actor f(i).
3*i*(i - 1)*(7*i + 2)
Let y(o) be the second derivative of -o**6/15 + o**4/2 - 2*o**3/3 + 15*o. Factor y(q).
-2*q*(q - 1)**2*(q + 2)
Let a = -127/2 - -65. What is p in 0 + 1/2*p**2 + p**4 - a*p**3 + 0*p = 0?
0, 1/2, 1
Let d(v) be the first derivative of -v**6/4 + 3*v**5/2 - 27*v**4/8 + 7*v**3/2 - 3*v**2/2 - 3. Solve d(u) = 0.
0, 1, 2
Suppose 3*d = 4*d + 4*q - 2, 2*d = -q + 4. Let i = 86 - 772/9. Determine u, given that 2/9 + i*u - 2/9*u**3 - 2/9*u**d = 0.
-1, 1
Let r(b) = b**3 - 6*b**2 - b + 6. Let d(v) = 5*v**2 - 5. Let s(k) = -6*d(k) - 5*r(k). Factor s(i).
-5*i*(i - 1)*(i + 1)
Let q(t) be the third derivative of -t**5/240 - 5*t**2. Find u, given that q(u) = 0.
0
Suppose -2*l - 29 = -5*c + 2*l, 0 = c - 5*l - 10. Suppose 4*s + 1 = 5*y, 3*y + 2 = c*s - 0*s. Factor -d**2 + 0*d + 0*d + y.
-(d - 1)*(d + 1)
Let z(s) be the third derivative of s**6/300 + 3*s**5/50 + 2*s**4/5 + 16*s**3/15 - 6*s**2. Suppose z(h) = 0. Calculate h.
-4, -1
Suppose 10 = -6*r + 11*r. What is a in -2/5*a + 1/5 + 1/5*a**r = 0?
1
Let l(m) be the second derivative of m**4/3 + 2*m**3/3 - 4*m**2 - 2*m. Solve l(d) = 0.
-2, 1
Let b be 25/4 - (-1)/(-4). Let a = b + -6. Factor a*l + 1/4*l**2 + 0.
l**2/4
Let i(k) be the second derivative of -k**7/420 + k**5/20 + k**4/6 - k**3/3 + 5*k. Let j(d) be the second derivative of i(d). Factor j(c).
-2*(c - 2)*(c + 1)**2
Let h(m) = -1 + 4*m**3 + m + 4*m**2 - 5*m + 0*m**2 - 3*m**2. Let u(k) = -k**3 - k**2 + k + 1. Let r(i) = -h(i) - 3*u(i). Factor r(q).
-(q - 2)*(q - 1)*(q + 1)
Let t(s) be the third derivative of -s**9/7560 + s**7/1260 + s**4/8 + 4*s**2. Let l(d) be the second derivative of t(d). Factor l(c).
-2*c**2*(c - 1)*(c + 1)
Let i(r) = -5*r**2 + 3*r - 10. Let f(n) = -4*n**2 + 2*n - 9. Let h(y) = 6*f(y) - 5*i(y). Factor h(x).
(x - 4)*(x + 1)
Suppose 0 = 5*x + 4*h - 8, 23 = 2*x + h - 6*h. Let j(q) be the third derivative of -2*q**2 + 0*q**x + 0 - 1/120*q**5 + 0*q**3 + 0*q. Factor j(l).
-l**2/2
Let p(b) = 6*b**4 + 9*b**3 + 6*b**2 - 3*b. Let z(x) = -17*x**4 - 26*x**3 - 17*x**2 + 8*x. Let k(r) = -8*p(r) - 3*z(r). Factor k(f).
3*f**2*(f + 1)**2
Let f(d) be the second derivative of -d**5/5 + 4*d**4/3 - 2*d**3 + 12*d. What is u in f(u) = 0?
0, 1, 3
Let f(o) be the second derivative of -o**7/420 - o**6/90 - o**5/60 + o**3/3 - 2*o. Let w(t) be the second derivative of f(t). Suppose w(q) = 0. What is q?
-1, 0
Suppose f = -0*f. Factor m**5 - 2*m**5 - m**4 + m**3 - 3*m**2 + 4*m**2 + f*m**2.
-m**2*(m - 1)*(m + 1)**2
Let o = 50/9 - -43/36. Let t = -21/4 + o. Suppose 1/2*v**4 - 2*v**3 + 2*v - 2 + t*v**2 = 0. What is v?
-1, 1, 2
Let g(o) be the third derivative of -o**7/35 - o**6/60 + 3*o**5/10 + 3*o**4/4 + 2*o**3/3 + 16*o**2. Solve g(n) = 0 for n.
-1, -1/3, 2
Factor -16/5*v + 0 + 0*v**2 + 4/5*v**3.
