**6 + 0*d + 0 + 1/15*d**3 + 2*d**2. Factor z(w).
2*(w + 1)**3/5
Let t(m) be the second derivative of -2*m**6/15 - 7*m. Factor t(k).
-4*k**4
What is u in -19*u - 26*u + 6*u**4 - 24 + 2 + 15*u**2 + 1 + 45*u**3 = 0?
-7, -1, -1/2, 1
Let r(j) be the second derivative of j**6/45 + j**5/30 + 12*j. Find y, given that r(y) = 0.
-1, 0
Let c = 16 + -13. Let s(k) be the first derivative of -1/15*k**6 + 1/5*k**4 + 16/15*k**c + 1 + 7/5*k**2 + 4/5*k - 4/25*k**5. Determine y, given that s(y) = 0.
-1, 2
Let v(m) = -28*m**3 - 36*m**2 + 24*m + 40. Let a(u) = -u**3 - u**2 + u + 1. Let h(o) = 24*a(o) - v(o). Let h(z) = 0. Calculate z.
-2, 1
Let q = 1/255 + 763/510. Factor -q*s - 3/2 + 3/2*s**3 + 3/2*s**2.
3*(s - 1)*(s + 1)**2/2
Suppose w - 3*w = 0. Let h(c) be the third derivative of -2*c**2 - 16/27*c**3 + w - 1/945*c**7 + 0*c + 8/27*c**4 + 2/135*c**6 - 4/45*c**5. Factor h(z).
-2*(z - 2)**4/9
Let n = -19 - -24. Let l(p) be the third derivative of 3*p**2 - 1/210*p**7 + 0*p**3 + 0 + 0*p + 0*p**n + 0*p**6 + 0*p**4. Determine i, given that l(i) = 0.
0
Factor 1/2*l**3 - 5/2*l**2 + 2*l + 0.
l*(l - 4)*(l - 1)/2
Let z(o) = -o**2 - o + 1. Let t(k) = 3*k**2 + 7*k + 3. Let j(r) = t(r) + z(r). Factor j(d).
2*(d + 1)*(d + 2)
Let y(v) = -v**3 - 19*v**2 - 13*v + 3. Let l(u) = 4*u**3 + 56*u**2 + 40*u - 8. Let c(m) = 3*l(m) + 8*y(m). Factor c(a).
4*a*(a + 2)**2
Solve 0 + 0*n**2 + 0*n + 3/8*n**3 = 0.
0
Let g be 2*(-1)/((-4)/10). Suppose -5*n = g*d - 10, -d + n + 5 = 1. Suppose -4/9*c - 40/3*c**d - 56/9*c**5 + 0 - 38/9*c**2 - 142/9*c**4 = 0. What is c?
-1, -2/7, -1/4, 0
Let t(o) be the first derivative of o**6/60 + o**5/10 + 9*o**4/40 + 7*o**3/30 + o**2/10 + 3. Factor t(n).
n*(n + 1)**3*(n + 2)/10
Let t(f) be the first derivative of -f**4/8 + f**3/6 + f**2/4 - f/2 + 7. Factor t(o).
-(o - 1)**2*(o + 1)/2
Let z(f) be the first derivative of 27/8*f**4 + 3/2*f**5 + 1/4*f**6 + 7/2*f**3 + 3/2*f**2 + 0*f - 6. Suppose z(q) = 0. Calculate q.
-2, -1, 0
Let n(j) be the first derivative of 0*j**2 + 2*j + 1/12*j**4 - 1/3*j**3 + 1. Let k(r) be the first derivative of n(r). Let k(h) = 0. Calculate h.
0, 2
Let j(g) be the first derivative of g**3 - 3*g**2 + 3*g - 13. What is w in j(w) = 0?
1
Let m(q) be the first derivative of -8*q**3/27 + 5*q**2/9 - 2*q/9 + 1. Factor m(x).
-2*(x - 1)*(4*x - 1)/9
Factor -24/5*w + 2/5*w**2 + 72/5.
2*(w - 6)**2/5
Suppose -1 = 4*f - 9. Solve 8*v + 52*v**4 + 68*v**3 + 14*v**5 + 36*v**f - 4*v**2 - 10*v - 4 = 0.
-1, 2/7
Let x(g) be the first derivative of 3*g + 3 + 1/2*g**2 + 1/12*g**4 - 1/3*g**3. Let l(o) be the first derivative of x(o). Factor l(b).
(b - 1)**2
Let o(j) be the third derivative of j**2 + 0*j - 1/10*j**5 + 0 + 1/4*j**4 + 1/60*j**6 - 1/3*j**3. Factor o(i).
2*(i - 1)**3
Let a(c) be the third derivative of 4*c**2 + 1/8*c**4 + 1/8*c**3 + 0 + 0*c + 1/80*c**6 + 1/16*c**5. Solve a(y) = 0.
