 0*m + 1/4*m**3 + 0 + 0*m**2 = 0.
0, 1
Let w(t) be the third derivative of -t**5/15 + t**4/6 + 4*t**3/3 + 12*t**2. Factor w(n).
-4*(n - 2)*(n + 1)
Suppose 3*m - 32 = 7. Suppose -4*p + 4 = -12. Determine x, given that -21*x**2 - 2 - 11*x**3 - p*x**2 - m*x + 0 - 3*x**3 = 0.
-1, -1/2, -2/7
Let x(u) be the first derivative of 5*u**4/2 + 26*u**3/3 + 4*u**2 - 8*u + 4. Suppose x(c) = 0. What is c?
-2, -1, 2/5
Let l = 862 - 6033/7. Factor 0*u + 2/7*u**2 + 0 - 1/7*u**3 - l*u**4.
-u**2*(u - 1)*(u + 2)/7
Determine o so that -29*o + 12*o - 5*o**2 + 5 + 5*o**3 + 12*o = 0.
-1, 1
Let x = -38/5 - -29/15. Let a = x + 6. Factor 0 + 4/3*o**2 - 1/3*o**5 - a*o - 2*o**3 + 4/3*o**4.
-o*(o - 1)**4/3
Let h be (-2)/(-3) - (-2 - (-1)/(-3)). Let i(b) be the first derivative of -3 + 0*b - 1/6*b**2 + 1/9*b**h. Factor i(k).
k*(k - 1)/3
Let b(g) = -7*g - 32. Let l be b(-5). Factor r**l - r**2 + 0 + 1/3*r - 1/3*r**4.
-r*(r - 1)**3/3
Suppose 0 = 9*q - 19 - 17. Let x(v) be the second derivative of v - 3/4*v**3 + 1/6*v**q + 0 + 1/2*v**2. Solve x(u) = 0.
1/4, 2
Let z(a) be the third derivative of a**5/60 - 2*a**3/3 - 6*a**2. Factor z(b).
(b - 2)*(b + 2)
Let w(l) be the first derivative of -l - 1/20*l**5 + 1/2*l**2 + 2 + 1/4*l**4 - 1/2*l**3. Let i(g) be the first derivative of w(g). Solve i(y) = 0.
1
Let z = -2203/9 + 245. Let g(x) be the first derivative of z*x**3 - 4 + 2/3*x**2 + 2/3*x. Factor g(a).
2*(a + 1)**2/3
Let d(r) be the second derivative of -r**6/360 + r**5/60 + r**4/8 - 5*r**3/6 - 3*r. Let i(h) be the second derivative of d(h). Factor i(v).
-(v - 3)*(v + 1)
What is s in 2*s + 1/5*s**2 + 5 = 0?
-5
Let a be 3 + -1*(2 + -1). Suppose s = 4*r + 18, s - 6*s - 3*r - a = 0. Solve 24/5*z + 12/5*z**s + 2/5*z**3 + 16/5 = 0.
-2
Let n(i) be the second derivative of -2*i**6/15 + 3*i**5/5 + 8*i**4 + 56*i**3/3 - 40*i + 1. Suppose n(w) = 0. What is w?
-2, 0, 7
Suppose 7*n**3 + 3*n**2 + 5*n**2 - 3*n**3 + 0*n**2 = 0. Calculate n.
-2, 0
Factor -1/2*p**2 - p + 2 + 1/4*p**3.
(p - 2)**2*(p + 2)/4
Factor 8*f**3 + 0 - 5*f**3 + 9*f + 9*f**2 + 3.
3*(f + 1)**3
Determine y, given that -2*y + 6*y + 2*y**3 - 29*y**2 + 23*y**2 = 0.
0, 1, 2
Suppose 0*u**3 + u**3 + u**2 - 6*u**2 - 6*u**3 = 0. What is u?
-1, 0
Let q(c) be the second derivative of -c**5/25 - c**4/5 - 4*c**3/15 - 7*c. Factor q(o).
-4*o*(o + 1)*(o + 2)/5
Let a(g) be the second derivative of g**7/42 - g**6/30 - g**5/20 + g**4/12 - 4*g. Solve a(w) = 0 for w.
-1, 0, 1
Let f(s) be the first derivative of 4*s**6/15 - 2*s**5/25 - s**4/20 - 7. Factor f(i).
i**3*(2*i - 1)*(4*i + 1)/5
Solve -4*n**5 - 9*n**3 + 8*n**4 + 5*n**3 + 0*n**4 = 0.
0, 1
Let x(g) be the first derivative of g**9/10584 - g**8/1470 + g**7/588 - g**6/630 - g**3/3 - 7. Let a(q) be the third derivative of x(q). Factor a(i).
