18*r**3 + 18*r**2 - 10*r. Let l(z) = z**5 - z**4 + z**3 - z**2 - 1. Let i(j) = 2*l(j) - m(j). Factor i(w).
2*(w - 1)**5
Let p(k) be the second derivative of 0 + 0*k**3 - 1/40*k**5 + 1/24*k**4 + 0*k**2 - k. Find j, given that p(j) = 0.
0, 1
Let j be 57/21 + (6/7)/3. Determine x, given that 0*x**2 + 0*x + 2/9*x**j + 0*x**4 - 2/9*x**5 + 0 = 0.
-1, 0, 1
Let j(n) = n**2 - 2. Let t be j(-2). Suppose 5*h + 4*l + 4 = 0, -2 = -2*h - 3*h + 2*l. Let h*f**2 + f**t + 0*f + f = 0. What is f?
-1, 0
Let t be (-1)/(-10)*2/1. Let v be 130/(-100) - ((-3)/(-2))/(-1). Suppose t*u**2 - 2/5*u + v = 0. What is u?
1
Suppose 0*s + 3/4*s**5 - 3/2*s**4 + 0*s**2 + 0*s**3 + 0 = 0. What is s?
0, 2
Find u such that 2/9*u - 2/3*u**2 + 2/3 - 2/9*u**3 = 0.
-3, -1, 1
Suppose b - 4 = 4. Let o be 6/(-2)*(-8)/b. Factor t - 3*t**2 + 2*t**3 - 4*t**3 + 0*t**3 + 4*t**o.
t*(t - 1)*(2*t - 1)
Let u be (-3)/(-2) + (-12)/(-8). What is d in 1/2*d**u + 1/2*d**2 - 1/2 - 1/2*d = 0?
-1, 1
Let v = -47 + 47. Factor -4/11*y**2 + 0 + 2/11*y**3 + v*y.
2*y**2*(y - 2)/11
Let d = -273 - -547/2. Factor d - 1/2*n**2 - 1/2*n**3 + 1/2*n.
-(n - 1)*(n + 1)**2/2
Let v be 4/10 - (-69)/15. Suppose 0*b - 10 = -v*b. Factor w**5 - 3*w**b + 0*w**2 - w**3 + 4*w**2 + w**4 - 2*w**4.
w**2*(w - 1)**2*(w + 1)
Let 2*q + 5/2*q**2 - 1/2 = 0. Calculate q.
-1, 1/5
Let r be (-98)/(-21) - (-1)/3. Let p(w) be the first derivative of 7/2*w**2 + 4/5*w**r + 13/4*w**4 + 5*w**3 + w + 2. Factor p(f).
(f + 1)**3*(4*f + 1)
Let x(j) be the second derivative of j**6/6 + 5*j**5/4 - 5*j**4/12 - 25*j**3/6 + 28*j. Determine o so that x(o) = 0.
-5, -1, 0, 1
Suppose -s - 2 = -2*a, 3*s + 5*a - 7 = -2. Factor 0*j**2 - 1/4*j**3 + 1/4*j + s.
-j*(j - 1)*(j + 1)/4
Let a(o) be the first derivative of -21*o**4/4 + 2*o**3/3 + 17*o**2/2 - 6*o - 7. Factor a(m).
-(m + 1)*(3*m - 2)*(7*m - 3)
Let t(p) = -2*p**2 + 2*p + 2. Let l be t(2). Let m(s) = -s**2 + s + 1. Let c(r) = -2 + 4 + 1 - 4*r**2 + 3 + 4*r. Let q(j) = l*m(j) + c(j). Factor q(a).
-2*(a - 2)*(a + 1)
Let k(l) be the third derivative of -l**5/150 + l**4/60 + 2*l**3/5 + 18*l**2. Let k(c) = 0. What is c?
-2, 3
Let k be (-4)/(-6) + (-13)/(-3). Suppose 0*i**3 + 2*i**2 + 3 - k - i + i**3 = 0. Calculate i.
-2, -1, 1
Let d be 1*2 + (-2 - -4). Suppose 0 = -5*q - 2*f, -3*f - 3 = 4*q + d. Factor q*t**4 + 2*t**4 - t**5 - 2*t**3 - t**5.
-2*t**3*(t - 1)**2
Let y(m) = -9*m**2 - 18*m - 9. Let r(t) = -17*t**2 - 35*t - 17. Let x(p) = 3*r(p) - 5*y(p). Find a such that x(a) = 0.
-2, -1/2
Suppose 0 = 4*x + 2*z - 3*z - 8, -2*z - 2 = -x. Factor 2 + 6*h - h**x + 2 + 3*h**2.
2*(h + 1)*(h + 2)
Let a = -7/34 - -239/170. Find c such that 6/5*c + 2/5*c**3 - 2/5 - a*c**2 = 0.
1
Let r be (-6)/(-14) - (-5)/((-420)/8). Let o(i) be the first derivative of -4/15*i**5 - r*i**2 - 2/3*i + 1 + 2/3*i**3 + 1/6*i**4. Solve o(z) = 0.
-1, -1/2, 1
Let n be -1*(-9 - -3)/3. Factor -n*c + 5*c + 9*c + 0*c**2 + 2*c**2 + 18.
2*(c + 3)**2
Let d(f) = f**2 - f - 3. Let v be d(3). Suppose -v*i = -6*i + 15. Solve -4*s**4 + 4*s - 6*s**3 + 3*s**3 + 0*s**i + s**2 - s**5 + 3*s**2 = 0 for s.
