- 1/80*d**5 + 0*d**2 + 1/24*d**3 - 2*d + 0*d**4. Let r(z) be the first derivative of l(z). Factor r(u).
-u*(u - 1)*(u + 1)/4
Let z be ((-6)/9)/(-2) - (-4)/(-18). Let w(y) be the first derivative of -z*y**2 + 1/9*y**4 + 0*y**5 - 3 - 1/27*y**6 + 0*y**3 + 0*y. Let w(h) = 0. Calculate h.
-1, 0, 1
Let b(v) be the first derivative of -v**5/60 + v**4/8 - v**3/3 - 14*v**2 - 39. Let z(c) be the second derivative of b(c). Factor z(h).
-(h - 2)*(h - 1)
Let p be 6/((-288)/(-70))*(-6)/(-15). Let c(v) be the first derivative of 4/9*v**3 + p*v**2 + 1/8*v**4 + 1/3*v + 5. Suppose c(q) = 0. Calculate q.
-1, -2/3
Let d be (-60)/(-43)*(57/(-27))/(-1). Let n = -12/43 + d. Determine u so that 4/3*u - 4/3 + 4/3*u**5 - n*u**3 + 8/3*u**2 - 4/3*u**4 = 0.
-1, 1
Let u(p) be the third derivative of 0 + 0*p**3 + 0*p + 3/8*p**6 - 5/24*p**4 - 5/42*p**8 - 1/21*p**7 + 1/6*p**5 + 20*p**2. Let u(s) = 0. Calculate s.
-1, -1/2, 0, 1/4, 1
Let h be (1 - 1)/(11 + -2 - 10). Let i(s) be the third derivative of 0*s**3 + 0 - 4*s**2 - 1/75*s**5 - 3/100*s**6 + 0*s**4 + h*s. Find n, given that i(n) = 0.
-2/9, 0
Let p(m) be the first derivative of -2*m**3/15 - 6*m**2/5 + 32*m/5 - 109. Determine x, given that p(x) = 0.
-8, 2
Let s(y) = y**5 + 21*y**4 + 63*y**3 - 421*y**2 - 1341*y + 4608. Let i(h) = h**4 + 2*h**3 + h**2 + h. Let r(p) = 3*i(p) - s(p). Let r(q) = 0. What is q?
-8, 3
Let v(o) = 6*o**5 - 7*o**4 - 30*o**3 + 31*o**2. Let x(c) = 15*c**5 - 18*c**4 - 75*c**3 + 78*c**2. Let g(r) = -12*v(r) + 5*x(r). Find t, given that g(t) = 0.
-2, 0, 1, 3
Let r = -13724/75 + 183. Let s(w) be the second derivative of -r*w**6 + 0 + 0*w**2 + 3*w - 1/15*w**3 + 1/50*w**5 + 1/30*w**4. Factor s(i).
-2*i*(i - 1)**2*(i + 1)/5
Factor -1 - x + 3/4*x**2 + x**3 + 1/4*x**4.
(x - 1)*(x + 1)*(x + 2)**2/4
Factor 2*o**3 - o + o**4 + 3*o**4 - 1540*o**2 - o + 6 + 1530*o**2.
2*(o - 1)**2*(o + 1)*(2*o + 3)
Let y(p) = -8*p**3 + 1762*p**2 + 57352*p - 59172. Let c(h) = -h**3 + 252*h**2 + 8193*h - 8453. Let f(q) = 44*c(q) - 6*y(q). Factor f(x).
4*(x - 1)*(x + 65)**2
Factor 2/7*a**3 + 4/7*a - 6/7*a**2 + 0.
2*a*(a - 2)*(a - 1)/7
Let q(s) be the second derivative of 0*s**2 + 4*s + 0*s**3 + 0 + 1/28*s**4. Solve q(n) = 0.
0
Suppose -3 - 13 = -3*z - 2*l, -4 = 3*z - 2*l. Suppose -z*a = -5*a + 6. Let -1 - 6*x**a + 4 + 0 + 3*x**2 = 0. Calculate x.
-1, 1
Let c = 20001/80 + -250. Let x(v) be the third derivative of 0 + c*v**5 + 0*v**4 - 7*v**2 + 0*v + 0*v**3 + 1/160*v**6. Solve x(j) = 0.
-1, 0
Factor 2/3*l**2 + 0 + 62/3*l.
2*l*(l + 31)/3
Find w, given that -3/5*w**2 - 93/5*w + 96/5 = 0.
-32, 1
Let i(h) be the third derivative of 0*h**5 + 0*h + 0 + 1/200*h**6 + 0*h**3 - 1/10*h**4 + 16*h**2. Let i(r) = 0. Calculate r.