2*i**2*(i - 2)*(i - 1)**2/7
Factor 1/4*d**2 + 0 + 0*d.
d**2/4
Let n(z) be the second derivative of 1/6*z**4 + 0 - 1/3*z**3 - 6*z - 2*z**2. Factor n(c).
2*(c - 2)*(c + 1)
Let v = 99 + -35. Let w be ((-30)/(-40))/(54/v). Suppose 2/9*x**2 + 8/9*x + w = 0. What is x?
-2
Let c be 1/5 - (-6)/(-36). Let v(k) be the second derivative of c*k**6 - 1/4*k**4 - 3*k + 0*k**5 + 0 - 1/3*k**3 + 0*k**2. Factor v(u).
u*(u - 2)*(u + 1)**2
Let u(q) be the second derivative of q**6/315 - q**4/84 - q**3/3 + q. Let n(l) be the second derivative of u(l). Factor n(p).
2*(2*p - 1)*(2*p + 1)/7
Suppose -1/4*w**3 + 1/2*w**2 + 0 - 1/4*w = 0. What is w?
0, 1
Let y = -5 + 7. Let z be 0 + 3 - (0 + -1). Factor 0*s + 0*s**y + 0 + 0*s**3 + 1/4*s**z.
s**4/4
Suppose -11 = -32*d + 85. Factor 2/15*x + 0*x**2 + 0 - 2/15*x**d.
-2*x*(x - 1)*(x + 1)/15
Suppose -4*t = -9 - 3. Let w(l) be the third derivative of 0 + 1/60*l**5 + 0*l + 1/24*l**4 + l**2 + 0*l**t. Factor w(s).
s*(s + 1)
Let s be 1 + -2 - (1 + -5). Factor -1/3*n**5 + 16/3*n**2 + 2/3 + 2*n**4 - 14/3*n**3 - s*n.
-(n - 2)*(n - 1)**4/3
Let t be 1/((-3)/6) + 3. Let r = 3 - t. Factor -2*n - 2*n**r + 2*n.
-2*n**2
Suppose 0 - 2/3*k**2 - 1/3*k - 1/3*k**3 = 0. Calculate k.
-1, 0
Suppose 0 = 4*h - 5 - 7. Let n = h - 1. Factor -z - 3*z + z + z**n + 2*z + 2*z**3.
z*(z + 1)*(2*z - 1)
Let p(k) be the second derivative of 1/12*k**3 + 1/24*k**6 + 1/168*k**7 + 0*k**2 + 9/80*k**5 + 7/48*k**4 - 4*k + 0. What is q in p(q) = 0?
-2, -1, 0
Suppose 8*l + 5 = 5*p + 3*l, 2*l = 5*p + 7. Let s = p - -4. Factor b - 1 + b**2 + 2*b**2 - s.
(b + 1)*(3*b - 2)
Let k(l) = -l**2 + 5*l - 3. Let w be k(5). Let s be 2 - 0*w/9. Factor 1/3*r**s + 1/3 + 2/3*r.
(r + 1)**2/3
Let v(d) = 40*d**5 + 265*d**4 + 900*d**3 + 1260*d**2 + 760*d + 170. Let l(r) = -r**5 + r**4 - r**3 - 1. Let n(y) = 10*l(y) + v(y). Find x such that n(x) = 0.
-4, -2, -2/3, -1/2
Let d = -22/377 + 91300/1131. Let h = d + -80. Factor h*y**3 - 2/3*y**2 + 0 + 2/3*y**4 - 2/3*y.
2*y*(y - 1)*(y + 1)**2/3
Let a(o) = 4*o**3 - 17*o**2 + 11. Let g(d) = -2*d**3 + 8*d**2 - 6. Let y(x) = -2*a(x) - 5*g(x). Factor y(s).
2*(s - 2)**2*(s + 1)
Find z, given that 3/2*z - 3/2 - 3/2*z**3 + 3/2*z**2 = 0.
-1, 1
Let f(v) be the third derivative of v**8/672 + v**7/105 + v**6/48 + v**5/60 - 16*v**2 + v. Factor f(u).
u**2*(u + 1)**2*(u + 2)/2
Let t be 6/(-40) + 10/25*1. Factor -3*m + 3/2*m**2 + 2 - t*m**3.
-(m - 2)**3/4
Let f(j) be the third derivative of -j**6/195 - j**5/390 - 3*j**2. Find p such that f(p) = 0.
-1/4, 0
Let k be 0/(-3) - (-1 - -8). Let q be (-19)/k - 4/(-14). Factor q + 2*h**2 - 7 + 0 + 2*h.
2*(h - 1)*(h + 2)
Suppose 10*r + 5*t = 9*r - 13, 2*t = -4*r + 2. Suppose -2/7*g**r + 0 + 0*g = 0. What is g?
