 i(j).
5*j*(j - 1)**3*(j + 1)
Let z(m) be the first derivative of -1 + 0*m - 2/9*m**3 - 1/3*m**2. Factor z(g).
-2*g*(g + 1)/3
Let o = -7 + 9. Let d = o + 1. Let 2/7*m**2 + 4/7*m**5 + 0 + 6/7*m**d - 2/7*m - 10/7*m**4 = 0. Calculate m.
-1/2, 0, 1
Let g(z) = z**3 + 1. Let c(k) = -k**3 - k**2 - k. Let a(o) = 11*o**3 + 3*o**2 + 4*o + 6. Let h(r) = -a(r) - 4*c(r). Let y(j) = 6*g(j) + h(j). Factor y(u).
-u**2*(u - 1)
Let l(t) be the second derivative of -t**8/224 + t**7/120 - t**5/240 + 2*t**2 - 2*t. Let r(d) be the first derivative of l(d). Determine h, given that r(h) = 0.
-1/3, 0, 1/2, 1
Let y(g) be the second derivative of -g**6/60 - g**5/10 + g**4/12 + g**3 - 9*g**2/4 + 6*g. Let y(f) = 0. What is f?
-3, 1
Solve 1/5 - 2/5*d + 1/5*d**2 = 0.
1
Let l be (-4)/(-2) + 956/(-480). Let y(v) be the third derivative of -1/6*v**3 - 1/8*v**4 + 0*v - v**2 - l*v**6 - 1/20*v**5 + 0. Let y(w) = 0. Calculate w.
-1
Factor 1/4*l**4 + 1/2*l + 0 + l**3 + 5/4*l**2.
l*(l + 1)**2*(l + 2)/4
Let u(h) be the first derivative of h**5/40 - h**3/4 - h**2/2 + 7*h - 6. Let p(t) be the first derivative of u(t). Factor p(w).
(w - 2)*(w + 1)**2/2
Let t(x) = 2*x + 37. Let d be t(-17). Find m such that -2/11*m**4 + 0*m + 2/11*m**2 - 2/11*m**d + 0 + 2/11*m**5 = 0.
-1, 0, 1
Let r(m) = 6*m**2 - 17*m + 1. Let q(h) = 6*h**2 - 18*h + 2. Let f(u) = 7*q(u) - 6*r(u). Let y(j) = 2*j**2 - 8*j + 3. Let o(n) = 5*f(n) - 16*y(n). Factor o(b).
-2*(b - 2)**2
Let d = 128396/5 - 910422/35. Let t = -332 - d. Find p, given that 2/7*p**5 + 4/7*p**3 - 6/7*p - 2/7 - 4/7*p**2 + t*p**4 = 0.
-1, 1
Let s = 23/33 - 1/33. Let v be (4/(-6))/((-3)/6). What is a in s*a + v - 2/3*a**2 = 0?
-1, 2
Factor 0 + 1/3*r**4 - 2/3*r**2 - 1/3*r**3 + 0*r.
r**2*(r - 2)*(r + 1)/3
Let p(z) be the third derivative of -z**9/30240 + z**8/3360 - z**7/1260 - z**4/12 - 3*z**2. Let g(x) be the second derivative of p(x). Factor g(q).
-q**2*(q - 2)**2/2
Let l be (-2)/(-3) - 8/12. Suppose -5*f + l*f = -20. Factor -2*x**3 - 2 - 2*x**4 + f*x**2 + 2*x**3.
-2*(x - 1)**2*(x + 1)**2
Suppose -5*i + 5 = -10. Suppose -3*t**3 + i - 3 - 3*t**2 = 0. Calculate t.
-1, 0
Suppose 3*p = -0*p + 6. Suppose p*r = x + 4*r - 2, 5*r = -3*x + 5. Determine u so that x*u - 10/9*u**3 + 2*u**5 - 2/9*u**2 - 2/3*u**4 + 0 = 0.
-1/3, 0, 1
Suppose 0 = -0*a - 2*a - 10. Let j = 10 + a. Determine t so that -3*t**3 + 0 + 2*t**2 - 1/2*t**j + 2*t**4 - 1/2*t = 0.
0, 1
Factor -1 + 5/2*j - 2*j**2 + 1/2*j**3.
(j - 2)*(j - 1)**2/2
Let z(i) = 16*i**3 + 20*i**2 - 18*i + 27. Let o(a) = a**3 + a**2 + a + 2. Let t(l) = 18*o(l) - 2*z(l). Let t(s) = 0. What is s?
-3, 3/7, 1
Let w be ((-24)/(-20))/((-2)/(-145)). Let y = 263/3 - w. Suppose -2/3*s**5 + 0*s**2 + 0*s + 0 + y*s**3 + 0*s**4 = 0. Calculate s.