4*v*(v - 2)*(v + 2)/5
Let k(w) be the third derivative of w**8/84 - 3*w**7/70 + w**6/20 - w**5/60 - 2*w**2. Determine l so that k(l) = 0.
0, 1/4, 1
Let x = -39 - -41. Factor 0 + 2*h**3 + 2/3*h - 2/3*h**4 - x*h**2.
-2*h*(h - 1)**3/3
Let g(f) be the third derivative of 1/90*f**6 + 0 + 1/315*f**7 + 0*f + 0*f**3 + 0*f**4 + 1/90*f**5 - f**2. Factor g(q).
2*q**2*(q + 1)**2/3
Let v(l) be the second derivative of l**4/27 + 16*l**3/27 + 14*l**2/9 - 8*l. Factor v(d).
4*(d + 1)*(d + 7)/9
Let j be (-34)/51*6/(-8). Factor 0*h**4 + 0*h**2 - h**3 + 1/2*h + 0 + j*h**5.
h*(h - 1)**2*(h + 1)**2/2
Let h(l) be the third derivative of -8*l**2 - 1/60*l**5 - 2/3*l**3 + 0*l + 1/6*l**4 + 0. Factor h(w).
-(w - 2)**2
Let l(z) be the second derivative of z**5/5 - 2*z**4/3 + 2*z**3/3 + 4*z. Factor l(r).
4*r*(r - 1)**2
Suppose -3*w + 9 = -6. Let 8*o**5 - 10*o**5 + 4*o**2 - 6*o**4 + 2*o**2 - o**w + 3*o = 0. What is o?
-1, 0, 1
Let w be (6 + (-6 - -3))/1. Let f(n) be the first derivative of 2*n - 2/5*n**5 + 0*n**w + 2*n**2 - n**4 + 1. Factor f(q).
-2*(q - 1)*(q + 1)**3
Factor -4/3 + 10*w**3 - 37/3*w**2 - 3*w**4 + 20/3*w.
-(w - 1)**2*(3*w - 2)**2/3
Suppose -9*x = -8 - 10. Factor 4/13*m + 2/13 + 2/13*m**x.
2*(m + 1)**2/13
Let s(l) = l**5 - l**4 + l**3 + l**2 - l - 1. Let c(n) = 5*n**5 + n**4 + n**3 - n**2 - 3*n - 3. Let d(u) = -c(u) + 3*s(u). Solve d(r) = 0 for r.
-2, -1, 0, 1
Let d(v) be the third derivative of v**6/240 + v**5/60 - v**4/16 - 16*v**2. Suppose d(a) = 0. Calculate a.
-3, 0, 1
Let d(s) be the third derivative of -s**5/210 + s**4/28 + 4*s**3/21 - 11*s**2. Factor d(q).
-2*(q - 4)*(q + 1)/7
Factor 2/11*g**2 - 2/11 - 2/11*g + 2/11*g**3.
2*(g - 1)*(g + 1)**2/11
Let o(z) = 6*z**2 + 2*z - 4. Let n(q) = 0*q + 5 + 4*q - 6*q - 7*q**2. Suppose 0 = -2*j - 3 - 5. Let w(t) = j*o(t) - 3*n(t). Let w(k) = 0. Calculate k.
-1, 1/3
Suppose -5*s = -4*r + 108, r = -0*r - 4*s + 27. Let t be r/42 + (-1)/(-2). Factor -t - 10/7*d**2 + 32/7*d - 50/7*d**3.
-2*(d + 1)*(5*d - 2)**2/7
Let q be ((-1)/9)/(1/(-3)). Let h(d) = -2*d - 13. Let z be h(-8). Determine j, given that -4/3*j**2 - 5/3*j - q*j**z - 2/3 = 0.
-2, -1
Let p(i) be the second derivative of i**7/147 + i**6/105 - i**5/70 - i**4/42 - 9*i. Solve p(a) = 0.
-1, 0, 1
Let g = -8 - -11. Suppose g*t = 9 + 3. What is d in 0*d - 2/5*d**3 + 2/5*d**t + 0 + 0*d**2 = 0?
0, 1
Let y = 406/3 - 135. Factor -y*p**3 + 0 - 2/3*p**2 - 1/3*p.
-p*(p + 1)**2/3
Let g(u) be the third derivative of u**6/210 - u**4/42 + 17*u**2. Factor g(d).
4*d*(d - 1)*(d + 1)/7
Let t(k) be the first derivative of -k**4/16 - k**3 - 6*k**2 - 16*k + 5. Factor t(r).
-(r + 4)**3/4
Let a(s) = -s**2 - s + 3. Let x be a(0). Let m = x + 0. Find j, given that j**m - 2*j - j**2 + j**4 + 0*j**3 + j = 0.
