 - 10*t**2.
t*(t - 1)
Let g(n) be the second derivative of 0 + 19/20*n**5 + 2*n**2 - 9/4*n**4 - 27*n + 4/3*n**3 - 2/15*n**6. Factor g(k).
-(k - 2)**2*(k - 1)*(4*k + 1)
Let j(v) be the second derivative of -7*v**6/135 - 37*v**5/90 - v**4/18 + 37*v**3/27 + 10*v**2/9 - v + 2. Let j(z) = 0. Calculate z.
-5, -1, -2/7, 1
Let y(u) = u**2 - 1. Suppose -i + 3*f - 11 = 0, i = -5*f + 4 + 17. Let n(a) = 3*a**2 - 2*a - 2. Let h(t) = i*n(t) - 2*y(t). Factor h(q).
q*(q - 2)
Let f(a) be the first derivative of -a**5/5 + 17*a**3/3 - 18*a**2 + 20*a - 201. Factor f(y).
-(y - 2)**2*(y - 1)*(y + 5)
Let o(x) = -x**3 - x + 1. Let z(l) = -4*l**2 - 12*l + 4. Let q(b) = b**3 - 7*b**2 + 4*b + 11. Let d be q(6). Let p(f) = d*z(f) + 4*o(f). Factor p(g).
-4*g*(g - 2)*(g + 1)
Let d(j) be the third derivative of -3*j**7/385 - j**6/33 - 2*j**5/165 + 134*j**2. Suppose d(p) = 0. Calculate p.
-2, -2/9, 0
Let z(a) = -82*a - 1636. Let w be z(-20). Solve -4/7*v**2 + 0 - 6/7*v**3 - 2/7*v**w + 0*v = 0 for v.
-2, -1, 0
Let b(r) be the first derivative of -r**4 - 4*r**3 + 18*r**2 - 20*r - 20. Factor b(j).
-4*(j - 1)**2*(j + 5)
Let v(n) = -15*n**5 - n**4 - 15*n**3 - 13*n**2 + 2*n. Let m(h) = 13*h**5 + 14*h**3 + 12*h**2 - 3*h. Let p(l) = 7*m(l) + 6*v(l). Solve p(j) = 0 for j.
-1, 0, 1, 3
Let g(r) be the third derivative of 0*r + 0*r**3 + r**2 - 1/12*r**5 - 5/12*r**4 + 0. What is z in g(z) = 0?
-2, 0
Suppose -2*k - 22 - 3 = -5*o, -4*k = o - 5. Let c(a) be the third derivative of -7*a**2 + 0*a + 0*a**3 + 0 + 1/3*a**4 - 1/15*a**o. Determine j so that c(j) = 0.
0, 2
Let q = 27699/5 - 5539. Factor -4/5*y + q*y**2 - 4/5 + 4/5*y**3.
4*(y - 1)*(y + 1)**2/5
Let u = 1420 - 1418. Let y(n) be the second derivative of -2*n + 0*n**u + 0 - 9/4*n**3 - 3/4*n**4 - 3/40*n**5. Factor y(b).
-3*b*(b + 3)**2/2
Let d = -32 + 35. Let -4*u - 27*u**3 - 16*u**2 + 20*u - 16*u**2 + 7*u**d = 0. What is u?
-2, 0, 2/5
Let f(h) = 2*h**2 + 90*h - 128. Let o(q) = -q**2 - 91*q + 122. Let t(u) = -5*f(u) - 6*o(u). What is k in t(k) = 0?
1, 23
Factor 5/2*g**3 - 1/4*g**5 - 13*g**2 + 3/4*g**4 - 8 + 18*g.
-(g - 2)**3*(g - 1)*(g + 4)/4
Find p, given that 21/4*p**3 - 27/2 - 99/4*p + 15/2*p**2 - 3/2*p**4 = 0.
-2, -1/2, 3
Let r(w) be the first derivative of 8/7*w**2 - 4/35*w**5 - 16/7*w - 2/7*w**4 - 19 + 4/7*w**3. Factor r(s).
-4*(s - 1)**2*(s + 2)**2/7
Let s(r) be the second derivative of r**4/30 - 8*r**3/15 + 3*r**2 + 2*r + 26. Let s(o) = 0. Calculate o.
3, 5
Factor 12/7 - 2/7*j - 2/7*j**3 - 8/7*j**2.
-2*(j - 1)*(j + 2)*(j + 3)/7
Let w be (0*4/(-12))/(-1). Suppose w + 8 = 4*k. Factor 0*l**k + l**3 + 0*l**3 + 4*l - 2*l + 3*l**2.
l*(l + 1)*(l + 2)
Let q(v) = 2*v - 23. Suppose 2*h = -3*r + 29, -3*r + 16 = -0*h + h. Let y be q(h). Find g such that 0 + g**2 - 2/5*g**y - 2/5*g = 0.
