= -j**4 - j**2 + j. Let t(o) be the second derivative of o**6/5 + o**4/6 - o**3/2 + 8*o. Let z(i) = 5*l(i) + t(i). Let z(k) = 0. What is k?
-2, 0, 1
Suppose 0 = h - 2 - 0. Let r(b) = -b + 8. Let i be r(6). Factor -m + 2 + 2*m**h + 0*m**i - 4*m**2 + m**3.
(m - 2)*(m - 1)*(m + 1)
Let c be ((-2)/(-3))/((-20)/(-12)). Let -4/5*t + c + 2/5*t**2 = 0. What is t?
1
Let q(r) be the third derivative of -r**8/40320 + r**7/10080 - r**5/12 - r**2. Let j(m) be the third derivative of q(m). Solve j(b) = 0.
0, 1
Let a(g) be the third derivative of g**6/1980 + g**5/660 - 2*g**3/3 + 4*g**2. Let i(c) be the first derivative of a(c). Let i(t) = 0. Calculate t.
-1, 0
Let n(o) be the second derivative of 1/15*o**5 + 0*o**3 + 0*o**2 + 0 + 1/30*o**6 - 1/9*o**4 + 5*o. Let n(u) = 0. What is u?
-2, 0, 2/3
Factor -18/17*i**3 + 0*i - 2/17*i**5 + 12/17*i**4 + 8/17*i**2 + 0.
-2*i**2*(i - 4)*(i - 1)**2/17
Suppose 313*r - 315*r = -6. Factor -2/3*n**r + 0*n + 2/3*n**4 + 0 + 0*n**2.
2*n**3*(n - 1)/3
Let s(a) be the third derivative of a**6/1800 + a**5/100 + 3*a**4/40 + 2*a**3/3 - 3*a**2. Let v(n) be the first derivative of s(n). Factor v(w).
(w + 3)**2/5
Let z be 30/70 + (-3)/7. Let d(s) be the third derivative of 0 + 0*s**4 + 0*s + 0*s**5 + s**2 + 1/120*s**6 + z*s**3. Factor d(j).
j**3
Let i(f) be the first derivative of -f**4/72 + f**2/12 - 3*f + 2. Let l(j) be the first derivative of i(j). Suppose l(d) = 0. What is d?
-1, 1
Let u(q) be the second derivative of -3*q**4/4 + 5*q**3 - 9*q**2/2 + 12*q. What is m in u(m) = 0?
1/3, 3
Let a(k) be the third derivative of -k**7/98 - k**6/140 + k**5/28 + k**4/28 + 19*k**2. Determine m so that a(m) = 0.
-1, -2/5, 0, 1
Let r be 91/234*(-1)/(-14). Let u(g) be the third derivative of 0*g + 0*g**6 - 1/45*g**5 + 0*g**3 - 2*g**2 + 1/504*g**8 + 0 + 2/315*g**7 - r*g**4. Factor u(n).
2*n*(n - 1)*(n + 1)**3/3
Let i be (-9)/15 - 58/(-30). Let w = 88/141 - -2/47. Factor 2/3 + i*k + w*k**2.
2*(k + 1)**2/3
Let j be 2 + -1 + 1/1. Factor -f**4 - 4*f - 2*f**j - 2*f**4 + 3*f**3 + f + 5*f**2.
-3*f*(f - 1)**2*(f + 1)
Let o(u) = u**2 - 6*u + 1. Let x be o(4). Let i(g) = -11*g**2 + 7*g + 23. Let a(d) = 6*d**2 - 4*d - 12. Let p(r) = x*a(r) - 4*i(r). Factor p(h).
2*(h - 2)*(h + 2)
Let -1/4*s**2 + 1/4*s + 0 = 0. What is s?
0, 1
Suppose 2*a + 10 = 4*a. Let x(d) be the first derivative of 1/12*d**3 + 0*d**2 + 1/16*d**4 - 1/24*d**6 - 1/20*d**a - 1 + 0*d. Find q, given that x(q) = 0.
-1, 0, 1
Let w(o) be the third derivative of 0*o + 5/336*o**8 + 1/30*o**5 + 0*o**3 + 1/120*o**6 + 0*o**4 - 4/105*o**7 + 0 - 2*o**2. Factor w(f).
f**2*(f - 1)**2*(5*f + 2)
Let h = -5 + 6. Let i = h - -3. Suppose 3*l + 3*l**3 - i*l**2 - l + 3*l**3 - 4*l**3 = 0. Calculate l.
0, 1
Determine k so that 1/5*k + 0 - 1/5*k**3 + 0*k**2 = 0.
