*z.
-z*(z + 2)/3
Let u(y) be the second derivative of 0 - 4*y - 1/27*y**4 + 0*y**2 + 1/27*y**3. Determine p so that u(p) = 0.
0, 1/2
Suppose -g = 5*r + 10, r = -4*r - 10. Suppose -w + 2*w**2 - w + g*w + 2*w**3 - 2 = 0. Calculate w.
-1, 1
Let v(j) be the second derivative of 5*j**7/42 + 5*j**6/6 + 7*j**5/4 - 5*j**4/12 - 20*j**3/3 - 10*j**2 + j. Let v(k) = 0. Calculate k.
-2, -1, 1
Factor 0 - 3*c**4 + 15/4*c**3 - 3/4*c**5 + 0*c + 0*c**2.
-3*c**3*(c - 1)*(c + 5)/4
Let d(l) be the third derivative of 1/60*l**4 + 0*l**3 + 0 + 0*l - l**2 + 1/150*l**5. Factor d(f).
2*f*(f + 1)/5
Let p(u) be the first derivative of 0*u**4 - 1/1080*u**6 + u**3 + 0*u**2 - 3 + 0*u + 1/360*u**5. Let h(d) be the third derivative of p(d). Solve h(c) = 0.
0, 1
Let z(k) be the third derivative of 0 - 1/84*k**4 + 1/210*k**5 + 0*k - 8*k**2 + 1/420*k**6 - 1/21*k**3. Factor z(s).
2*(s - 1)*(s + 1)**2/7
Let d be 45/105 + (-25)/(-7). Let 21*m**4 - 86*m**3 - 6 + 41*m**2 + d*m**2 + 29*m**3 - 3*m = 0. What is m?
-2/7, 1
Let m(f) be the second derivative of -f**6/9 + 2*f**5/5 - 2*f**4/9 + 14*f. Factor m(w).
-2*w**2*(w - 2)*(5*w - 2)/3
Let x(p) be the first derivative of -p**7/525 + p**6/300 - 3*p**2/2 + 1. Let l(n) be the second derivative of x(n). Factor l(w).
-2*w**3*(w - 1)/5
Let p(a) be the second derivative of -a**4/54 - 2*a**3/27 + a**2/3 - 27*a. Factor p(q).
-2*(q - 1)*(q + 3)/9
Suppose 0 = 2*u - 2 - 2. Factor 7*m**4 + 5*m**4 - 20*m**3 - 8*m + 4*m**5 - 12*m**u + 24*m**3.
4*m*(m - 1)*(m + 1)**2*(m + 2)
Let r = 629/742 + 1/106. Factor 2/7*l**2 + 8/7*l + r.
2*(l + 1)*(l + 3)/7
Let j(r) be the first derivative of r**6/12 - r**5/10 - 15. Factor j(d).
d**4*(d - 1)/2
Let w(u) be the second derivative of u**5/40 + 3*u**4/16 + u**3/2 + 9*u**2/2 - 2*u. Let o(d) be the first derivative of w(d). Factor o(p).
3*(p + 1)*(p + 2)/2
Let w(x) = -x - 1. Let g be w(-5). Let h = g + -1. Factor -2 + 0 - n**4 - 3*n**3 + 4*n**3 + 2*n + 3*n**2 - h*n.
-(n - 2)*(n - 1)*(n + 1)**2
Let r = -2 + 3. Let v = -1 + r. Factor v + 2/9*p**2 + 2/9*p.
2*p*(p + 1)/9
Let k be (72/(-81))/((2/(-6))/1). Find v, given that -10/3*v**2 - 2/3*v + 0 - k*v**3 = 0.
-1, -1/4, 0
Let c(m) be the first derivative of -m**7/126 + m**6/30 - m**5/20 + m**4/36 + 3*m + 1. Let w(p) be the first derivative of c(p). Factor w(u).
-u**2*(u - 1)**3/3
Suppose -2/5*y**3 - 1/5*y**4 - 4/5 + 3/5*y**2 + 4/5*y = 0. What is y?
-2, 1
Factor 4*o**3 - o**2 - 5*o**2 + 4*o**2 - 5*o**3.
-o**2*(o + 2)
Let w(p) be the first derivative of -p**5/10 + p**4/8 + p**3/3 + 2. Factor w(j).
-j**2*(j - 2)*(j + 1)/2
Let j(y) be the first derivative of -y**5/15 + y**4/2 - 13*y**3/9 + 2*y**2 - 4*y/3 - 25. Solve j(t) = 0.
1, 2
Let m(a) be the third derivative of a**6/420 - a**5/105 + 3*a**2. Let m(w) = 0. Calculate w.
0, 2
Suppose -z = -4*g + 10 - 2, -4*g + 32 = 5*z. Let 2 - 4*r**z + r**5 + 6*r**3 - 2 + r - 4*r**2 = 0. Calculate r.
0, 1
Let r = 240 - 238. Factor 0 - 2/9*h**r + 0*h.
-2*h**2/9
Let y(p) be the second derivative of p**5/20 - p**4/3 + 5*p**3/6 - p**2 - p. Suppose y(x) = 0. Calculate x.
1, 2
Let f = -1819/5 + 365. Factor -2/5*y + 0 - f*y**3 + 6/5*y**2 + 2/5*y**4.
2*y*(y - 1)**3/5
Suppose -3*d + 4*g = 0, g = -5*d + 5*g. Solve f**2 + 6*f - 5*f + d*f = 0 for f.
-1, 0
Suppose -o + 5 = -0. Suppose 5 - 21 = -2*r - 3*x, 5*r - o*x + 10 = 0. Suppose -2*s**4 - 4*s - 2*s**4 + 0*s**4 + 6*s**r + 2*s**4 = 0. What is s?
-2, 0, 1
Let k(v) = -6*v**5 + v**4 - 5*v - 5. Let t(r) = -r**5 - r - 1. Let w(o) = -k(o) + 5*t(o). Factor w(g).
g**4*(g - 1)
Let a(g) be the first derivative of -g**7/420 - g**6/90 - g**5/60 - 2