j(y) be the third derivative of -y**8/168 + y**7/35 - y**6/20 + y**5/30 + 3*y**2. Suppose j(u) = 0. Calculate u.
0, 1
Let i(v) be the third derivative of -v**5/90 - v**4/18 - v**3/9 - v**2. Let i(h) = 0. What is h?
-1
Let z = 3 + -3. Suppose z*j - 4 = -j. Solve -k**2 + k**4 - 3*k**3 - 6*k**4 - k**5 + 2*k**j = 0 for k.
-1, 0
Let z(j) = 80*j**4 - 100*j**2 + 90*j. Let t(s) = -9*s**4 + 11*s**2 - 10*s. Let d(l) = -35*t(l) - 4*z(l). Determine i so that d(i) = 0.
-2, 0, 1
Factor -1/6 + 5/2*c**2 + 7/3*c.
(c + 1)*(15*c - 1)/6
Suppose 0 + 4/5*n**3 + 11/5*n**2 - 3/5*n = 0. What is n?
-3, 0, 1/4
Let w(l) be the third derivative of -1/33*l**3 - 1/132*l**4 + 1/330*l**5 + 0*l + 1/660*l**6 + 0 - 3*l**2. Solve w(z) = 0.
-1, 1
Suppose -5*y + 1240 = 5*d, 2*y - 3*d = 6*y - 994. Let c be 1960/y*(-10)/(-4). Let 0 + 0*z**4 + 0*z**2 - c*z**5 + 106/5*z**3 - 8/5*z = 0. Calculate z.
-1, -2/7, 0, 2/7, 1
Suppose 2/7*a**2 + 1/7*a**5 + 12/7*a + 0*a**4 - a**3 - 8/7 = 0. What is a?
-2, 1, 2
Let 1/5*g**2 - 1/5*g**4 + 0 + 1/5*g - 1/5*g**3 = 0. What is g?
-1, 0, 1
Let b = 11 + -31/3. Let q(h) be the second derivative of -3/2*h**4 - 2*h - 7/10*h**5 - b*h**3 + 0 + 0*h**2. Factor q(l).
-2*l*(l + 1)*(7*l + 2)
Factor 4*p**3 + 2 - 2*p**5 - 4*p**4 + 5*p**4 + 0*p**2 - 4*p**2 + p**4 - 2*p.
-2*(p - 1)**3*(p + 1)**2
Suppose -12*d**3 - 11*d + 2 + 14*d**2 + 5*d**3 + 2*d**2 = 0. Calculate d.
2/7, 1
Let j(f) be the first derivative of f**5 - 5*f**4/2 - 20*f**3/3 + 5*f**2 + 15*f - 7. Solve j(i) = 0.
-1, 1, 3
Let v(o) be the first derivative of o**3/6 - o**2/4 + 4. Find g such that v(g) = 0.
0, 1
Let u(d) be the first derivative of -d**6/33 + 2*d**5/55 - 6. Determine s so that u(s) = 0.
0, 1
Determine o, given that 5/6*o - 1/6*o**3 + 1/6*o**4 - 1/3 - 1/2*o**2 = 0.
-2, 1
Let c(s) = -s - 5. Let j be c(-8). Factor 3*l + l**j - 4*l**3 + 2 + 2*l**3.
-(l - 2)*(l + 1)**2
Determine v, given that -2*v**3 - 26*v**2 + 126 + 70*v + 4*v**3 - 28 = 0.
-1, 7
Factor -167 + 14*m**3 + 167 + 5*m**2 - 10*m - 9*m**3.
5*m*(m - 1)*(m + 2)
Let u be (12/(-7))/((-26)/91). Let i(q) be the third derivative of 1/360*q**u + 0 + 1/45*q**5 + 3*q**2 + 0*q + 0*q**3 + 1/18*q**4. Factor i(n).
n*(n + 2)**2/3
Find t, given that 4/5*t**3 + 2/5*t + 1/5*t**4 + 0 + t**2 = 0.
-2, -1, 0
Let r = 11 + -15. Let j = r - -7. Factor k**3 - j*k**2 + k + k - 1 + k.
(k - 1)**3
Let v(y) = -3*y - 1. Let a be v(-7). Factor -2*z**2 - a*z**3 - 2*z**2 - 8*z**4 + 2*z + 6*z**3.
-2*z*(z + 1)**2*(4*z - 1)
Factor 147 + 21*z + 3/4*z**2.
3*(z + 14)**2/4
Let u(v) be the first derivative of -1/5*v**2 + 1/10*v**4 + 1/15*v**3 + 0*v - 1/25*v**5 - 6. Solve u(q) = 0.
-1, 0, 1, 2
Let d = 3973/4641 + -50/119. Let x = 3/13 + d. Factor x - 2/3*u**2 - 2/3*u**3 + 2/3*u.