-1, -1/2
Let d(f) = -f**4 - 2*f**3 - f**2 + 12*f + 8. Let v(r) = r**2 - r - 1. Let m(w) = -3*d(w) - 12*v(w). Factor m(p).
3*(p - 2)*(p + 1)**2*(p + 2)
Let h(u) be the first derivative of u**6/60 - u**5/30 - 3*u**2 + 4. Let x(n) be the second derivative of h(n). Factor x(c).
2*c**2*(c - 1)
Factor 2/5 - 7/5*y + 7/5*y**2 - 2/5*y**3.
-(y - 2)*(y - 1)*(2*y - 1)/5
Suppose -2/11 + 26/11*p**3 + 14/11*p - 30/11*p**2 - 8/11*p**4 = 0. Calculate p.
1/4, 1
Let r = 2035 - 154663/76. Let v = r + 173/532. Determine p, given that 1/7*p**2 - v - 1/7*p = 0.
-1, 2
Let q(j) be the third derivative of j**5/30 - 5*j**4/6 + 25*j**3/3 + 49*j**2. Solve q(u) = 0.
5
Let g = 817 + -814. Factor 0*f - 3/5*f**g - 3/5*f**2 + 0.
-3*f**2*(f + 1)/5
Let j = 32/11 - 3829/1320. Let u(t) be the third derivative of j*t**5 + t**2 + 1/80*t**6 + 0*t + 0 - 1/16*t**4 - 1/12*t**3. Factor u(w).
(w - 1)*(w + 1)*(3*w + 1)/2
Let y(i) = -3*i**3 - 2*i**2 - i + 4. Suppose -7 = 3*d - 1. Let g(f) = 7*f**3 + 4*f**2 + 3*f - 9. Let h(m) = d*g(m) - 5*y(m). Solve h(k) = 0 for k.
-2, -1, 1
Let g(t) = -5*t**2 - 2*t - 6. Let u(n) = -9*n**2 - 4*n - 12. Let v(c) = -7*g(c) + 4*u(c). Let y(f) = f**2 + 2*f + 7. Let a(z) = -6*v(z) - 5*y(z). Factor a(l).
(l + 1)**2
Let w(p) = -p**2 - 8*p + 4. Let f be w(-8). Suppose -3*z - 3*m + 2 + 13 = 0, -f*z = 2*m - 18. Let -z*i**2 - 3*i**3 - 8*i**3 + i**3 = 0. Calculate i.
-2/5, 0
Suppose -4*x + 4*q = -28, 0 = 5*x - 9*q + 6*q - 25. Factor -1/2*c**x + 0*c + 1/2.
-(c - 1)*(c + 1)/2
Let d(p) be the third derivative of 1/120*p**6 - 1/40*p**5 + 1/3*p**3 - 1/12*p**4 + 0*p + p**2 + 0 + 1/420*p**7. Factor d(g).
(g - 1)**2*(g + 2)**2/2
Let d(h) = 17*h**3 - 17*h**2 + 11*h. Let f(l) = -3*l**3 + 4*l + 9*l**2 + 9*l**3 - 15*l**2. Let t(w) = -4*d(w) + 11*f(w). What is n in t(n) = 0?
0, 1
Let d(g) be the second derivative of -1/8*g**2 + 1/12*g**4 + 2*g + 0 + 1/8*g**3. Determine n, given that d(n) = 0.
-1, 1/4
Let y = -37 - -41. Let k(n) be the third derivative of -1/240*n**5 + 0*n + 0 + 0*n**y + 2*n**2 + 1/24*n**3. Factor k(c).
-(c - 1)*(c + 1)/4
Suppose t = 2*j + 14, 3*j + 33 = 2*t - 2*j. Let x(d) be the second derivative of 0 + 0*d**3 + 0*d**2 + 1/10*d**5 + 1/6*d**t + 3*d. Factor x(u).
2*u**2*(u + 1)
Let f(i) be the second derivative of 1/3*i**3 + 1/2*i**2 - i + 0 + 1/12*i**4. Determine g, given that f(g) = 0.
-1
Suppose 53 = 2*i + 3*y, -3*i + 2*y + y = -87. Solve 12*c - 23*c**3 - i*c**5 - 104*c**4 - 16*c**2 - 85*c**3 + 4*c = 0 for c.
-2, -1, 0, 2/7
Suppose 2*t + 4*r - 20 = -3*t, 2*t + 2*r = 8. Find u, given that -t*u - 2*u**3 + u**3 + 0*u**3 + 2*u**3 = 0.
-2, 0, 2
Let g = 0 + 0. Let h(i) be the second derivative of -2*i + 0*i**2 - 2/15*i**6 + 1/3*i**4 + g - 1/21*i**7 + 1/3*i**3 + 0*i**5. Let h(q) = 0. What is q?
