 g(j).
-j*(j - 1)**2/3
Let l = 4 + -5. Let i(x) = 4*x**4 - 6*x**3 - 4*x**2 + 6. Let y(n) = n**4 - n**3 - n**2 + 1. Let j(f) = l*i(f) + 6*y(f). Let j(c) = 0. Calculate c.
-1, 0, 1
Let j(q) be the second derivative of -q**7/7560 + q**6/1080 - q**5/360 + q**4/12 + 3*q. Let w(o) be the third derivative of j(o). Suppose w(c) = 0. Calculate c.
1
Factor -64/5 - 4/5*q**2 - 32/5*q.
-4*(q + 4)**2/5
Let z(n) be the first derivative of -n**6/6 + 2*n**5/5 - n**4/4 - 39. Solve z(i) = 0 for i.
0, 1
Suppose -2*d + 90 = 3*d. Let q be 1/((-2 - -4)/d). Factor -8*o**3 - o**3 - 39*o**2 - 8 + q*o**2 + 0*o**3 - 28*o.
-(o + 2)*(3*o + 2)**2
Let q(y) be the first derivative of 2*y**3/9 - 5*y**2/3 - 28*y/3 + 4. Factor q(k).
2*(k - 7)*(k + 2)/3
Suppose -3/4 + 3/4*m + 3/4*m**2 - 3/4*m**3 = 0. Calculate m.
-1, 1
Find d such that 3/2*d - 3/4*d**4 + 0 + 3/4*d**2 - 3/2*d**3 = 0.
-2, -1, 0, 1
Determine v, given that 6/7*v + 2/7*v**2 + 4/7 = 0.
-2, -1
Let n(v) be the first derivative of -2/7*v - 2/35*v**5 - 1/21*v**6 - 2 + 1/7*v**4 + 4/21*v**3 - 1/7*v**2. Factor n(r).
-2*(r - 1)**2*(r + 1)**3/7
Let v = 62/231 - -10/33. Factor -2/7*i**5 - v*i**2 + 4/7*i**4 + 0 + 0*i**3 + 2/7*i.
-2*i*(i - 1)**3*(i + 1)/7
Let z(v) be the second derivative of v**6/75 - v**5/50 + 13*v. Find q such that z(q) = 0.
0, 1
Let s(g) be the second derivative of -g**4/24 + 9*g. Let s(c) = 0. What is c?
0
Let d(j) = -3*j**4 - 20*j**3 - 10*j**2 - 12*j - 3. Let i(z) = z**4 + 7*z**3 + 3*z**2 + 4*z + 1. Let g(b) = 3*d(b) + 8*i(b). Suppose g(n) = 0. What is n?
-1
Factor 6*k**3 + 9*k - 5*k**3 + 5*k**3 + 9*k**2 - 3*k**3 + 3.
3*(k + 1)**3
Let b(h) be the third derivative of -1/40*h**4 + 1/100*h**6 + h**2 + 1/50*h**5 - 1/10*h**3 - 1/350*h**7 - 1/560*h**8 + 0 + 0*h. Suppose b(w) = 0. What is w?
-1, 1
Let l(z) be the second derivative of 2/9*z**3 - 3*z + 0 + 1/36*z**4 + 1/2*z**2. Solve l(m) = 0.
-3, -1
Let o(x) = -x**5 + 20*x**4 - 25*x**3 + 10*x**2 - 4*x - 4. Let v(c) = -2*c**5 + 20*c**4 - 25*c**3 + 10*c**2 - 3*c - 3. Let b(i) = -3*o(i) + 4*v(i). Factor b(w).
-5*w**2*(w - 2)*(w - 1)**2
Let f(c) = -4*c**3 + 4*c**2 - 4*c - 4. Let b(v) = -v**2 + v + 1. Let a(j) = 8*b(j) + f(j). Factor a(n).
-4*(n - 1)*(n + 1)**2
Let a(f) = -f**4 - 2*f**3 - 4*f**2 - 3*f + 5. Let u(r) = r**2 + r - 1. Let i(j) = -4*a(j) - 20*u(j). Factor i(s).
4*s*(s - 1)*(s + 1)*(s + 2)
Let y(p) be the second derivative of p**4/12 - 9*p. Determine k so that y(k) = 0.
0
Suppose -12/7*q**3 + 24/7*q**2 + 2/7*q**4 + 6/7 - 20/7*q = 0. What is q?
1, 3
Suppose -5*h**2 - 5*h**3 - h**4 - 4*h**2 - 4*h + 0*h**4 + h**2 = 0. Calculate h.
-2, -1, 0
Let v(u) = 6*u - 4*u + u**3 + 2*u**2 + 0*u - 5*u**3. Let a(t) = -1 + t**3 - t**2 + 1. Let x(k) = 2*a(k) + v(k). Factor x(q).