-1, 0, 1
Let x(c) be the second derivative of c**5/4 + 5*c**4/6 - 5*c**3/6 - 5*c**2 + c. Suppose x(o) = 0. What is o?
-2, -1, 1
Let l(j) be the first derivative of j**3/30 + 3*j**2/20 - 2*j/5 - 6. Factor l(t).
(t - 1)*(t + 4)/10
Let d be 0/1 - (-8 + 5). Let t(g) be the third derivative of 0*g - 1/30*g**5 + 1/12*g**4 + 2/3*g**d + 0 - 3*g**2. Solve t(v) = 0.
-1, 2
Let z(w) = -29*w**2 - 9*w. Let o(g) = -8*g**2 - g - 2. Let i(y) = 7*y**2 + 3. Let t(b) = 2*i(b) + 3*o(b). Let v(j) = 11*t(j) - 4*z(j). What is p in v(p) = 0?
-1/2, 0
Let a(j) be the third derivative of -j**8/6720 + j**6/1440 + j**3/3 - j**2. Let r(w) be the first derivative of a(w). Factor r(o).
-o**2*(o - 1)*(o + 1)/4
Let o(d) = -d**2 + 5*d + 3. Let y be o(5). Determine s, given that 5*s**3 + 7 - 5 - 6*s + y*s**3 = 0.
-1, 1/2
Let 1/3*m**2 + 0 - m = 0. Calculate m.
0, 3
Let r(o) = 8*o**4 + 5*o**3 - 24*o**2 - 21*o + 5. Let u(l) = 4*l**4 + 3*l**3 - 12*l**2 - 11*l + 3. Let q(z) = 3*r(z) - 5*u(z). Suppose q(y) = 0. Calculate y.
-1, 0, 2
Let i(x) be the third derivative of 3*x**2 - 1/300*x**5 + 0*x + 0 + 1/60*x**4 - 1/30*x**3. Let i(n) = 0. What is n?
1
Let c(w) = w**3 + 8*w**2 + 8*w + 10. Let x be 75/(-11) - 8/44. Let t be c(x). Factor t*h**2 + 2 - 9*h**3 + 2*h + 7*h**3 - 5*h**2.
-2*(h - 1)*(h + 1)**2
Let m be (3/(-22))/((-9)/24). Factor 2/11*f - m*f**3 - 2/11*f**4 - 2/11 + 2/11*f**5 + 4/11*f**2.
2*(f - 1)**3*(f + 1)**2/11
Factor 0 + 0*w - 2/5*w**4 + 2/5*w**2 + 0*w**3.
-2*w**2*(w - 1)*(w + 1)/5
Let j(b) be the third derivative of -b**8/84 + 2*b**7/35 + 12*b**2. Factor j(w).
-4*w**4*(w - 3)
Suppose 5*d - o - 1 = -0*o, -5*d + 4*o + 4 = 0. Let b(q) be the first derivative of 0*q**3 + 1/9*q**6 + 0*q**5 - 1 - 1/6*q**4 + 0*q + d*q**2. Factor b(t).
2*t**3*(t - 1)*(t + 1)/3
Let r(b) be the second derivative of 3/8*b**5 + 3/28*b**7 + 0*b**2 - 7/20*b**6 + 0*b**3 + 0 - 1/8*b**4 - 5*b. Factor r(k).
3*k**2*(k - 1)**2*(3*k - 1)/2
Let f = 5 + -3. Suppose 2 + k**4 - 2*k**2 + 2*k**3 + k**4 - f*k - 2 = 0. What is k?
-1, 0, 1
Let s(j) be the first derivative of -2*j**5/45 + j**4/6 + 2*j**3/27 - j**2/3 - 10. Determine b, given that s(b) = 0.
-1, 0, 1, 3
Let v = 11 + -8. Factor 4*o**4 + 0*o**4 + 6*o**3 + o**2 - 2*o**v - 2 - 3*o**2 - 5*o + o**5.
(o - 1)*(o + 1)**3*(o + 2)
Let i(g) = -g**2 - 16*g + 51. Let x(m) = 3*m**2 + 33*m - 103. Let y(q) = 5*i(q) + 2*x(q). Find f such that y(f) = 0.
7
Factor -k**4 - 21*k - 12 - 2*k**4 - 39*k**2 - 15*k - 18*k**3.
-3*(k + 1)**2*(k + 2)**2
Let w = 76 - 72. Let r(t) be the first derivative of -3/4*t**w + 0*t - 1/2*t**2 - 1 - t**3 - 1/5*t**5. Find z, given that r(z) = 0.
-1, 0
Let j(m) be the third derivative of m**7/70 + m**6/20 - m**5/20 - m**4/4 - 38*m**2. What is b in j(b) = 0?
-2, -1, 0, 1
Suppose -15 = -2*o - o, 5*