-1, 0, 1
Suppose 0 = -5*a - 4*b + 15, a + 2*b - 4 + 1 = 0. Solve 8/3*h - 5/3*h**2 - 4/3 + 1/3*h**a = 0 for h.
1, 2
Let f(m) be the third derivative of m**7/840 - m**5/80 + m**4/48 - 30*m**2. Factor f(b).
b*(b - 1)**2*(b + 2)/4
Let s(i) = -i**2 + 21*i + 2. Let c be s(21). Let l(k) be the second derivative of 1/60*k**4 + 1/100*k**5 + 0 + 0*k**c + 2*k + 0*k**3. Solve l(d) = 0.
-1, 0
Find z, given that 0*z - 8/9*z**3 + 2/3*z**4 + 0 - 8/9*z**2 = 0.
-2/3, 0, 2
Let c(w) be the third derivative of 1/600*w**6 + 0*w**4 + 0*w**3 + 0 + 0*w - 1/300*w**5 - 6*w**2. What is z in c(z) = 0?
0, 1
Let r(h) be the third derivative of -7*h**8/96 + 5*h**7/12 - 11*h**6/30 - 23*h**5/15 + 7*h**4/3 - 4*h**3/3 - 3*h**2. Suppose r(d) = 0. Calculate d.
-1, 2/7, 2
Let g(j) = 4*j**4 + 7*j**3 + 8*j**2 - j. Let w(y) = -5*y**4 - 8*y**3 - 9*y**2 + 2*y. Let p(n) = 4*g(n) + 3*w(n). Solve p(v) = 0.
-2, -1, 0
Suppose -5*f = -6 - 9. Let r(g) be the third derivative of 1/20*g**5 + 0*g + 0 - 1/4*g**4 + 2*g**2 + 1/2*g**f. Determine m, given that r(m) = 0.
1
Let q = -3/47 + 139/705. Let r(u) be the first derivative of -4/5*u - 1/2*u**4 + 6/25*u**5 + 2 + u**2 - q*u**3. Solve r(a) = 0.
-1, 2/3, 1
Let f = 0 + 10. Suppose -4*y + 2 = -f. Factor -21/2*i**2 + 7/2*i**4 - 10*i + i**y - 2.
(i - 2)*(i + 1)**2*(7*i + 2)/2
Solve 2 - 16*z**4 - 4*z**3 - 23*z**2 - 5*z - 7*z**5 + 37*z**2 + 16*z = 0.
-1, -2/7, 1
Let z = -4/3 + 2. Factor 0 + 0*i + z*i**2.
2*i**2/3
Factor -a**2 - 1/2*a**3 - 1/2*a + 0.
-a*(a + 1)**2/2
Let g(u) be the second derivative of u**6/255 - 2*u**5/85 + u**4/17 - 4*u**3/51 + u**2/17 + 13*u. Factor g(c).
2*(c - 1)**4/17
Let z(g) = -6*g**2 + 8*g + 11. Let r(d) = -6*d**2 + 8*d + 12. Let l(k) = -k**2 - 8*k + 6. Let a be l(-9). Let w(o) = a*r(o) + 4*z(o). What is t in w(t) = 0?
-2/3, 2
Let s(i) = -3*i**2 - 9*i - 2. Let q(a) = 17*a**2 + 46*a + 11. Let x(n) = 4*q(n) + 22*s(n). What is p in x(p) = 0?
0, 7
Let w = 32 + -32. Factor 0*k + 2/9*k**5 + w - 2/9*k**4 + 2/9*k**2 - 2/9*k**3.
2*k**2*(k - 1)**2*(k + 1)/9
Suppose -6 = -4*t + t. Let m = 6 + -2. Determine i so that 0*i**3 + 0 + 1/2*i**5 - 1/2*i - i**t + i**m = 0.
-1, 0, 1
Solve -3*v**4 + 12*v**2 - 3*v**3 - 2*v + 6*v + 0*v**3 + 8*v = 0 for v.
-2, -1, 0, 2
Let k(v) = 5*v + 147. Let d be k(-29). Factor 10/9*z**d + 14/9*z + 4/9.
2*(z + 1)*(5*z + 2)/9
Let x(f) = -23*f + 26. Let u be x(1). Solve 0*b**2 + 12/5*b - 4/5*b**u + 8/5 = 0.
-1, 2
Let d(s) = 6*s**2 - 24*s + 23. Let l(i) = -3*i**2 + 12*i - 12. Let h(c) = 3*d(c) + 5*l(c). What is w in h(w) = 0?
1, 3
Let m be 3*(-29)/(-6) - -1. Let t = m - 15. Factor 0 - 1/2*l**2 + 1/2*l**3 - t*l + 1/2*l**4.
l*(l - 1)*(l + 1)**2/2
Let m(n) be the third derivative of n**7/18