0, 1/2, 2
Let x(d) = 20*d + d + 14*d**2 - 13*d**2. Let k(l) = -l**2 - 43*l. Let h(s) = 6*k(s) + 10*x(s). Factor h(g).
4*g*(g - 12)
Let i(u) be the first derivative of u**4/6 - 8*u**3/9 + 110. Factor i(t).
2*t**2*(t - 4)/3
Let h(k) be the third derivative of k**8/112 + 3*k**7/70 + k**6/20 - 23*k**2 - 4. Determine q so that h(q) = 0.
-2, -1, 0
Let c = -151 - -102. Let h = -47 - c. Solve 3/5*j - 2/5 - 1/5*j**h = 0.
1, 2
Factor -256/3*l - 14/3*l**3 + 296/9*l**2 + 512/9 + 2/9*l**4.
2*(l - 8)**2*(l - 4)*(l - 1)/9
Let u(q) = q**2 + 31*q - 64. Let x be u(-33). Factor 4/3*h + 2/3*h**3 - 2*h**x + 0.
2*h*(h - 2)*(h - 1)/3
Let s = -35962/9 + 4010. Let i be -7*10/(-210)*6. Factor 2/9*w**3 + 32/3*w - 8/3*w**i - s.
2*(w - 4)**3/9
Let a(w) be the first derivative of -w**6/3 - 2*w**5 - 7*w**4/2 + 2*w**3/3 + 8*w**2 + 8*w + 289. Solve a(u) = 0 for u.
-2, -1, 1
Let v(p) be the first derivative of -p**7/1260 - p**6/60 - 3*p**5/20 - 3*p**4/4 - 9*p**3/4 + p**2 + 6. Let c(i) be the second derivative of v(i). Factor c(n).
-(n + 3)**4/6
Let p be (-7 + 0 + 11)/2. Let g(r) be the third derivative of 0*r**7 + 0*r + 1/1344*r**8 + 0*r**4 + 0*r**3 - 1/480*r**6 + 0*r**5 + 4*r**p + 0. Factor g(a).
a**3*(a - 1)*(a + 1)/4
Let h(d) be the first derivative of -4/21*d**3 - 1/7*d**4 + 6/35*d**5 - 1/21*d**6 - 2/7*d + 22 + 3/7*d**2. Suppose h(k) = 0. Calculate k.
-1, 1
Let q be (-1)/(-8) - (-7629)/24. Factor 318*w - q*w + w**3.
w**3
Let o = -86301/4 + 21576. Solve -1521/4*a - 117/4*a**2 - o*a**3 - 6591/4 = 0 for a.
-13
Suppose 0 = -4*l - 4*i + 124, -2*i - 2 = 6. Let q be 7/l + (-38)/(-10). Factor -4*f**3 - 4*f**q + 0*f - 50*f**2 + 58*f**2 + 0*f.
-4*f**2*(f - 1)*(f + 2)
Let y(g) be the first derivative of -g**3/3 + g - 74. Solve y(t) = 0.
-1, 1
Let q = -67 - -103. Let s be 38/12 + (-6)/q. Factor 11*j + 16*j**4 + 6*j**2 - 13*j + 22*j**s - 8*j**5 + 2*j.
-2*j**2*(j - 3)*(2*j + 1)**2
Let v(n) be the second derivative of n**4/21 - 64*n**3/7 + 4608*n**2/7 + 336*n. What is w in v(w) = 0?
48
Suppose -34 + 18 = w + 2*y, 4*w = -4*y - 24. Factor 0*j + 2/3*j**3 + 0*j**2 - 1/3*j**w + 0.
-j**3*(j - 2)/3
Let c(g) = g**2 + 6*g + 8. Let w be c(-4). Let h = 75 + -73. Find a such that 1/2*a + 1/2*a**3 + w - a**h = 0.
0, 1
Let m(r) = r**3 + r**2 - 4. Let h be m(0). Let p be (-8 + 4)*1 - 17/h. Factor p*g + 1/4*g**2 + 0.
g*(g + 1)/4
Let c = 63 + -60. Solve -16*k**4 + 48*k**5 + 0*k**5 + 4*k + 61*k**c - 97*k**3 = 0 for k.
-1/2, 0, 1/3, 1
Let s(d) = 16*d**4 + 26*d**3 - 72*d**2 + 42*d - 6. Let y(u) = -u**4 + u**3 + 2*u**2 + u. Let j(f) = -s(f) + 2*y(f). Let j(o) = 0. Calculate o.
-3, 1/3, 1
Factor -2/5*n**2 - 34/5 - 36/5*n.
-2*(n + 1)*(n + 17)/5
Suppose 0 = -3*o + 4*k + 9, -2*k + 27 = 2*o + o. Let l = 29 - 25. Determine a so that o*a - 4*a**2 - a**3 - 5*a - a**3 - 2*a**l + 6*a**2 = 0.