-2*q*(q - 1)*(q + 1)
Let q(r) = -r**2 + 4*r. Let z(f) = f. Let u(m) = -q(m) + 5*z(m). Let j be u(-2). Factor 0 - 1/2*o + 1/2*o**3 + 0*o**j.
o*(o - 1)*(o + 1)/2
Let t(r) be the second derivative of 2/9*r**4 + 1/5*r**5 + 0 + 0*r**2 + 1/9*r**3 + 4/45*r**6 + 3*r + 1/63*r**7. Factor t(o).
2*o*(o + 1)**4/3
Let r(q) = -q**2 + 11*q + 15. Let l be r(11). Find v, given that -13*v**3 + 4*v**3 - 61 - l*v + 64 + 21*v**2 = 0.
1/3, 1
Factor 4/5 + 4/5*x**2 - 8/5*x.
4*(x - 1)**2/5
Factor 9*y**3 - 2*y**5 + 3*y + 3 + 14*y**2 - 2 - 9*y - 25*y**3 + 9*y**4.
-(y - 1)**4*(2*y - 1)
Let y(i) be the third derivative of i**5/60 - i**4/8 + i**3/3 + 2*i**2. What is w in y(w) = 0?
1, 2
Suppose 3*g - 10 = -4. Let f = g + 2. Factor -4*q**3 + 3 + f*q - 2*q**2 - 2 + q**2.
-(q - 1)*(q + 1)*(4*q + 1)
Factor 2/7*s**4 + 6/7*s**3 + 4/7*s**2 + 0*s + 0.
2*s**2*(s + 1)*(s + 2)/7
Factor 2/3*z**2 + 4*z + 6.
2*(z + 3)**2/3
Let h(j) be the third derivative of -j**8/336 - j**7/105 + j**6/60 + j**5/15 - j**4/24 - j**3/3 - 6*j**2. Determine v, given that h(v) = 0.
-2, -1, 1
Let v = -7597/9 - -845. Let v + 2/9*t**2 - 8/9*t = 0. What is t?
2
Determine v so that 1/5*v**3 + 1/5 + 3/5*v + 3/5*v**2 = 0.
-1
Let t(k) be the first derivative of 1 - 4/9*k**3 + 0*k - 1/3*k**2 - 1/6*k**4. Solve t(s) = 0.
-1, 0
Let x(z) be the third derivative of 0*z**3 - 1/240*z**6 - 1/48*z**4 + 0*z - 5*z**2 + 0 + 1/60*z**5. Find g, given that x(g) = 0.
0, 1
Let f(j) be the first derivative of -j**5/15 + j**4/12 + j**3/9 - j**2/6 + 6. Factor f(m).
-m*(m - 1)**2*(m + 1)/3
Suppose 8*u**4 - 7*u**3 + 8*u**3 - 4*u**5 - 5*u**3 = 0. Calculate u.
0, 1
Factor 77*k - 32*k**2 + 52*k + 64 - k - 96*k**3 + 0 + 36*k**4.
4*(k - 2)**2*(3*k + 2)**2
Suppose 220 = 2*z + t - 255, z - 5*t - 254 = 0. Find m such that 143*m**2 + 64*m**3 - 8 - z*m**2 - 50*m - 10*m = 0.
-1/4, 2
Let y(z) be the second derivative of -z**6/480 + z**5/80 - z**4/32 + 5*z**3/6 + 6*z. Let x(u) be the second derivative of y(u). Factor x(j).
-3*(j - 1)**2/4
Let p = 5 - 2. Suppose p*t - 32 = -t. Solve j - 3*j + t*j - 2*j**2 - 4 = 0.
1, 2
Let t(r) = -3*r**4 - 21*r**3 - 16*r**2 + 2. Let f(w) = w**2 + 1. Let m(i) = -2*f(i) + t(i). Factor m(u).
-3*u**2*(u + 1)*(u + 6)
Let i = 4 + -2. Let j(s) = s. Let n be j(i). What is z in z**3 + z**n + 0*z**3 - 4*z**3 = 0?
0, 1/3
Suppose 5*d - 15 - 1 = 2*t, 4*d = 2*t + 12. Factor -5 + 5 + d*c**2 - 4*c**3.
-4*c**2*(c - 1)
Let p be 3 + (-1 - 123/63). Let w = 2/7 + p. Suppose 1/3*i - 1/3*i**2 + 1/3*i**4 - w*i**3 + 0 = 0. What is i?
-1, 0, 1
Let b be 4 - 3 - (-4 - (2 - 5)). Let m = 5 - 2. Find t such that 3*t**3 - t**3 - 5*t**3 + b*t**5 + t**m = 0.
-1, 0, 1
Let d(r) be the third derivative of -r**7/210 + r**6/60 - r**5/60 + 3*r**2. Solve d(k) = 0.
0, 1
Let d(h) be the second derivative of -1/4*h**4 - h**2 - 7/6*h**3 + 7/20*h**5 + 0 + 3*h + 1/6*h**6. Factor d(o).