-2, 0, 2
Let n(i) = -i**3 - i**2 + i + 7. Suppose 4*z - z = 0. Let h be n(z). Suppose -3*w**2 + 5*w**3 - w**4 - h*w**3 + 2*w**2 = 0. What is w?
-1, 0
Let s(k) be the second derivative of -k**7/126 - k**6/10 - k**5/4 - 7*k**4/36 - 293*k - 3. Factor s(n).
-n**2*(n + 1)**2*(n + 7)/3
Let d(l) = -2*l**3 + 3*l**2 + 2*l + 7. Let o be d(3). Let f(z) = -z**2 - 11*z + 44. Let i be f(o). Determine w, given that -1/5*w**i - 6/5*w - 9/5 = 0.
-3
Let n(f) = 75*f**3 - 356*f**2 - 1211*f - 409. Let w(p) = 15*p**3 - 71*p**2 - 242*p - 82. Let i(d) = 2*n(d) - 11*w(d). Factor i(o).
-3*(o - 7)*(o + 2)*(5*o + 2)
Suppose 16*w = -4*v + 17*w + 3, v - w - 3 = 0. Let p(q) be the first derivative of 0*q + 1/8*q**4 + 0*q**2 + 1/20*q**5 - 7 + v*q**3. Factor p(i).
i**3*(i + 2)/4
Let q(d) = -23*d**3 + 23*d**2. Let k(s) = 11*s**3 - 11*s**2. Let i(b) = 13*k(b) + 6*q(b). Let i(g) = 0. Calculate g.
0, 1
Let k = -21329/30 + 711. Let n(u) be the first derivative of -10 + 1/3*u - 1/12*u**2 + 1/24*u**4 + k*u**5 - 1/6*u**3. Solve n(y) = 0.
-2, -1, 1
Factor 34/11*k + 2/11*k**3 + 16/11 + 20/11*k**2.
2*(k + 1)**2*(k + 8)/11
Let n(k) = 5*k**2 - 2*k + 1. Let w(u) = 2*u**2 - u. Let g(q) = 3*n(q) - 8*w(q). Let i be g(0). Factor -3/2*p**4 + 3/4*p + 0 - 3/4*p**5 + 0*p**i + 3/2*p**2.
-3*p*(p - 1)*(p + 1)**3/4
Let h(x) be the third derivative of x**8/252 + x**7/90 + x**6/180 - x**5/180 + x**2 - 7*x. Let h(f) = 0. What is f?
-1, 0, 1/4
Suppose 2*w - 19*y = -15*y + 24, 4*y = -2*w - 16. Let -4/5*i**w - 4/5*i + 0 = 0. Calculate i.
-1, 0
Let v(x) be the third derivative of x**8/42 - x**7/21 - x**6/30 + 19*x**5/120 - x**4/6 + x**3/12 - 21*x**2 - 2. Let v(a) = 0. Calculate a.
-1, 1/4, 1/2, 1
Let k = 14 + -6. Let j = -5 - -14. Factor j*s**3 - k*s**3 + 0*s + s**2 - 2*s.
s*(s - 1)*(s + 2)
Let x(m) = -21*m + 121. Let d be x(6). Let w be ((-6)/9)/(d/(20/24)). Factor -2/9 + 1/3*b + 0*b**2 - w*b**3.
-(b - 1)**2*(b + 2)/9
Let m be ((-8)/(-18))/((-12)/702*-13). Let h(n) be the first derivative of 2/3*n**3 + 18*n + 5 + 6*n**m. Determine o so that h(o) = 0.
-3
Let y(o) be the third derivative of -o**8/2184 - o**7/195 - 19*o**6/780 - 5*o**5/78 - 4*o**4/39 - 4*o**3/39 + 56*o**2. Suppose y(a) = 0. Calculate a.
-2, -1
Suppose -21*q + 154 = -266. Let y be 1/q - -3*(-3)/(-45). Suppose 3/4*t**2 + 0 - y*t = 0. Calculate t.
0, 1/3
Suppose -50/3*s - 16 - 2/3*s**2 = 0. What is s?
-24, -1
Suppose 4/7*v**3 + 16/7 - 16/7*v + 0*v**2 - 1/7*v**4 = 0. Calculate v.
-2, 2
Let d(j) be the second derivative of 13*j**4/4 + 15*j**3 + 12*j**2 + 376*j. Suppose d(a) = 0. Calculate a.
-2, -4/13
Factor 15 - 5 - 10*y**3 - 10 + 4*y + 6*y**2.
-2*y*(y - 1)*(5*y + 2)
Let i(a) be the second derivative of a**5/12 + 5*a**4/12 + 5*a**3/6 - a**2 - 25*a. Let h(j) be the first derivative of i(j). Factor h(v).
