*w. Suppose k(q) = 0. Calculate q.
-1, 1/3
Let h(a) be the first derivative of -2*a**6/105 + 3*a**5/70 - a**3/21 + 2*a + 2. Let t(r) be the first derivative of h(r). Factor t(k).
-2*k*(k - 1)**2*(2*k + 1)/7
Let u be ((-6)/5)/(3/(-20)). Suppose 2*h = 4*h - u, 2*v + 5*h = 20. Factor -2*q**3 + v*q + 0*q + 2*q.
-2*q*(q - 1)*(q + 1)
Let m(r) be the third derivative of r**8/1512 + r**7/315 + r**6/270 - r**5/135 - r**4/36 - r**3/27 - 4*r**2. Factor m(o).
2*(o - 1)*(o + 1)**4/9
Let h(j) = -j**5 - j**4 - j**3. Let x(y) = -3*y**5 + 12*y**4 + 30*y**3 + 24*y**2. Let r(p) = -6*h(p) + x(p). Factor r(i).
3*i**2*(i + 2)**3
Factor 4*s - 16/5 - 4/5*s**2.
-4*(s - 4)*(s - 1)/5
Let u = 13 - 10. Let r(c) be the second derivative of 1/36*c**4 - 2*c - 1/18*c**u + 0 + 0*c**2. Find g such that r(g) = 0.
0, 1
Let l be ((-2)/4)/(1/(-4)). Let x(v) be the first derivative of 2/5*v**5 - 4/9*v**3 + 1/3*v**4 - 2/3*v - v**l + 1/9*v**6 - 1. Let x(i) = 0. What is i?
-1, 1
Let j(o) = o**2 - 5*o + 2. Let d be j(5). Let f(u) be the first derivative of 1 - 1/3*u**d + 1/6*u**4 + 2/15*u**5 + 0*u - 2/9*u**3. Find r such that f(r) = 0.
-1, 0, 1
Let h be (-3)/(-2) - (-1)/2. Suppose -4*m - w = -2*w, 0 = 3*m + 4*w. Factor m + 0*c**h + 2/5*c**3 - 2/5*c.
2*c*(c - 1)*(c + 1)/5
Factor 6*m + 118 - 118 - 3*m**2.
-3*m*(m - 2)
Suppose 0 = 2*t + 5*w - 64, 2*w = -2*t - w + 56. Solve 4*v + 14*v**2 - v - t*v**3 + v + 4*v**2 = 0 for v.
-2/11, 0, 1
Let n(r) be the second derivative of 4*r + 0 + 1/36*r**3 + 1/72*r**4 + 0*r**2. Factor n(j).
j*(j + 1)/6
Let 1/2 + 3/2*a**4 - 7/2*a**3 - 1/4*a**5 - 9/4*a + 4*a**2 = 0. Calculate a.
1, 2
Let o be 10*(-5)/((-75)/9). Let k be (-2)/9*(-9)/o. Find h such that -1/3*h**3 + 0 + 0*h - k*h**2 = 0.
-1, 0
Suppose -18*k = -7*k. Factor 0*c**2 + k + 6/5*c**3 + 0*c + 21/5*c**4.
3*c**3*(7*c + 2)/5
Suppose -21 = -9*o + 2*o. Suppose -2*y = -o*j + 3*y + 14, -4*y + 5 = 3*j. Factor 16/7*m + 10/7*m**2 + 8/7 + 2/7*m**j.
2*(m + 1)*(m + 2)**2/7
Let w(z) be the second derivative of z**6/240 - 3*z**5/160 - z**4/32 + 7*z**3/48 + 3*z**2/8 + 2*z. Factor w(f).
(f - 3)*(f - 2)*(f + 1)**2/8
Let g(l) be the first derivative of -1/75*l**6 - 1/50*l**5 - 1 - 2*l + 1/30*l**4 + 0*l**2 + 1/15*l**3. Let f(o) be the first derivative of g(o). Factor f(a).
-2*a*(a - 1)*(a + 1)**2/5
Suppose 2*l = -2*b + 8, -b + 4*l - 5 - 1 = 0. Let g = b - 2. Factor -n**4 + n**2 + 1/3*n + g - 1/3*n**3.
-n*(n - 1)*(n + 1)*(3*n + 1)/3
Let u(d) = -d**3 - 8*d**2 - 18*d - 15. Let y be u(-5). Factor 2/9*s**5 - 4/3*s**4 + 2*s**3 + y + 0*s**2 + 0*s.
2*s**3*(s - 3)**2/9
Suppose 0 = -17*v + 2*v + 30. Let o(p) be the second derivative of -1/6*p**4 + 0 + 0*p**v + 1/3*p**3 + 2*p. Factor o(q).
