2*y**2 - 3*y. Let j(z) = -f(z) + 3*p(z). Factor j(r).
-r**2*(r - 1)*(3*r - 1)
Let n(d) be the first derivative of -d**6/2 + 6*d**5/5 - 2*d**3 + 3*d**2/2 - 3. What is i in n(i) = 0?
-1, 0, 1
Let -4/5*j + 6/5*j**2 + 2/5*j**5 + 0 - 6/5*j**4 + 2/5*j**3 = 0. Calculate j.
-1, 0, 1, 2
Let q(x) be the first derivative of -40*x**6/3 - 12*x**5/5 + 62*x**4 - 124*x**3/3 - 24*x**2 + 16*x + 1. Solve q(p) = 0 for p.
-2, -2/5, 1/4, 1
Let 0 + 2/11*d**4 + 0*d**3 + 0*d - 2/11*d**5 + 0*d**2 = 0. Calculate d.
0, 1
Let o(d) = -5*d + 6 + 8*d + 9*d**2 - 3 + 2. Let s(i) = i**2 - i + 1. Let v(b) = -o(b) + 5*s(b). Suppose v(t) = 0. Calculate t.
-2, 0
Let j(f) be the second derivative of f**5/60 + f**4/18 + f**3/18 + 4*f. Factor j(s).
s*(s + 1)**2/3
Determine x so that -4*x**5 - 14*x**3 - 6*x**2 - 12*x**4 - x**3 + x**5 = 0.
-2, -1, 0
Let i(f) = -27*f - 187. Let q be i(-7). Factor 0*h**q + 2/7*h**3 + 0 - 2/7*h.
2*h*(h - 1)*(h + 1)/7
Let o = -18 + -21. Let g = -116/3 - o. Suppose -g*r**2 + 1/3*r**3 + 1/3*r**4 + 0 - 1/3*r = 0. What is r?
-1, 0, 1
Let o be 0/((-14)/((-112)/(-40))). Factor 8/9*a**2 + o + 2/9*a + 8/9*a**3.
2*a*(2*a + 1)**2/9
Let t(o) = -o**4 - 5*o**3 + 13*o**2 + 11*o - 12. Let p(d) = -6*d**4 - 26*d**3 + 66*d**2 + 54*d - 60. Let g(f) = 3*p(f) - 14*t(f). Factor g(c).
-4*(c - 1)**2*(c + 1)*(c + 3)
Suppose 379 = 8*f + 347. Determine x so that -4*x**3 + 8/3 + 26/3*x**2 - 8*x + 2/3*x**f = 0.
1, 2
What is j in 5 - 25*j**2 + j**3 - 5*j + 1 + 23*j**2 = 0?
-2, 1, 3
Let i(a) be the second derivative of -a**6/15 + a**4/6 + 6*a. Factor i(b).
-2*b**2*(b - 1)*(b + 1)
Let w = -39 - -35. Let d be (-4)/(w/(-3)) + 6. Determine f, given that 88/9*f - 14/9*f**4 + 74/9*f**d - 44/3*f**2 - 16/9 = 0.
2/7, 1, 2
Let o be (0 + -3 + 5)*2. Factor 6*u**2 + 3*u**o + u**4 - 7*u**4 + 3*u**3.
-3*u**2*(u - 2)*(u + 1)
Let u(c) be the third derivative of -c**9/272160 - c**8/45360 - c**7/22680 + c**5/30 + c**2. Let f(m) be the third derivative of u(m). What is z in f(z) = 0?
-1, 0
Suppose -16*f = -12*f. Factor 1/4*c**2 - 1/2*c**3 + 1/4*c**4 + 0 + f*c.
c**2*(c - 1)**2/4
Let i(h) = h + 1. Let t(d) = d**2 + 4 - 4 - 4*d - 3 + 2. Let z(u) = 4*i(u) + 2*t(u). Factor z(q).
2*(q - 1)**2
Suppose 5*y = -0*y - 2*y. Factor -2/3*k**2 + y - 2/3*k.
-2*k*(k + 1)/3
Suppose 51 - 15 = 2*h. Let k be h/110 + (-2)/(-10). Factor 0*r**2 + 4/11*r**3 + 2/11 - k*r - 2/11*r**4.
-2*(r - 1)**3*(r + 1)/11
Factor -27/2*a**3 + 0 + 30*a**2 - 6*a.
-3*a*(a - 2)*(9*a - 2)/2
Let b(j) = -j**2 - 5*j - 2. Let y = -1 + -3. Let c be b(y). Factor -a**c - a**2 + 3 - 2 + a**2.
-(a - 1)*(a + 1)
Let -5*p**2 - 4/3 + 7/3*p**3 + 13/3*p - 1/3*p**4 = 0. Calculate p.