-2*(u - 1)*(u + 1)**2/3
Let o(m) be the second derivative of m**9/6048 + m**8/1120 + m**7/560 + m**6/720 - m**3/2 + m. Let f(s) be the second derivative of o(s). Factor f(j).
j**2*(j + 1)**3/2
Let a(s) = -152*s**2 + 64*s - 17. Let n(k) = -101*k**2 + 43*k - 11. Suppose 4*f = 3*f - 5. Let v(w) = f*a(w) + 8*n(w). Factor v(o).
-3*(4*o - 1)**2
Let n = 28 - 55/2. Factor 0*h + n*h**2 + 0 + 1/2*h**4 + h**3.
h**2*(h + 1)**2/2
Let z(l) be the second derivative of 1/6*l**4 - 1/3*l**3 - 3*l + 0 - 2*l**2. Factor z(j).
2*(j - 2)*(j + 1)
Let c(u) be the third derivative of -2*u**7/105 - 2*u**6/15 + 6*u**5/5 - 10*u**4/3 + 14*u**3/3 - 28*u**2. Solve c(f) = 0.
-7, 1
Let p(b) = -b**5 - 7*b**4 - 11*b**3 - 5*b**2 - 4*b. Let q(s) = s**4 + s**3 - s**2 + s. Let k(o) = -5*p(o) - 10*q(o). Factor k(r).
5*r*(r + 1)**3*(r + 2)
Let a be 3*(-1 - 10/(-6)). Factor 5*z**2 + 3*z**3 - 3*z**2 - a*z**3 + z.
z*(z + 1)**2
Let f = -166 - -333/2. Factor 3/2 - f*v**2 + v.
-(v - 3)*(v + 1)/2
Let m(x) = x**3 - 2*x**2 + 5*x + 5. Let s(i) = 5*i + i**2 + 2*i**3 - 3*i**2 + i + 6. Let g(o) = -4*m(o) + 3*s(o). Let g(f) = 0. What is f?
-1, 1
Let h(j) = j**3 + 25*j**2 + j + 30. Let n be h(-25). Let u(z) be the first derivative of -2 - 9/2*z**2 + n*z**3 - 6*z. Let u(f) = 0. Calculate f.
-2/5, 1
Let y(g) = g**2 + 6*g + 1. Let f be y(-7). Let h = f + -6. Solve -3 + 3 - h*d**2 + 2 = 0.
-1, 1
Find u, given that -3*u**5 + u**5 - 13*u**4 - 4*u**3 + 19*u**4 = 0.
0, 1, 2
Let i(j) be the third derivative of -3/40*j**6 + 1/24*j**4 + 0*j - 4*j**2 + 0*j**3 - 1/84*j**8 + 0 - 1/60*j**5 - 11/210*j**7. Determine o, given that i(o) = 0.
-1, 0, 1/4
Let j(k) = 5*k**2 + 2*k. Let o = 11 - 14. Let q(w) = 4*w**2 + 2*w. Let t(d) = o*j(d) + 4*q(d). Factor t(z).
z*(z + 2)
Suppose 5*w + 5*f - 5 = 0, 2*w = -3*f + 2*f + 1. Let n be (-2 + 0)*(-7)/(-105)*-3. Factor w + 2/5*t**2 - n*t.
2*t*(t - 1)/5
Let t be ((-4)/2)/(-2) - -2. Let 4*q**2 - t*q**4 + 0*q**2 - 24*q**3 + 49*q**5 + 12*q**4 + 12*q**4 = 0. Calculate q.
-1, 0, 2/7
Let n(m) be the third derivative of m**8/13440 + m**7/2520 - m**6/1440 - m**5/120 - m**4/12 - 4*m**2. Let c(b) be the second derivative of n(b). Factor c(g).
(g - 1)*(g + 1)*(g + 2)/2
Let c(s) be the second derivative of s**6/6 + 3*s**5/4 + 5*s**4/4 + 5*s**3/6 + 4*s. Factor c(t).
5*t*(t + 1)**3
Let i(q) = -q**4 - 5*q**3 - 2*q**2 + 5*q - 3. Let u(s) = -s**3 - s**2 + s - 1. Let x(t) = i(t) - 3*u(t). Factor x(r).
-r*(r - 1)*(r + 1)*(r + 2)
Let o be ((2/1)/(-2))/(0 - 20). Let a(u) be the second derivative of 1/12*u**4 - 1/2*u**2 + o*u**5 - 1/6*u**3 + 0 - u. Suppose a(p) = 0. What is p?
-1, 1
Let v = 12468 - 61944/5. Factor 314/5*z**3 + 162/5*z**5 + 0 + 8/5*z + 88/5*z**2 + v*z**4.
2*z*(z + 1)**2*(9*z + 2)**2/5
Let t(r) be the first derivative of r**2 + 5 + r + 1/3*r**3. Solve t(z) = 0.