(o - 1)*(o + 1)**2*(5*o + 2)
Let t(r) = r**2 - r - 2. Let f be t(2). Suppose -2*k + 3*i = f, 0 = -4*k + i - 4*i. Factor 0*v**3 - 1/5 - 1/5*v**4 + 2/5*v**2 + k*v.
-(v - 1)**2*(v + 1)**2/5
Let h(q) = q**3 - 3*q**2 + 2*q + 2. Suppose -m + 12 = 2. Let x(n) = 3*n**3 - 7*n**2 + 5*n + 5. Let g(y) = m*h(y) - 4*x(y). Solve g(i) = 0.
-1, 0
Let b(j) be the third derivative of -j**7/10 + 2*j**6/5 - j**5/5 - 4*j**2. Suppose b(f) = 0. Calculate f.
0, 2/7, 2
Determine g so that -3/7*g**2 - 18/7*g**3 - 3/7*g**4 + 6/7*g + 6/7*g**5 + 0 = 0.
-1, 0, 1/2, 2
Let r = 111 - 109. Factor -3/4*j**3 - 3/4 - 9/4*j - 9/4*j**r.
-3*(j + 1)**3/4
Let o = 487 - 1909/4. Find b, given that 3/4*b**4 + 9/2*b**3 + o*b**2 + 3 + 9*b = 0.
-2, -1
Factor 2*d**3 + 0*d**3 - 5*d**3 - 6*d**2 + 6 + 3*d.
-3*(d - 1)*(d + 1)*(d + 2)
Let t(s) = 2*s**2 + 5*s. Let x be t(-3). Solve 2/7*a - 2/7*a**x + 2/7*a**2 - 2/7 = 0.
-1, 1
Let u(h) be the first derivative of -2*h**5/95 + 4*h**3/57 - 2*h/19 + 12. Factor u(p).
-2*(p - 1)**2*(p + 1)**2/19
Let z(v) be the first derivative of -v**5 - 5*v**4/2 + 5*v**3/3 + 5*v**2 - 6. Factor z(u).
-5*u*(u - 1)*(u + 1)*(u + 2)
Let t = 9 - 17. Let y = -8 - t. Factor 1/4*l**3 + 0 + y*l + 0*l**2 - 1/4*l**4.
-l**3*(l - 1)/4
Suppose -5*f + 27 = 2*y, 0 = -7*f + 3*f + 5*y + 15. Factor 3/4*v**3 + 1/4*v**f + 0*v + 0 + 1/4*v**2 + 3/4*v**4.
v**2*(v + 1)**3/4
Let y(o) = -3*o**3 + 5*o**2 + o. Let i(m) = -2*m**3 + 4*m**2 + 2*m. Let h(b) = 3*i(b) - 4*y(b). Determine u, given that h(u) = 0.
0, 1/3, 1
Let g(i) be the first derivative of i**6/2 - 3*i**4/2 + 3*i**2/2 + 5. Factor g(v).
3*v*(v - 1)**2*(v + 1)**2
Suppose l + 2*f = -4, -l + 4*f + 8 = 4*l. Let t(k) be the third derivative of k**2 + 1/21*k**3 - 1/210*k**5 + 0*k**4 + l + 0*k. Solve t(c) = 0 for c.
-1, 1
Factor -8 - 4*u**3 + 5*u**4 + 200*u + 88 + 165*u**2 + 42*u**3 + 12*u**3.
5*(u + 1)**2*(u + 4)**2
Let l = -16 - -12. Let u be 2/(1 + l/12). Factor -2/3*o**4 + 2*o**2 + 0*o**u - 4/3*o + 0.
-2*o*(o - 1)**2*(o + 2)/3
Let l(o) be the third derivative of o**6/480 - o**5/80 + o**4/48 - 39*o**2. Determine i, given that l(i) = 0.
0, 1, 2
Let l(a) be the second derivative of 0*a**2 + 3*a + 0 + 1/12*a**3 + 1/16*a**4 + 1/80*a**5. Factor l(f).
f*(f + 1)*(f + 2)/4
Let x(p) = -p**3 - 5*p**2 - 6*p. Let i be x(-4). Let j = i - 8. Solve -1/4*n - 3/4*n**2 - 3/4*n**3 + j - 1/4*n**4 = 0.
-1, 0
Solve 0*g - 3/2*g**2 + 0*g**4 + 0 + 9/4*g**3 - 3/4*g**5 = 0 for g.
-2, 0, 1
Suppose -55 = 3*u + 11. Let g = 100 + u. Solve -4 + 20*m**3 - 15*m - 66*m**2 - 18*m**4 - 15*m - g*m**3 = 0 for m.
-1, -2/9
Let a(n) = -n - 10. Let m be a(-9). Let k(x) = x**3 - 2*x - 1. Let o be k(m). Suppose 0*f**3 + 0 + 2/5*f**4 + 0*f**2 + 2/5*f**5 + o*f = 0. Calculate f.
-1, 0
Let l