-2*q*(q - 1)
Suppose -w = 5*z - 6, 2*z - w = 4*z. Suppose a - 2 - z = 0. Factor 0*y**3 - 2/5*y**5 - 4/5*y**a + 0 + 4/5*y**2 + 2/5*y.
-2*y*(y - 1)*(y + 1)**3/5
Factor 16*z**2 - 4 - 83*z**3 + 2*z - 86*z**3 - 88*z**3 + 267*z**3.
2*(z + 1)**2*(5*z - 2)
Suppose 4*j - 4*i + 0*i = 0, 4 = 4*j - 3*i. Determine v so that 0 - 6/5*v**2 - 6/5*v**3 - 2/5*v - 2/5*v**j = 0.
-1, 0
Let r = 117 - 111. Let q(c) be the third derivative of 0*c**3 - 1/44*c**r + 1/66*c**4 - 4*c**2 + 0 + 0*c - 1/264*c**8 - 1/330*c**5 - 19/1155*c**7. Factor q(u).
-2*u*(u + 1)**3*(7*u - 2)/11
Let d(z) be the first derivative of -2*z**6/9 - 8*z**5/15 + z**4/3 + 8*z**3/9 - 2. Suppose d(p) = 0. Calculate p.
-2, -1, 0, 1
Factor -5*r**2 - 13*r - 10 - r**3 + 2 + r - r**2.
-(r + 2)**3
Let v(s) be the second derivative of -s**7/98 + s**6/35 + 6*s**5/35 - 4*s**4/7 - 8*s**3/7 + 48*s**2/7 - 5*s + 4. Factor v(l).
-3*(l - 2)**3*(l + 2)**2/7
Let d be 30/324*(-12)/(-20). Let g(p) be the second derivative of 0 - 2/9*p**3 + 1/3*p**2 + 3*p + d*p**4. Factor g(v).
2*(v - 1)**2/3
Factor 1/7*v + 0 + 1/7*v**3 + 2/7*v**2.
v*(v + 1)**2/7
Let t(k) be the first derivative of -k**4/16 - k**3/3 - 5*k**2/8 - k/2 - 4. What is q in t(q) = 0?
-2, -1
Determine v so that 3272*v**2 - 3269*v**2 + 2*v - 3*v**4 + 0*v - 2*v**3 = 0.
-1, -2/3, 0, 1
Let q = -16 + 16. Let h(g) be the third derivative of 0*g + q + 0*g**3 - 1/120*g**4 - 1/600*g**6 + 1/150*g**5 + g**2. Factor h(l).
-l*(l - 1)**2/5
Suppose -3*r = 5*x - 37, x - 3*r = -2*x + 27. Let c be ((-2)/x)/((-9)/12). Let 1/3*y**2 - 1/3*y**4 + 0 + 0*y - 1/3*y**5 + c*y**3 = 0. What is y?
-1, 0, 1
Find r, given that 0*r - 1/5*r**3 + 0 + 1/5*r**2 = 0.
0, 1
Suppose 5*j = -25, s + j + 15 = -2*j. Let c(x) be the third derivative of s + 1/840*x**7 + 0*x**4 - x**2 + 1/480*x**6 + 0*x**3 + 0*x**5 + 0*x. Factor c(m).
m**3*(m + 1)/4
Let r = 0 + -1. Let n = r + 3. Solve m**n + 2*m + m - m + 1 + 0 = 0.
-1
Let z = 27 - 22. Let p(t) be the second derivative of t + 4*t**2 + 1/10*t**z + 5/6*t**4 + 8/3*t**3 + 0. Suppose p(l) = 0. Calculate l.
-2, -1
Let u(z) be the first derivative of 3*z**5/10 - 3*z**3/2 + 3*z**2/2 - 3. Factor u(x).
3*x*(x - 1)**2*(x + 2)/2
Let k be 8/(-6)*6/(-4). Let y(f) = -f**2 + 9*f + 70. Let c be y(14). Let 1/3*i**5 + 0 + c*i**3 - 1/3*i + 2/3*i**4 - 2/3*i**k = 0. Calculate i.
-1, 0, 1
Let f(a) be the third derivative of 1/120*a**5 - 4*a**2 + 0 + 0*a - 1/480*a**6 + 0*a**3 + 0*a**4. Find l, given that f(l) = 0.
0, 2
Let q(l) be the third derivative of 7*l**6/60 - l**5/6 - l**4/6 + 5*l**2 + 7*l. Let q(g) = 0. What is g?
-2/7, 0, 1
Let n(k) be the second derivative of -1/35*k**5 + 0 - 1/7*k**2 + 2/21*k**3 + 1/105*k**6 + 4*k + 0*k**4. Determine u, given that n(u) = 0.
-1, 1
Let q = 165 - 231. Let n = q + 200/3. Suppose n*b + 4/3*b**2 + 2/3*b**3 + 0 = 0. Calculate b.