-1, 0, 1
Let i(b) = -14*b**5 + 10*b**4 - 4*b**3 + 12*b**2 + 18*b. Let a(u) = -u**3 + u**2 + u. Let p(y) = 44*a(y) - 2*i(y). Let p(o) = 0. Calculate o.
-1, -2/7, 0, 1
Let b(k) = k**2 - 4*k + 5. Let y(c) = 3*c**2 + 8*c - 10. Let a(n) = -n**2. Let l(i) = -6*a(i) - y(i). Let v(q) = -5*b(q) + 2*l(q). Solve v(s) = 0 for s.
-5, 1
Let o(m) be the third derivative of -m**6/30 + 4*m**5/15 - m**4/2 + 17*m**2. Find g such that o(g) = 0.
0, 1, 3
Let j be ((-2)/16)/(205/(-574)). Let g(n) be the second derivative of 11/12*n**4 - 7/6*n**3 + 9*n - n**2 - 3/10*n**6 + 0 + j*n**5. Suppose g(p) = 0. What is p?
-1, -2/9, 1
Let b(h) = 2*h**3 - 16*h**2 - 32*h - 29. Let a(n) = 3*n**3 - 30*n**2 - 64*n - 59. Let p(w) = -3*a(w) + 5*b(w). Factor p(t).
(t + 2)*(t + 4)**2
Let n = 65 + -65. Let c(t) = 2*t. Let r be c(0). Solve n - 2/9*k**3 + r*k - 2/9*k**2 = 0 for k.
-1, 0
Let k(l) = l**5 + l**4 - l**2. Let j(s) = -3*s**2 + 6*s**2 + 7*s**3 + s - 5*s**3 - 4*s**5 - 2*s - 3*s**4. Let i(x) = -5*j(x) - 15*k(x). Factor i(n).
5*n*(n - 1)**2*(n + 1)**2
Let m(c) be the first derivative of -2/33*c**3 - 2*c**2 - 1 + 0*c + 1/44*c**4 - 1/330*c**5. Let g(r) be the second derivative of m(r). Factor g(a).
-2*(a - 2)*(a - 1)/11
Let o(a) be the first derivative of 2*a**4 - 4*a**2 + 0*a + 2/3*a**3 - 11 - 2/5*a**5. Let o(u) = 0. What is u?
-1, 0, 1, 4
Let s(k) be the first derivative of k**6/4 - 9*k**5/5 + 15*k**4/4 - 33*k**2/4 + 9*k + 242. Find g such that s(g) = 0.
-1, 1, 2, 3
Let v(g) be the second derivative of -35/12*g**4 - 2*g - 1/4*g**5 - 25/2*g**3 - 45/2*g**2 - 10. Factor v(x).
-5*(x + 1)*(x + 3)**2
Suppose -12*y + 10*y = 8. Let n be 2/(-5) + -1*y/10. Suppose -2/7*p**3 + 8/7*p**5 + n*p**2 - 6/7*p**4 + 0 + 0*p = 0. Calculate p.
-1/4, 0, 1
Let u(i) = -i**2 + 13*i + 32. Let a be u(15). Let q be -4 - -11*1/a. Let -7/3*v**3 - 1/3 - 1/6*v**5 - v**4 - q*v - 8/3*v**2 = 0. Calculate v.
-2, -1
Let m(p) = -30*p**2 + 155*p + 115. Let i(n) = -15*n**2 + 78*n + 58. Let j(a) = -5*i(a) + 2*m(a). Determine b, given that j(b) = 0.
-2/3, 6
Find j, given that 0 - 108/7*j**2 - 8*j + 4/7*j**4 - 48/7*j**3 = 0.
-1, 0, 14
Let y(i) = -i**2 + 3*i + 6. Let b be y(5). Let d be 10/b*(-24)/30. Factor -3*a**4 + 4*a**5 - a**4 - d*a**3 - 6*a**5.
-2*a**3*(a + 1)**2
Let c(z) be the third derivative of 2*z**7/105 - 7*z**5/15 - z**4 - 18*z**2 - 5*z. Find j, given that c(j) = 0.
-2, -1, 0, 3
Suppose -3*f - 462*j + 22 = -460*j, 5*f - 5 = 3*j. Factor -5*p**3 + 5/3*p**f + 5*p**2 - 5/3*p + 0.
5*p*(p - 1)**3/3
Let m = 113 - 107. Let o(f) be the second derivative of 0*f**2 - 1/6*f**4 + 0 + 1/10*f**5 + 3*f - 1/3*f**3 + 1/15*f**m. Factor o(s).
2*s*(s - 1)*(s + 1)**2
Let s(q) be the first derivative of q**4/16 + 7*q**3/12 + 5*q**2/4 