-1, 0, 1
Let h(j) be the first derivative of -2*j**3 + 4/5*j**5 + 2*j + 2 + 1/2*j**4 - j**2. Factor h(c).
2*(c - 1)*(c + 1)**2*(2*c - 1)
Let s(l) = -l**4 - 8*l**3 + 3*l - 9. Let u(p) = -p**4 - 4*p**3 + p - 5. Let g(a) = 3*s(a) - 5*u(a). Find z, given that g(z) = 0.
-1, 1
Suppose 2 = -4*l + 2. Let t(y) be the third derivative of 0*y + 0 - 2*y**2 - 1/30*y**5 + l*y**4 + 0*y**3 - 1/120*y**6. Factor t(g).
-g**2*(g + 2)
Let a be (-1)/(-3)*14/21. Let f(t) be the first derivative of 2/3*t - 1/6*t**4 - a*t**3 + 1/3*t**2 + 2. Determine y, given that f(y) = 0.
-1, 1
Let h(g) = -g**2 + 3*g - g**3 - 6*g + 5 + 2*g. Let m be h(0). What is j in j**2 - m*j**2 - 24*j**3 + 45*j**4 + 8*j**2 - 25*j**5 = 0?
0, 2/5, 1
Let c(k) be the first derivative of -k**6 - 3*k**5/5 + 3*k**4/2 + k**3 - 3. Suppose c(n) = 0. Calculate n.
-1, -1/2, 0, 1
Let v(y) be the third derivative of 1/660*y**6 + 0*y**4 + 0 + 0*y**5 + y**2 + 0*y + 0*y**3. Let v(c) = 0. What is c?
0
Let i be 63/105 + 3/20. Factor 0 + 3/4*b + 3/4*b**2 - 3/4*b**3 - i*b**4.
-3*b*(b - 1)*(b + 1)**2/4
Let t = -1 + 0. Let x be -2*((-15)/6 - t). What is y in -y**3 - 3*y**x + y**5 + 2*y + y**5 = 0?
-1, 0, 1
Let r be 2 + 14/6 + -4. Factor r + u + u**2 + 1/3*u**3.
(u + 1)**3/3
Let g(a) be the first derivative of -6 - 2/5*a**2 - 4/15*a**3 - 1/5*a. Solve g(u) = 0.
-1/2
Let c(l) be the third derivative of -3*l**8/112 - l**7/14 + l**6/40 + l**5/4 + l**4/4 - l**2. Find k such that c(k) = 0.
-1, -2/3, 0, 1
Let c(t) be the second derivative of -t**6/105 - t**5/70 + t**4/14 + 5*t**3/21 + 2*t**2/7 + 64*t. Factor c(k).
-2*(k - 2)*(k + 1)**3/7
Let a = 104/153 - 2/153. Let m(p) be the third derivative of 3*p**2 - 1/30*p**5 - a*p**3 + 0 + 0*p + 1/4*p**4. Solve m(b) = 0 for b.
1, 2
Let m(h) = h**2 + 8*h + 9. Let s be m(-7). Let z be (-3 - -2)*-4*4/56. Factor 4/7*p - 2/7 - z*p**s.
-2*(p - 1)**2/7
Let t(u) be the first derivative of -u**9/3024 + u**8/840 - u**6/180 + u**5/120 - 2*u**3/3 - 3. Let x(m) be the third derivative of t(m). Factor x(b).
-b*(b - 1)**3*(b + 1)
Let g(h) be the first derivative of 3/10*h**2 + 1/5*h + 1/20*h**4 + 1/5*h**3 - 1. Find m such that g(m) = 0.
-1
Let 9*i**3 + 4*i**2 + 8*i**5 - 5*i**4 - 10*i**3 + i**4 - 7*i**3 = 0. What is i?
-1, 0, 1/2, 1
Suppose 2*b = 2*c - 4, 4*b - c - 2*c + 6 = 0. Let w = 2 + b. Solve -2*y**4 + 4*y - 4*y**3 + 0*y**4 - w + 4 = 0.
-1, 1
Let o(h) = -h**4 + h**3 - h**2 - h + 1. Let w(f) = -5*f**4 + 6*f**3 - 3*f**2 - 6*f + 4. Let c(p) = 4*o(p) - w(p). Factor c(y).
y*(y - 2)*(y - 1)*(y + 1)
Solve 44*n + 3*n**2 - 36*n + n**2 = 0.
-2, 0
Solve 5*z**2 - 29*z**2 - 2*z**3 + 7*z**3 + 5*z**3 + 18*z - 4 = 0.
2/5, 1
Let u = 5 - 7. Let g be u/3 + (-110)/(-75). Determine v, given that -g - 2/5*v**2 - 6/5*v = 0.