-1
Let r(n) be the third derivative of n**9/60480 - n**7/5040 - n**5/60 - 4*n**2. Let c(t) be the third derivative of r(t). What is m in c(m) = 0?
-1, 0, 1
Let z = -3/59 - -257/413. Suppose 0 = 5*y - 0*y. Suppose -2/7*b**2 + z*b + y = 0. Calculate b.
0, 2
Let c(g) = -g**3 + 7*g**2 + 5. Let a be c(7). Let t = a + -5. Suppose -1/2*d**3 + 1/2*d**2 + t - 1/2*d**4 + 1/2*d**5 + 0*d = 0. What is d?
-1, 0, 1
Let s(b) = b**3 - 3*b**2 + 2*b + 2. Let i be s(2). Solve -12*z**2 + i - 6*z**5 - 4*z**3 - 5 + 10*z + 1 + 14*z**4 = 0 for z.
-1, 1/3, 1
Let r(c) be the third derivative of c**6/1980 + c**5/330 + c**3/2 + c**2. Let n(m) be the first derivative of r(m). Factor n(q).
2*q*(q + 2)/11
Let t be (-486)/3240 + 1/(10/4). Determine r, given that 0 - 1/4*r - t*r**2 = 0.
-1, 0
Factor -u - 4/5 - 1/5*u**2.
-(u + 1)*(u + 4)/5
Factor 0 + 25/2*b**3 + 0*b - 10*b**2 - 5/2*b**4.
-5*b**2*(b - 4)*(b - 1)/2
Let v(k) = 11*k - 20 + 0 + 55*k**2 - 3. Let o(t) = 9*t**2 + 2*t - 4. Let s be -3 + -3*(2 - 1). Let p(m) = s*v(m) + 34*o(m). Factor p(r).
-2*(3*r - 1)*(4*r + 1)
Let -16*i + 3*i + 8*i**3 - 4*i**2 + 2*i**4 - 11*i + 18 = 0. Calculate i.
-3, 1
Suppose 3*c = 5*f + 12, -c - 2*f + 4*f = -4. Suppose 4*s + 0*r - 2*r = c, -4 = -5*s + 2*r. Factor 0 + s*j**2 + 1/2*j**3 + 0*j**4 - 1/4*j**5 - 1/4*j.
-j*(j - 1)**2*(j + 1)**2/4
Suppose 4*w = j - 3, 5*j + 3*w = 8*w - 15. Let f be -2 - j - (-2)/2. Determine o so that o - 4 + o**2 + f = 0.
-1, 0
Let q(v) be the third derivative of 0*v**3 - 1/84*v**4 + 0 + 0*v + 1/420*v**5 - 3*v**2. Find o such that q(o) = 0.
0, 2
Let m(n) = -n**3 - n**2 + n. Let k be ((0 - -2) + -2)/1. Let a be m(k). Solve -1 + 2 + 2*o**2 + a*o**2 - 3*o**2 = 0 for o.
-1, 1
Suppose 2*t + 4*b - 12 = 0, -4*t = 3*b - 6*b + 20. Let r be t/((24/10)/(-3)). Factor -7/2*z**3 + z**4 + 1/2 + 9/2*z**2 - r*z.
(z - 1)**3*(2*z - 1)/2
Let p be (-21)/180 - (-1)/5. Let n(v) be the first derivative of 0*v + 1/16*v**4 + 1 + p*v**3 - 1/4*v**2. Factor n(t).
t*(t - 1)*(t + 2)/4
Suppose z + 0 + 6 = 0. Let l be z/4*-2*1. Factor 0*n + 4/7*n**2 + 0 + 18/7*n**4 - 18/7*n**l.
2*n**2*(3*n - 2)*(3*n - 1)/7
Suppose u + 4*p = p + 16, 0 = u - 2*p + 4. Factor 2/3*j**3 - 2/3*j**u + 0 + 0*j + 0*j**2.
-2*j**3*(j - 1)/3
Let z(j) = j**3 - j**2 + j - 1. Let m(u) = 24*u**3 - 75*u**2 - 72*u + 3. Let p(g) = m(g) + 12*z(g). Let p(h) = 0. What is h?
-1/3, -1/4, 3
Suppose -8*m = 4*m + 2*m. Factor 2/7*y - 4/7*y**2 + 2/7*y**3 + m.
2*y*(y - 1)**2/7
Let g(p) be the second derivative of -p**5/180 + p**4/36 - p**3/27 - 5*p. Factor g(v).
-v*(v - 2)*(v - 1)/9
Suppose 9*x - 10*x = -4. Suppose 0*f = -x*f + 8. Determine j so that -1/2*j**f + 1/2 + 0*j = 0.
-1, 1
Let m(f) be the second derivative of 0 + 1/18*f**4 + 3*f - 1/45*f**6 - 1/30*f**5 + 1/9*f**3 + 0*f**2. Solve m(s) = 0.