5*(v + 1)**2
Let m be (-21)/(-4)*80/30. Suppose u + m*u = 4*u. Factor -1/4*l**3 + u*l + 0*l**2 + 0.
-l**3/4
Let g(t) be the second derivative of t**6/15 + 3*t**5/20 - t**4/2 - 5*t**3/6 + 3*t**2 - 2*t + 121. Let g(i) = 0. Calculate i.
-2, -3/2, 1
Let h(o) be the third derivative of o**7/840 + 7*o**6/480 + 3*o**5/80 - 7*o**4/96 - 5*o**3/12 - 17*o**2 + 2. Suppose h(u) = 0. Calculate u.
-5, -2, -1, 1
Let -3*p**4 + 6*p**4 + 6*p**2 + 8*p - 8*p**3 + 26 - 34 - p**4 = 0. What is p?
-1, 1, 2
Let s(m) be the second derivative of -m**4/32 + 5*m**3/4 + 63*m**2/16 - 16*m - 1. Let s(q) = 0. What is q?
-1, 21
Suppose 5*j - 22*b - 7 = 15, 5*j - b - 1 = 0. What is x in 3/4*x**4 + 9/4*x**3 - 3*x + 0 + j*x**2 = 0?
-2, 0, 1
Let b(k) be the third derivative of k**8/2352 - k**7/490 - 3*k**6/140 - k**5/105 + k**4/7 + 195*k**2. Factor b(p).
p*(p - 6)*(p - 1)*(p + 2)**2/7
Suppose 0 = -3*x + 5*w + 16 + 16, 0 = 2*x + 2*w. Suppose 5*u = -x*f + 44, -u - 2*u = f - 18. Factor f*a - 3*a**3 + 5*a - 11*a.
-3*a**3
Let x(i) be the first derivative of -3/8*i**3 - 3/80*i**5 - 7*i + 3/8*i**2 - 4 + 3/16*i**4. Let t(z) be the first derivative of x(z). Factor t(g).
-3*(g - 1)**3/4
Let b = -19 - -31. Let m = b + -8. Factor -q - 1 + 8*q**2 - m*q**2 + q**3 - 3*q**2.
(q - 1)*(q + 1)**2
Let t = -395 - -399. Let u(z) be the second derivative of 1/42*z**t + 0*z**2 + 0 - 4*z - 1/7*z**3. Factor u(o).
2*o*(o - 3)/7
Let b(c) be the second derivative of -4*c**2 + 0 + 1/20*c**5 + 5*c + 1/8*c**4 - c**3. Let d(i) be the first derivative of b(i). Suppose d(n) = 0. Calculate n.
-2, 1
Factor -12 - 4/3*a**2 - 40/3*a.
-4*(a + 1)*(a + 9)/3
Let k(j) be the first derivative of -2*j**6/3 + 2*j**4 - 2*j**2 + 47. Factor k(t).
-4*t*(t - 1)**2*(t + 1)**2
Let a(p) = 3*p**2 + 14*p + 13. Let g(h) = 2*h**2 - h - 1. Let x(o) = -4*a(o) + 4*g(o). Factor x(c).
-4*(c + 1)*(c + 14)
Let y(q) be the second derivative of -q**7/147 + 2*q**6/35 - 13*q**5/70 + 2*q**4/7 - 4*q**3/21 - q - 16. What is p in y(p) = 0?
0, 1, 2
Let f(k) be the second derivative of k**5/60 + 2*k**4/9 - 8*k**3/3 + 326*k. Solve f(o) = 0 for o.
-12, 0, 4
Let k(u) be the second derivative of u**7/378 - u**6/135 + 12*u. Solve k(d) = 0 for d.
0, 2
Let s be (-20)/50 + 2*11/5. Find q, given that 4*q**3 - 8*q**s + 0*q**5 + 10*q**5 - q**5 - 5*q**5 = 0.
0, 1
Let k = 0 - -18. Suppose 26 = 4*f - k. Determine b so that -17*b**3 - 3 - 21*b**2 - b**4 - 4*b**4 + 1 - f*b = 0.
-1, -2/5
Let d(l) = -l**2 + 2*l - 1. Let v = 60 - 34. Let c(u) = 24*u**2 - 2 + 3*u + 0*u - v*u**2. Let t(a) = -4*c(a) + 7*d(a). Solve t(r) = 0 for r.
-1
Let k(n) = -21*n**2 + 2*n - 13. Let p = 8 - 21. Let j(d) = 10*d**2 - d + 6. Let c(r) = p*j(r) - 6*k(r). Factor c(g).
-g*(4*g - 1)
Suppose -36*o**3 + 0*o**4 + 152 + 3*o**4 + 16 + 133*o + 11*o - 12 - 51*o**2 = 0. What is o?
-2, -1, 2, 