n**5 + 5*n**4 - 2*n**4.
-2*n**4*(n + 1)
Let a(n) be the first derivative of -n**4/30 - n**3/15 + 2*n**2/5 - n + 1. Let f(y) be the first derivative of a(y). Factor f(d).
-2*(d - 1)*(d + 2)/5
Let y(k) = k**3 + 5*k**2 - k - 2. Let t be y(-5). What is r in 6*r**2 + r**2 - r**t - 5*r**2 = 0?
0, 2
Let y(o) be the third derivative of o**8/7560 + o**7/1890 + o**6/1620 - o**3/6 + o**2. Let n(s) be the first derivative of y(s). Suppose n(i) = 0. Calculate i.
-1, 0
Suppose -4*w + 5*t + 7 = 27, 4 = -5*w + t. Let d be (-72)/(-63) - 0/(-1). Suppose d*r**2 - 8/7*r - 2/7*r**3 + w = 0. What is r?
0, 2
Suppose 3/4*y**4 - 3/4*y**5 + 0 + 3/2*y + 9/4*y**3 - 15/4*y**2 = 0. What is y?
-2, 0, 1
Let l(b) = 4*b**3 - b**2 + 2*b - 1. Let z be l(1). Suppose -f = f - z. Suppose 3/5*h - 2/5*h**f + 2/5 - 3/5*h**3 = 0. Calculate h.
-1, -2/3, 1
Let s(r) be the first derivative of -9*r**2 + r**2 - 2 - 4*r**3 - 24*r - 14*r**2. Find h, given that s(h) = 0.
-3, -2/3
Let h be (-2)/(-4)*0/(-8 + 4). Factor h - 5/4*g**3 - 1/4*g**5 - g**4 - 1/2*g**2 + 0*g.
-g**2*(g + 1)**2*(g + 2)/4
Let q = 19 + -21. Let b = q - -4. Factor -g**b - 1/3 - 1/3*g**3 - g.
-(g + 1)**3/3
Let c(v) be the second derivative of -2*v + 1/40*v**6 + 0 + 1/48*v**4 + 1/168*v**7 + 0*v**3 + 0*v**2 + 3/80*v**5. Factor c(u).
u**2*(u + 1)**3/4
Let h(r) be the third derivative of 0*r + 1/35*r**5 + 0*r**3 + 0 - 3/56*r**4 - 1/280*r**6 - 2*r**2. Factor h(v).
-3*v*(v - 3)*(v - 1)/7
Suppose 21*k - 59 + 12*k**2 - 20*k**3 + 27*k + 75 = 0. What is k?
-1, -2/5, 2
Let m(s) = s**2 + 1. Let y(a) = 2*a**3 - 3*a**2 + 2*a + 1. Let b = 0 - -1. Let f(g) = b*m(g) - y(g). Factor f(j).
-2*j*(j - 1)**2
Let t(f) = -f. Let l(u) = u**2 + u - 3. Let n(r) = r - 6. Let k be n(9). Let q(c) = k*t(c) + l(c). Find x, given that q(x) = 0.
-1, 3
Suppose 0 = 3*m + 207 - 222. What is i in 104/3*i**2 - 434/3*i**4 + 0 + 92/3*i**3 - 196*i**m + 16/3*i = 0?
-2/3, -2/7, 0, 1/2
Factor 101*n**2 + 6*n - 97*n**2 + 10*n + 12.
4*(n + 1)*(n + 3)
Let p(u) be the first derivative of -2/3*u**5 - 8/9*u**3 + 0*u + 0*u**2 + 1 - 4/3*u**4 - 1/9*u**6. Factor p(a).
-2*a**2*(a + 1)*(a + 2)**2/3
Factor 2*l**2 + 0*l**2 - 3*l + 0*l + l**2.
3*l*(l - 1)
Let c be 1*10 + 0/(-2). Let g(f) = 7*f**2 + 2*f + 1. Suppose 3*k = -1 + 19. Let b(y) = -14*y**2 - 5*y - 1. Let m(h) = c*g(h) + k*b(h). Let m(j) = 0. What is j?
-1, 2/7
Suppose -29 - 35 + 54 - 9*i + i**2 = 0. What is i?
-1, 10
Let g be (18 + -20)/(4/(-2) + 1). Let o(y) be the second derivative of -1/24*y**4 + 0*y**3 - 1/16*y**5 + 0*y**g + 0 + y + 7/120*y**6. Factor o(v).
v**2*(v - 1)*(7*v + 2)/4
Let t(n) be the second derivative of 5*n**4/42 + n**3/3 + 2*n**2/7 + 5*n. Factor t(y).