-1, 0, 1
Let t(d) = 14*d**4 + 23*d**3 + 23*d**2. Let a(x) = 5*x**4 + 8*x**3 + 8*x**2. Let w = -12 + 1. Let y(p) = w*a(p) + 4*t(p). Factor y(v).
v**2*(v + 2)**2
Let s(a) be the second derivative of 0*a**3 - 1/120*a**5 + a**2 + 2*a + 0 + 0*a**4 - 1/240*a**6. Let v(p) be the first derivative of s(p). Factor v(z).
-z**2*(z + 1)/2
Suppose -12*x**2 - 16 + 2*x**3 - 32*x + 2*x**3 + 3*x**3 + 4*x**4 + x**3 = 0. What is x?
-2, -1, 2
Let t be ((13 - -5)/3)/(6/4). Factor 0 - 2/5*l**2 - 2/5*l**t - 4/5*l**3 + 0*l.
-2*l**2*(l + 1)**2/5
Let p be 29/90 + 18/(-81). Let y(z) be the second derivative of 0*z**3 + 2*z + 1/6*z**4 + 0*z**2 + p*z**5 + 0. Factor y(g).
2*g**2*(g + 1)
Let h = 4 + -6. Let v be ((-3)/h)/(9/24). Factor -3*u + 3*u**2 - 4*u**3 - 3*u**4 + 7*u**5 - 9*u**v + 11*u**2 - 2.
(u - 1)**3*(u + 1)*(7*u + 2)
Let a(v) be the third derivative of v**5/240 - v**4/48 + v**3/24 + 4*v**2. Factor a(m).
(m - 1)**2/4
Let c(n) be the third derivative of -1/270*n**5 + 0*n**4 - 1/270*n**6 + 0 + 0*n + 1/756*n**8 + 0*n**3 + 2*n**2 + 1/945*n**7. Find q such that c(q) = 0.
-1, -1/2, 0, 1
Let -14*a - 8 - 4*a**4 + 10*a - 4*a**5 + 18*a**2 + a**5 + 13*a**3 = 0. Calculate a.
-2, -1, 2/3, 2
Let v(l) be the second derivative of -l**5/60 + 2*l**3/9 + 28*l. Factor v(b).
-b*(b - 2)*(b + 2)/3
Let l(w) = 7*w**3 + 2*w**2 - 1. Let d be l(1). Suppose 4*q - d = 20. Factor -6*h + 6*h + q*h**4 - 3*h**2 + h**2 + 5*h**3.
h**2*(h + 1)*(7*h - 2)
Let w(j) be the first derivative of -j**6/360 + j**5/90 - j**4/72 - 2*j**2 - 4. Let z(f) be the second derivative of w(f). Determine p, given that z(p) = 0.
0, 1
Let g(l) be the first derivative of -10*l**3/9 + l**2 + 4*l/3 - 31. Factor g(n).
-2*(n - 1)*(5*n + 2)/3
Let z = -380103/511630 + 1/14618. Let d = 8/7 + z. Suppose d*k**3 - 2/5*k**5 - 2/5*k**2 + 0*k + 0 + 2/5*k**4 = 0. Calculate k.
-1, 0, 1
Let v(w) be the second derivative of w**7/630 - w**6/120 + w**5/60 - 2*w**4/3 - 3*w. Let y(h) be the third derivative of v(h). Factor y(a).
2*(a - 1)*(2*a - 1)
Let d be ((-64)/20 - -4)/(4/10). Let -3/2*z**3 + 0*z**d + 0 - z**4 + 1/2*z = 0. What is z?
-1, 0, 1/2
Let d = -770 + 770. Factor 0*z - 2/7*z**3 + 2/7*z**5 + 0*z**4 + d + 0*z**2.
2*z**3*(z - 1)*(z + 1)/7
Let p(b) be the third derivative of 2*b**2 + 0*b + 1/120*b**6 - 1/210*b**7 - 1/24*b**4 + 0 + 1/60*b**5 + 0*b**3. Determine v so that p(v) = 0.
-1, 0, 1
Let h be -3 - (-2 - (-183)/(-177)). Let f = h - -51/236. Factor 1/4*t + 1/4 - f*t**3 - 1/4*t**2.
-(t - 1)*(t + 1)**2/4
Let k = 19 - 15. Let v be k/(-16) + 27/12. Determine x, given that 2*x**v - 1/3 + 11/3*x**4 - 14/3*x**3 + 1/3*x - x**5 = 0.
-1/3, 1
Let j(b) be the first derivative of 12/5*b**5 + 25*b**2 + 1 + 76/3*b**3 + 25/2*b**4 + 12*b. Find k such that j(k) = 0.