0
Let y = 5 + 11. Determine p, given that 14*p + 0*p**3 + p**2 + p**3 - y*p = 0.
-2, 0, 1
Let r(m) = m**3 - 18*m**2 - 2*m + 38. Let a be r(18). Factor 0 + 0*z + 10/7*z**5 + 16/7*z**4 - 4/7*z**a + 2/7*z**3.
2*z**2*(z + 1)**2*(5*z - 2)/7
Let r(s) be the first derivative of 3*s**5/5 - 3*s**4/4 - 14. Let r(g) = 0. Calculate g.
0, 1
Suppose 4*s = 7*s - 12. Let z(v) be the second derivative of 1/10*v**5 + 0*v**2 + 2/21*v**3 + 0 + 3/14*v**s + 2*v. Factor z(w).
2*w*(w + 1)*(7*w + 2)/7
Let z(h) = 5*h**3 - 7*h**2 - 8*h + 19. Let v(w) = -w**3 + w**2 - 1. Let l(a) = 3*v(a) + z(a). Factor l(g).
2*(g - 2)**2*(g + 2)
Let j(l) = l + 1. Let v be j(6). Let f(b) = b**2 + 7*b + 4. Let m(o) = 2*o**2 + 20*o + 11. Let d(p) = v*f(p) - 2*m(p). Factor d(w).
3*(w + 1)*(w + 2)
Let s(d) be the first derivative of 2*d**3/33 + d**2/11 - 9. What is k in s(k) = 0?
-1, 0
Let a(x) = -x**2 - 5*x - 4. Let n be a(-1). Factor n*v + 0 + 10/3*v**3 - 4/3*v**2 + 2*v**4.
2*v**2*(v + 2)*(3*v - 1)/3
Suppose 5*o = 2*t + 19, o - 1 = -o + 3*t. Suppose -3 = -4*x + o. Factor -2*i - 4/3 + 0*i**x + 2/3*i**3.
2*(i - 2)*(i + 1)**2/3
Let z(b) be the second derivative of 2*b**7/21 - 2*b**6/5 + 2*b**5/5 + 12*b. Factor z(t).
4*t**3*(t - 2)*(t - 1)
Let p(r) be the third derivative of -r**6/120 + r**5/60 + r**4/24 - r**3/6 - 2*r**2. Factor p(s).
-(s - 1)**2*(s + 1)
Let w(o) = o**2 + 4*o + 3. Let a(h) = -h**3 - 7*h**2 - 7*h - 9. Let l be a(-6). Let c be w(l). Solve c - 2/11*u + 2/11*u**2 = 0 for u.
0, 1
Let l be 1*-1 - (1 + -6). Let i be 1/(-1)*(-4)/1. Factor -14*z**i - l*z - 32*z**3 + 6 - 6 - 22*z**2.
-2*z*(z + 1)**2*(7*z + 2)
Suppose m - 43 = -0*m. Let v = -26 + m. Suppose -k**4 - 17*k**3 + k**2 + v*k**3 = 0. What is k?
-1, 0, 1
Factor 15*m**2 + 7*m**4 - 10*m**4 + 3*m**3 - 9*m - 6*m**3.
-3*m*(m - 1)**2*(m + 3)
Let y(l) be the second derivative of -l**9/18900 + l**7/3150 - l**4/4 - 5*l. Let m(n) be the third derivative of y(n). Factor m(r).
-4*r**2*(r - 1)*(r + 1)/5
Let l(k) = -2*k**2 - 4*k - 2. Let m(a) = a**2 + 2*a + 1. Let n(t) = -6*l(t) - 14*m(t). Find u such that n(u) = 0.
-1
Let g be (2/4)/(3/6*1). Solve 5/4*a**2 + g + 1/4*a**3 + 2*a = 0 for a.
-2, -1
Let q(j) be the third derivative of j**5/360 - j**3/9 - 9*j**2. Factor q(l).
(l - 2)*(l + 2)/6
Let t(n) = -n - 1. Suppose 0 = 2*k - 4 - 0. Let c(i) = 3*i + 0*i**2 + 2 + 0*i - 2*i**2 + 3*i**k. Let l(h) = c(h) + t(h). Factor l(o).
(o + 1)**2
Let u(g) be the second derivative of g**5/130 + g**4/39 - 6*g. Factor u(i).
2*i**2*(i + 2)/13
Let l(q) be the second derivative of q**4/28 + q**3/14 + 11*q. Let l(w) = 0. What is w?
-1, 0
Let g(h) be the third derivative of -h**6/105 + h**5/70 + h**4/84 + 5*h**2. Factor g(q).
-2*q*(q - 1)*(4*q + 1)/7
Let k(y) = -16*y**3 + 101*y**2 - 425*y + 576. Let s(q) = 11*q**3 - 67*q**2 + 283*q - 384. Let h(j) = 5*k