2*(y + 1)*(5*y + 2)/7
Let b(y) be the second derivative of y**8/560 + 5*y**7/504 + y**6/720 - y**5/60 + y**4/6 + 4*y. Let k(g) be the third derivative of b(g). Factor k(z).
(z + 2)*(3*z + 1)*(4*z - 1)
Suppose 8*l + 108 = -132. Let i be -6*(32/l - -1). Factor -2/5*g + i*g**2 - 2/5 + 2/5*g**3.
2*(g - 1)*(g + 1)**2/5
Let u(v) be the third derivative of v**6/720 - v**5/180 + 18*v**2. Suppose u(t) = 0. What is t?
0, 2
Let s(r) = 6*r - 2. Let i be s(1). Let f(o) be the first derivative of -2 - 2/3*o**2 + 5/6*o**i + 2/3*o**3 + 0*o. Determine j, given that f(j) = 0.
-1, 0, 2/5
Determine w, given that 3/8*w**2 + 1/8*w**4 + 0 + 1/8*w + 3/8*w**3 = 0.
-1, 0
Let s be (-48)/(-18) - 3/(-9). Let u(f) be the first derivative of -1/9*f**4 + 1/9*f**2 - 4/27*f**s + 2/9*f + 1 + 2/45*f**5 + 1/27*f**6. Factor u(p).
2*(p - 1)**2*(p + 1)**3/9
Suppose -5*g + 2*g = 3. Let f be (5 - 4)/(g/(-2)). Let -6*y**3 + 13*y**2 - 7*y**2 + 3*y - f*y**4 + 3*y**5 - y**4 - 3 = 0. Calculate y.
-1, 1
Let o be (-18 - -16)*(-3)/2. Suppose -r + 4*r - 6*r - o*r**2 = 0. What is r?
-1, 0
Let s be (-6)/(-2) - 0/(-2). Let a**2 - 4*a**3 + 0*a**4 - s*a**2 + 2*a**4 + 2*a + 2*a**3 = 0. Calculate a.
-1, 0, 1
Let n(q) be the second derivative of -1/150*q**6 + 0*q**2 + 0 - 1/30*q**3 + 2*q + 1/100*q**5 + 1/60*q**4. What is s in n(s) = 0?
-1, 0, 1
Let b(f) be the second derivative of f**6/120 - f**5/8 + 37*f**4/48 - 5*f**3/2 + 9*f**2/2 - 4*f - 2. Determine u, given that b(u) = 0.
2, 3
Factor 3 - 21/4*f**3 + 69/4*f**2 - 15*f.
-3*(f - 2)*(f - 1)*(7*f - 2)/4
Let v = 235 - 231. Factor -16/3 + 4/3*l**3 + v*l**2 + 0*l.
4*(l - 1)*(l + 2)**2/3
Let g(f) be the first derivative of 4*f**6 - 46*f**5/5 + 13*f**4/2 - 4*f**3/3 + 14. What is l in g(l) = 0?
0, 1/4, 2/3, 1
Let w(g) be the first derivative of -3*g**5/25 + 9*g**4/10 - 9*g**3/5 + 69. Solve w(u) = 0 for u.
0, 3
Suppose -9*g + 33 - 6 = 0. Let o(w) be the first derivative of -g + 1/10*w**5 + 3/8*w**4 + 0*w + 1/4*w**2 + 1/2*w**3. Factor o(r).
r*(r + 1)**3/2
Let y = -52 + 55. Let d(i) be the first derivative of -1/3*i**y - 1/4*i**4 - 2 + i + 1/2*i**2. Factor d(u).
-(u - 1)*(u + 1)**2
Let v(p) be the first derivative of -p**6/60 + p**5/40 - p**3/3 + 4. Let a(i) be the third derivative of v(i). Let a(d) = 0. What is d?
0, 1/2
Let z be 96/198*(-32)/23. Let m = -2/253 - z. Suppose 2/3*l**2 - m*l + 0 = 0. What is l?
0, 1
Let s(r) = -48*r**4 + 165*r**3 - 174*r**2 + 60*r - 6. Let m(g) = 96*g**4 - 331*g**3 + 347*g**2 - 119*g + 12. Let j(c) = 3*m(c) + 5*s(c). Factor j(z).
3*(z - 2)*(z - 1)*(4*z - 1)**2
Let z(m) be the second derivative of 1/25*m**5 + 0*m**3 - 2/75*m**6 - 3*m + 0 + 0*m**4 + 0*m**2 + 1/210*m**7. Factor z(s).
s**3*(s - 2)**2/5
Let b(z) be the second derivative of 1/54*z**4 + 0 + 6*z + 2/9*z**3 + z**2. Factor b(c).
2*(c + 3)**2/9
Suppose 0 = a + a. Let q(j) be the first derivative of 1/2*j - 2 - 1/6*j**3 + a*j**2. What is i in q(i) = 0?