1, 4
Let j(y) = -2*y**3 + 9*y**2 + 5*y + 4. Let f be j(5). Factor o**3 - 3/2*o + o**2 - 3/2*o**f + 1/2 + 1/2*o**5.
(o - 1)**4*(o + 1)/2
Suppose -5*b = -3*b - 6. Let q = 0 + 1. Factor 1 + j**b - j**5 - q.
-j**3*(j - 1)*(j + 1)
Let h = 344/835 - 2/167. Factor -1/5*s**3 - 2/5 + 1/5*s + h*s**2.
-(s - 2)*(s - 1)*(s + 1)/5
Let p(y) be the first derivative of y**3/9 + y**2/2 - 14. Solve p(r) = 0.
-3, 0
Let c(i) be the first derivative of 0*i**4 + 1 + 1/24*i**3 + 1/2*i**2 - 1/240*i**5 + 0*i. Let t(n) be the second derivative of c(n). Factor t(y).
-(y - 1)*(y + 1)/4
Suppose 2*j - 2 = b, -b + 0*b - 6 = -4*j. Let 18*o**4 - 2*o**5 - 15*o**4 + o**j + o**5 - 3*o**3 = 0. What is o?
0, 1
Let u(b) be the second derivative of b**4/3 - 10*b**3/3 + 8*b**2 + 9*b. Let u(p) = 0. What is p?
1, 4
Let f(b) be the third derivative of b**6/1980 - b**5/660 + 5*b**3/6 + b**2. Let m(y) be the first derivative of f(y). Factor m(p).
2*p*(p - 1)/11
Let j(x) be the second derivative of -2*x**7/21 + 8*x**6/15 - x**5 + 2*x**4/3 + 15*x. Factor j(u).
-4*u**2*(u - 2)*(u - 1)**2
Factor 3 - q**4 - 2*q**4 + 8*q**3 - 6*q - 2*q**3.
-3*(q - 1)**3*(q + 1)
Suppose 14*f - 20*f = -12. Determine t so that 0 + 4/7*t + 2/7*t**f - 2/7*t**3 = 0.
-1, 0, 2
Let u(w) be the second derivative of w**6/360 - w**5/20 + 3*w**4/8 + w**3 + 6*w. Let o(t) be the second derivative of u(t). Find m, given that o(m) = 0.
3
Let a(d) be the second derivative of 0*d**3 + 0 + 2*d - 1/45*d**4 + 0*d**2 - 1/150*d**5. Solve a(x) = 0 for x.
-2, 0
Suppose 16 = 4*n - 4. Let m be (-8)/(-20) + 8/n. Factor 3*r**2 - m*r**2 - 2*r + r.
r*(r - 1)
Let z(a) = -4*a**2 + 13*a + 4. Let d(q) = q**2 - 4*q - 1. Let b(x) = -7*d(x) - 2*z(x). Let c be b(1). Factor 2/3*p**5 + 2*p**4 + 2/3*p**c + 0 + 2*p**3 + 0*p.
2*p**2*(p + 1)**3/3
Let m = 56/13 - -83/26. Suppose m*d**4 - 15/2*d**2 + 0 + 3*d - 3*d**3 = 0. Calculate d.
-1, 0, 2/5, 1
Let j be 7/(-4) + 2 + 19/(-84). Let b(u) be the third derivative of 0*u - 1/210*u**5 + 0 + j*u**4 + 0*u**3 + 2*u**2. Let b(g) = 0. Calculate g.
0, 2
Find p such that 0 + 3/4*p**4 + 0*p**3 - 3*p**2 + 0*p = 0.
-2, 0, 2
Let q(u) = 5*u**2 - 5. Let k be (-5)/((-15)/2)*-33. Let t(j) = -j**2 + 1. Let i(f) = k*t(f) - 4*q(f). Let i(g) = 0. Calculate g.
-1, 1
Let k = 4 + 1. Factor 7*x**4 + 2*x**k + 7*x**3 + 2*x**2 - 6*x + 6*x.
x**2*(x + 1)*(x + 2)*(2*x + 1)
Let z(j) be the second derivative of -j**7/42 + j**6/5 - 7*j**5/10 + 4*j**4/3 - 3*j**3/2 + j**2 - 7*j. Find o such that z(o) = 0.
1, 2
Suppose 2*t = k + k - 14, k + t - 1 = 0. Suppose 0 = h - k*h + 6. Let -2*f**h + 0 + 10*f + 10*f**2 + 2*f**3 + 4 = 0. Calculate f.
-2, -1
Let p(q) be the first derivative of -1/54*q**4 - 1/2*q**2 + 1/27*q**3 + 1/270*q**5 + 2 + 0*q. Let f(l) be the second derivative of p(l). Factor f(s).
2*(s - 1)**2/9
Let n(m) be the first derivative of -m**3/9 - m**2/6 + 2*m/3 + 8. Find z, given that n(z) = 0.