-2, -1
Suppose 12*j = s + 8*j - 14, -25 = -5*s + 5*j. Let c(g) be the second derivative of 0 + 0*g**2 + s*g - 5/8*g**4 - 1/2*g**3. Factor c(u).
-3*u*(5*u + 2)/2
Suppose -6*w - 5 = -2*d - w, 22 = 4*d + 2*w. Suppose -3*l + 6 = -d*v - 0, 0 = 3*v. Factor -p**l - 4 - 2*p**2 + 2*p**2 + 4*p.
-(p - 2)**2
Let k(h) = -3*h + 1. Let s be k(-1). Let u = s - 0. Let -u + i**2 + 4 = 0. Calculate i.
0
Factor 40/7 + 4/7*r**2 + 4*r.
4*(r + 2)*(r + 5)/7
Let o(s) = -s**3 - 9*s**2 - 13*s + 13. Let c be o(-7). Solve c - 4*d + 2/3*d**2 = 0 for d.
3
Suppose -3*y - 3*f = -9 - 3, 2*y = f + 5. Let h be 30/8*1/y. Let h*b**4 + 0*b - 4*b**3 + 25/4*b**5 + 0 + b**2 = 0. Calculate b.
-1, 0, 2/5
Let c be (1 - 0)/(1/6). Let z(p) be the second derivative of 1/40*p**c + 1/2*p**2 - 2*p + 1/80*p**5 - 7/48*p**4 - 1/168*p**7 + 0*p**3 + 0. Solve z(b) = 0 for b.
-1, 1, 2
Let b(s) be the second derivative of s**5/20 - s**4/12 + s. Let o be b(1). Solve 2*n**2 - 1 - 3*n**2 + o*n**2 + 2*n = 0 for n.
1
Let g(h) be the first derivative of 5*h**4/12 + h**3/2 - h**2 + 2*h + 4. Let n(p) be the first derivative of g(p). Factor n(l).
(l + 1)*(5*l - 2)
Let h(g) = 3*g**3 - 25*g**2 + 133*g - 203. Let w(d) = d**3 - 8*d**2 + 44*d - 68. Let t(q) = -4*h(q) + 11*w(q). Factor t(z).
-(z - 4)**3
Let c(i) be the first derivative of i**6/10 + 3*i**5/5 + 9*i**4/10 - 2*i**3/5 - 21*i**2/10 - 9*i/5 - 47. Find v such that c(v) = 0.
-3, -1, 1
Let g(b) be the second derivative of b**4/6 - b**2 + 16*b. Find l, given that g(l) = 0.
-1, 1
Suppose -r + 8 = 3*r. Solve -5*k - 2 - k - 2*k**r + 2*k = 0 for k.
-1
Let q(t) be the second derivative of -t**4/48 + t**3/24 + t**2/4 + t. Find p such that q(p) = 0.
-1, 2
Factor 12*a**2 + 1 - 3*a**3 - 6*a - 12 - 1 + 9*a.
-3*(a - 4)*(a - 1)*(a + 1)
Suppose -2*c + 3*n = -10, 2*c = 7*c + 3*n - 4. Suppose -5*u + 2 = -2*d, -d - c*u = -5*d + 12. What is q in 7*q + d*q**3 - 4 + 11*q - 24*q**2 + 6*q**3 = 0?
2/5, 1
Determine s so that -10*s**3 - 66*s**2 + 12*s**3 + 72*s**2 + 4*s = 0.
-2, -1, 0
Let s(c) be the second derivative of -3*c**5/10 - 5*c**4/8 - 20*c. Find d, given that s(d) = 0.
-5/4, 0
Let h(w) be the third derivative of -w**5/60 - w**4/12 - w**3/6 + 7*w**2. Factor h(i).
-(i + 1)**2
Let d(m) = m**5 - m**3 + m**2 - m + 1. Let t(o) = 3*o**5 + 5*o**4 - 5*o**3 + o**2 - 4*o + 6. Let x(a) = -30*d(a) + 5*t(a). Find y, given that x(y) = 0.
-1, 0, 2/3, 1
Let q = -5 - -5. Let -2*a**3 + 0*a**4 + 2*a + q*a**4 - 3*a**2 + 4*a**2 - a**4 = 0. Calculate a.
-2, -1, 0, 1
Let s(u) = u**3 - 3*u**2 + 3*u - 1. Let x be s(4). Suppose -9*l = -6*l - 6. Let 28*k**2 - x*k**l + 1 + 1 - 3*k = 0. What is k?
1, 2
Let q be 338/(-3) - (-4)/6. Let v be 2/8*q/(-70). Factor -4/5 - v*z**2 - 6/5*z.
-2*(z + 1)*(z + 2)/5
Let h(f) be the second derivative of -f**6/30 + 3*f**5/10 - f**4/12 - 4*f**3 - 8*f**2 - 20*f. Factor h