-3/2, -1, -2/3
Let a(y) be the second derivative of y**5/90 - y**4/12 + 2*y**3/9 - 2*y**2 - 3*y. Let s(x) be the first derivative of a(x). Factor s(c).
2*(c - 2)*(c - 1)/3
Suppose 3*n = 2*o - 4, 2*o + o = n + 13. Factor -g + 0 - 1/2*g**n.
-g*(g + 2)/2
Let p be ((-160)/(-50))/((-4)/(-30)). Determine z so that 5*z**4 + p*z**2 - 16 + 132*z**2 + 5*z**4 + 242*z**3 - 84*z**5 - 8*z = 0.
-1, -2/3, -1/2, 2/7, 2
Factor -15*z**2 - 1/4 + 13/4*z - 16*z**4 + 28*z**3.
-(z - 1)*(4*z - 1)**3/4
Let z(j) be the second derivative of -j**7/700 - j**6/600 + j**5/100 + j**4/40 + j**3/3 - 5*j. Let i(d) be the second derivative of z(d). Solve i(x) = 0.
-1, -1/2, 1
Let q(g) be the first derivative of -g**7/147 + g**6/105 + g**5/70 - g**4/42 - 3*g - 2. Let j(v) be the first derivative of q(v). Factor j(f).
-2*f**2*(f - 1)**2*(f + 1)/7
Suppose -1/6*c**2 - 25/6 + 5/3*c = 0. What is c?
5
Let z(x) be the second derivative of 3*x + 0*x**2 - 2/3*x**4 + 0 + 1/5*x**5 + 2/3*x**3. Let z(m) = 0. Calculate m.
0, 1
Let g = 33 - 33. Let s(o) be the third derivative of 0 + 0*o + 0*o**3 - 1/180*o**5 + g*o**4 + o**2 + 1/360*o**6. Factor s(l).
l**2*(l - 1)/3
Let l(t) be the second derivative of t**7/231 + 2*t**6/165 + t**5/110 + 3*t. Determine f so that l(f) = 0.
-1, 0
Let z(n) = n - 8. Let w be z(11). Suppose l + w = 5. Factor -1/3*k**l + 4/3*k**3 + 0 + 0*k.
k**2*(4*k - 1)/3
Let h = -4 - -17/4. Factor -1/4*b**2 + 1/2 + h*b.
-(b - 2)*(b + 1)/4
Let y be (-13)/(-5) + (-24)/40. Let a(t) be the first derivative of t - 1 - 1/2*t**y + 1/12*t**3. Let a(s) = 0. Calculate s.
2
Let f(n) = -n**3 + 5*n**2 + n - 2. Let a be f(5). Suppose -4*y + 2*y**4 - 2*y**2 - 2*y + 2*y**3 + 2*y**a + 2*y = 0. What is y?
-2, -1, 0, 1
Suppose 2*y - 2 = -0*y. Let h be (0/(-7))/(y/1). Factor 2/3*o**3 + h*o**4 + 0 - 2/3*o**5 + 0*o**2 + 0*o.
-2*o**3*(o - 1)*(o + 1)/3
Let z(k) be the first derivative of -k**4/4 - 7*k**3/6 - k**2 + 2*k - 3. Let b(u) be the first derivative of z(u). Factor b(s).
-(s + 2)*(3*s + 1)
Solve 56/3*y - 20/3 + 4/3*y**4 + 8/3*y**3 - 16*y**2 = 0 for y.
-5, 1
Suppose 4*q + 3*u - 4 = -0*u, -2*u = -2*q + 16. Let a(b) be the second derivative of 2*b + 0 - 1/3*b**3 + 0*b**2 + 0*b**q + 1/10*b**5. Factor a(l).
2*l*(l - 1)*(l + 1)
Solve 40*u**2 - 2*u**4 - 15*u**3 + 0*u**4 + 5*u**5 - 8*u**4 - 20*u = 0.
-2, 0, 1, 2
Let w(i) be the first derivative of 2*i**3/9 + 2*i**2/3 + 2*i/3 - 1. Determine k, given that w(k) = 0.
-1
Let s(b) = 21*b**2 + 51*b. Let d(k) = 4*k**2 + 10*k. Let f(r) = -11*d(r) + 2*s(r). Find l such that f(l) = 0.
-4, 0
Let q(z) be the first derivative of -z**3 - 3*z**2 - 23. Solve q(v) = 0.
-2, 0
Let n(o) = 28*o**3 + 2*o - 1. Let v be n(1). Let 23*s**2 + 8 + 15*s**3 - 15*s - v*s**2 - 2 = 0. Calculate s.
-1, 2/5, 1
Let k be -2 + (-2)/5*(-70)/12. Factor 5/6