-1, 1
Let w = -4 - -8. Factor 0*z + 0*z**2 + 2 + 2*z**2 - w*z.
2*(z - 1)**2
Let x(o) be the second derivative of o**7/840 + o**6/240 + o**5/240 - 4*o**2 + 3*o. Let j(c) be the first derivative of x(c). Find a, given that j(a) = 0.
-1, 0
Let j = -961/3 - -321. Factor -1/3*q**2 - q - j.
-(q + 1)*(q + 2)/3
Let g(o) = 16*o**2 - 46*o + 41. Let x(w) = -3*w**2 + 9*w - 8. Let r(n) = 2*g(n) + 11*x(n). Let p be r(6). Factor 2*j + j**2 - 2*j**3 - 3*j**2 + 2*j**4 + p*j**3.
2*j*(j - 1)**2*(j + 1)
Let p(c) be the second derivative of 5*c**4/12 + 11*c**3/42 - 3*c**2/7 + c + 5. Factor p(s).
(5*s + 3)*(7*s - 2)/7
Let u(m) = 2*m**2 + 12*m + 6. Let t(h) = -6*h**2 - 35*h - 18. Let g(p) = -4*t(p) - 11*u(p). Factor g(z).
2*(z + 1)*(z + 3)
Let f = -62 - -312/5. Factor -f*d**3 + 2/5*d**5 + 2/5*d**4 + 0*d - 2/5*d**2 + 0.
2*d**2*(d - 1)*(d + 1)**2/5
Let r(s) = -20*s**2 + 12*s + 12. Let i(w) = -40*w**2 + 24*w + 23. Let k(h) = 4*i(h) - 7*r(h). Find d, given that k(d) = 0.
-2/5, 1
Let n(u) be the third derivative of u**6/660 - u**5/165 - 9*u**2. Factor n(k).
2*k**2*(k - 2)/11
Let q(h) be the second derivative of h**7/6300 - h**6/900 + h**5/300 + 5*h**4/12 - 2*h. Let t(w) be the third derivative of q(w). Factor t(r).
2*(r - 1)**2/5
Suppose -2*a - 2*r + 5*r + 3 = 0, 0 = 3*a + 5*r - 14. Factor 0*v**2 - v**2 - 2*v**2 + v**a + 3*v - 1 + 0*v.
(v - 1)**3
Let k = -4 - -6. Let t be ((-1)/15)/(k/(-12)). Factor t - 4/5*b + 2/5*b**2.
2*(b - 1)**2/5
Factor -4/3*z**3 - 2/3*z - 7/3*z**2 + 1/3.
-(z + 1)**2*(4*z - 1)/3
Let n(m) be the first derivative of 0*m - 2/21*m**3 + 0*m**2 - 3 + 1/7*m**4 - 2/35*m**5. What is x in n(x) = 0?
0, 1
Let h(u) be the second derivative of -u**7/84 - u**6/90 + u**5/12 + u**4/6 - u**3/2 - u. Let z(p) be the second derivative of h(p). Factor z(t).
-2*(t - 1)*(t + 1)*(5*t + 2)
Let x = 1 - -10. Let h be (x - 11)*(-1)/2. Factor h*k + 1/3*k**2 - 1/3.
(k - 1)*(k + 1)/3
Factor -1/5*c + 0 + 3/5*c**3 - 2/5*c**2.
c*(c - 1)*(3*c + 1)/5
Let f(k) be the second derivative of k**6/2 + k**5/4 - 5*k**4/4 - 5*k**3/6 - 10*k. Factor f(t).
5*t*(t - 1)*(t + 1)*(3*t + 1)
Let q(w) = -4*w**3 + 1. Let r be q(-1). Let y(g) be the third derivative of -1/6*g**3 + 0*g - 1/12*g**4 + 2*g**2 + 0 - 1/60*g**r. Let y(j) = 0. Calculate j.
-1
Let x be (1/(-4))/(-5 + (-99)/(-24)). Factor x*d**2 + 2/7*d + 0.
2*d*(d + 1)/7
Let o = 61 - -115. Let i be o/(-231)*(-6)/4. Solve 2*r + i*r**2 - 4/7 = 0 for r.
-2, 1/4
Let l(n) = 2*n - 13. Let q be l(9). Let z(d) be the second derivative of 0*d**2 + 0 - 1/18*d**4 + 1/20*d**q + 3*d - 1/18*d**3. Suppose z(w) = 0. Calculate w.
-1/3, 0, 1
Let v(s) be the first derivative of s**6/6 - 3*s**5/5 + s**4/2 + 2*s**3/3 - 3*s**2/2 + s - 11. Determine b so that v(b) =