-2, 1
Let i(n) = -n**2 - 2*n + 1. Let t be i(-1). Factor 0 + 0*w - 1/4*w**t + 1/4*w**3.
w**2*(w - 1)/4
Let r be (-14)/(3/(6/4)). Let n be (-19)/r - (-2)/7. Solve 2*a**3 - a**n + 0*a**3 - a = 0.
-1, 0, 1
Let a(w) = 5*w**4 + 3*w**3 - 3*w**2 - w. Let q(d) = d**4 + d**3. Let x(k) = -a(k) + 6*q(k). Factor x(p).
p*(p + 1)**3
Suppose -6*k - 27 = -15*k. Suppose 3/5*u**2 - 4/5*u**k + 4/5*u - 4/5 + 1/5*u**4 = 0. Calculate u.
-1, 1, 2
Let u(v) be the second derivative of -1/150*v**5 + 0 + 0*v**2 + 0*v**3 + v + 1/45*v**4. Factor u(j).
-2*j**2*(j - 2)/15
Let h = -19 + 22. Factor 3*i**2 - 2*i**4 + i**2 - 4*i**4 - 2*i**h.
-2*i**2*(i + 1)*(3*i - 2)
Let d(x) = -11*x**2 + 16*x - 2. Let p(g) = -23*g**2 + 34*g - 5. Let f(k) = -5*d(k) + 2*p(k). Factor f(o).
3*o*(3*o - 4)
Let i(y) = -14*y**4 + 30*y**3 - 6*y**2 + 2*y + 2. Let a(g) = -43*g**4 + 91*g**3 - 17*g**2 + 7*g + 7. Let l(u) = 2*a(u) - 7*i(u). Factor l(x).
4*x**2*(x - 2)*(3*x - 1)
Factor 15*k**2 - 13*k**3 - 15*k + 12*k**3 + 5 - 4*k**3.
-5*(k - 1)**3
Let q = -169 + 508/3. Suppose 3*u - 4*u = -5*m - 27, 3*m = 5*u - 25. Factor -2/3*b**u + 0*b**3 + 1/3*b**5 - q*b + 2/3*b**4 + 0.
b*(b - 1)*(b + 1)**3/3
Let a(f) be the first derivative of f**5/30 - f**4/9 + f**3/9 + 5*f - 5. Let y(g) be the first derivative of a(g). Find q such that y(q) = 0.
0, 1
Let p(h) be the second derivative of -h**5/30 + h**4/12 + 2*h**3/3 + h**2 - 2*h. Let d(r) be the first derivative of p(r). Determine l, given that d(l) = 0.
-1, 2
Let h(l) be the first derivative of l**4/10 - 3*l**2/5 - 4*l/5 + 11. Factor h(b).
2*(b - 2)*(b + 1)**2/5
Let i = 9 + -5. Suppose 0 = -7*x + i*x. Determine n, given that -4/3*n**3 + x + 2/3*n**5 + 2/3*n + 0*n**2 + 0*n**4 = 0.
-1, 0, 1
Let o(s) be the first derivative of s**6/135 - s**5/90 + 2*s + 3. Let l(h) be the first derivative of o(h). Solve l(g) = 0 for g.
0, 1
Suppose -6 = -r + u - 1, -2*r - 2 = 2*u. Factor 4/5*y**r - 2/5*y + 0 - 2/5*y**3.
-2*y*(y - 1)**2/5
Suppose -2*n - 5*w - 10 = 0, 5*n - 4*w - 12 = -4. Factor 8*h**3 + 3*h**2 + 4*h**3 - 9*h**3 + n*h**3.
3*h**2*(h + 1)
Let x = 30 - 30. Let r(b) be the third derivative of 0*b**3 - 1/168*b**8 - 3*b**2 - 1/35*b**7 + 0*b**4 + 0*b - 1/30*b**5 + x - 1/20*b**6. Factor r(s).
-2*s**2*(s + 1)**3
Let f(d) be the second derivative of -3*d**5/20 + 15*d**4/4 - 75*d**3/2 + 375*d**2/2 + 9*d. Factor f(c).
-3*(c - 5)**3
Let u(s) be the second derivative of 0 + 2/15*s**6 + 2/63*s**7 + 1/9*s**4 + 3*s + 1/5*s**5 + 0*s**3 + 0*s**2. Determine f so that u(f) = 0.
-1, 0
Suppose 7*d = -1 + 15. Suppose 7*a = d*a. Factor -3/5*r**2 + 1/5*r**3 + 2/5*r + a.
r*(r - 2)*(r - 1)/5
Let g(k) = 5*k. Let s(m) = -m**3 + 6*m**2 + 35*m. Let y(x) = -40*g(x) + 5*s(x). Determine j so that y(j) = 0.
0, 1, 5
Let w(s) = s**3 - 14*s**2 + s - 10. Let f