-1, 0
Suppose 0 = -j + 38 - 36. Solve -4/9*t + 2/9*t**j + 2/9 = 0.
1
Let -4*y**3 + 7*y + 9*y**2 - 5*y**2 + y = 0. What is y?
-1, 0, 2
Let x be 18/52 - 6/(-39). Let o = -23 + 26. Suppose -x*g + 1/2*g**o + 1/2 - 1/2*g**2 = 0. What is g?
-1, 1
Factor -4*m - m**2 - 3 - 6*m**2 + 6*m**2 + 0*m**2.
-(m + 1)*(m + 3)
Let r(n) be the third derivative of -n**7/1155 + n**6/220 - n**4/33 + 22*n**2. Find f, given that r(f) = 0.
-1, 0, 2
Suppose 7 + 17 = 6*f. Determine o, given that 0*o - 2/3*o**2 + 0 + 2/3*o**f + 0*o**3 = 0.
-1, 0, 1
Let y = -12152/25 - -486. Let n = y - -31/75. Suppose -n*g**2 - 4/3*g - 4/3 = 0. Calculate g.
-2
Suppose 5 = 3*t - 4*c, 3*t - 3 = 2*c + 4. Suppose k - t + 1 = 0. Solve 1/3*n**3 - 1/3*n**k - 1/3*n + 1/3*n**4 + 0 = 0.
-1, 0, 1
Let g(y) be the first derivative of -y**3/9 + y**2/3 - 15. Factor g(l).
-l*(l - 2)/3
Let h(c) = 0*c + 2 + c - c**2 + 3*c - 2*c. Let p be h(2). Let 0*s**5 + 0*s**5 + 3*s - 4*s**3 + s**5 + 2*s**p + 0*s - 2 = 0. What is s?
-2, -1, 1
Let r(x) = -x**4 - 2*x**3 - 3*x**2 + 3. Let p(v) = -v**3 - v**2 + 1. Suppose 7*m - 3*m = 24. Let i(z) = m*p(z) - 2*r(z). Factor i(d).
2*d**3*(d - 1)
Let b(c) be the third derivative of 7/24*c**4 - 1/112*c**8 + 0*c + 4/105*c**7 - 1/30*c**6 + 0 - 1/3*c**3 + 2*c**2 - 1/10*c**5. Determine k so that b(k) = 0.
-1, 2/3, 1
Let n(q) = -q**3 - 11*q**2 - 10*q + 7. Let i be n(-10). Let j = -3 + i. Suppose -4/3*z + 0*z**2 - 2/3*z**j + 2/3 + 4/3*z**3 = 0. Calculate z.
-1, 1
Factor 4*i**4 + 12288 + 1668*i - 96*i**3 + 1152*i**2 - 7812*i - i**4.
3*(i - 8)**4
Suppose 4*l + 23 = -3*x, 0 = 3*l - 2*x + 20 - 7. Let a be ((-8)/(-20))/((-1)/l). Factor 4*o**4 - o**4 + 5*o**3 + 0*o**3 + a*o**2.
o**2*(o + 1)*(3*o + 2)
Suppose 6*p = 2*p. Let i(f) be the first derivative of -32/45*f**5 + p*f**2 - 4/27*f**3 + 1 - 7/27*f**6 - 11/18*f**4 + 0*f. Factor i(m).
-2*m**2*(m + 1)**2*(7*m + 2)/9
Let p(z) be the third derivative of -3*z**5/20 + z**3/6 - 10*z**2. Solve p(y) = 0 for y.
-1/3, 1/3
Let u(s) be the second derivative of -s**5/25 - s**4/20 + s**3/30 + 6*s. Find o, given that u(o) = 0.
-1, 0, 1/4
Let z(w) be the first derivative of -4*w**3/9 + 2*w**2/3 - 9. Let z(x) = 0. Calculate x.
0, 1
Let u(s) be the second derivative of -s**9/7560 + s**8/1120 - s**7/420 + s**6/360 + 5*s**4/12 - 5*s. Let f(i) be the third derivative of u(i). Factor f(g).
-2*g*(g - 1)**3
Let c = 37 - 40. Suppose -14 + 2 = z. Let i(k) = -k. Let y(u) = u**4 + 3*u**3 + 3*u**2 + 5*u. Let g(h) = c*y(h) + z*i(h). Factor g(q).
-3*q*(q + 1)**3
Let l(v) = 15*v**2 - 41*v + 40. Let h(z) = -8*z**2 + 20*z - 20. Let f(m) = 7*h(m) + 4*l(m). Let f(t) = 0. Calculate t.
1, 5
Suppose u + 2*c = 2*u - 10, -3*c - 20 = -2*u. Find f such that -2*f**2 - u - 2*f**3 + 10 = 0.
-1, 0
Let u be (-1)/(-1 - 0) + 1. Let -6*w**u - 3*w - 6*w**2 - 10*w**4