-2, -1, 0, 1
Let y(d) be the second derivative of -3*d + 1/6*d**4 - 1/5*d**5 + 0*d**2 + 0*d**3 + 1/15*d**6 + 0. Factor y(n).
2*n**2*(n - 1)**2
Let r(p) be the third derivative of 3*p**8/112 - 3*p**7/70 - 13*p**6/120 + 13*p**5/60 + p**4/6 - 2*p**3/3 + 26*p**2. Solve r(m) = 0 for m.
-1, -2/3, 2/3, 1
Suppose -6*a + 14 = 3*s - 4*a, 0 = 2*s + 4*a - 12. Suppose r**4 - 3*r**2 + r**s + 3*r**2 + 2*r**2 - 4*r**3 = 0. What is r?
0, 1
Let r = 8 + -5. Let o be (-2 - -4) + (-15)/(-6). Factor 7/2*h**r + 0 - o*h**2 + h.
h*(h - 1)*(7*h - 2)/2
Find q, given that 14*q**2 + 3*q**3 - 2*q**2 + 9*q - 14 + 14 = 0.
-3, -1, 0
Let m(y) be the second derivative of -3*y**5/5 + y**4/3 + 2*y**3 - 2*y**2 - 12*y. Factor m(s).
-4*(s - 1)*(s + 1)*(3*s - 1)
Let w(f) = -f - 6. Let k be w(-6). Let n be 2/(1/(k - -2)). Factor -1/3*v**3 + 1/3*v**n + 0*v + 1/3*v**5 + 0 - 1/3*v**2.
v**2*(v - 1)*(v + 1)**2/3
Let p(t) be the second derivative of -7*t**9/216 + t**8/30 - t**7/105 - t**3/6 - 2*t. Let k(l) be the second derivative of p(l). Factor k(o).
-2*o**3*(7*o - 2)**2
Factor 4/7 - 6/7*b + 2/7*b**2.
2*(b - 2)*(b - 1)/7
Suppose -v + 20 = 4*r + 3*v, -2*r - 10 = -2*v. Factor r*w**3 + 3/2*w**4 + 0*w + 3/2 - 3*w**2.
3*(w - 1)**2*(w + 1)**2/2
Let s be (-22)/(-60) + (-3)/15. Let m(l) be the second derivative of 0*l**2 + s*l**3 - l + 0 + 1/12*l**4. Factor m(y).
y*(y + 1)
Let h(j) = -j - 4. Suppose -4*r = -3*r - 4*y + 14, 0 = -2*y + 4. Let p be h(r). Factor 8*o - 7*o - p*o**2 + o**2.
-o*(o - 1)
Let t(i) be the first derivative of 3*i**6/10 - 3*i**5/20 - 5*i**4/12 - i**3/6 + 3*i + 3. Let r(d) be the first derivative of t(d). Factor r(v).
v*(v - 1)*(3*v + 1)**2
Let z = 1/111 - -73/111. Let g(p) be the first derivative of 3/4*p**4 + 1/4*p**2 + 1/12*p**6 + 0*p - 2 + z*p**3 + 2/5*p**5. Factor g(s).
s*(s + 1)**4/2
Let l(j) be the third derivative of j**5/80 + 5*j**4/96 + j**3/12 + 17*j**2. Factor l(r).
(r + 1)*(3*r + 2)/4
Let q(k) = -4*k**3 - 7*k**2 + 13*k - 19. Let o(c) = c**3 - c + 1. Let b(g) = -5*o(g) - q(g). Let d be b(6). Factor -2/3*w**d + 0 + 4/3*w.
-2*w*(w - 2)/3
Determine k, given that -4/5*k - 6/5*k**2 + 2/5*k**5 + 0 + 6/5*k**4 + 2/5*k**3 = 0.
-2, -1, 0, 1
Let n(c) = -7*c**2 - 5*c - 8. Let d(j) = 4*j**2 + 2*j + 4. Let u(f) = 10*d(f) + 6*n(f). Solve u(t) = 0.
-4, -1
Let k be (-46)/(-12) + (-1)/(-6). Factor -d**3 + 6*d - d**3 + 4 - k + 4.
-2*(d - 2)*(d + 1)**2
Let -1/7*q**3 + 1/7*q + 0*q**2 + 0 = 0. Calculate q.
-1, 0, 1
Determine k so that -3/7*k**5 + 0 + 3/7*k**3 + 0*k + 3/7*k**4 - 3/7*k**2 = 0.
-1, 0, 1
Let d = -7703/63 + 2030/9. Let k = -103 + d. Suppose -4/7*r - k*r**2 + 0 = 0. What is r?
-2, 0
Suppose x + 5*s = -18, 2*s = -2*x + 7*s + 24. Suppose -x*m - m = -6. Factor 0 + 0*o + 1/5*o**m.
o**2/5
Let p(o) = -8*o**2 + 91*o. Let t(i) = -12*i**2 + 136*i. Let a(x) = 8*p(x) - 5*t(x). Factor a(c).
-4*c*(c - 12)
Let l(p) = -11*p**5 + 35*p**4 - 48*p**3 + 29*p**2 + 5. Let n(w) = 6*w**5 - 18*w**4 + 24*w**3 - 15*w**2 - 3. Let h(z) = 3*l(z) + 5*n(z). Factor h(s).
-3*s**2*(s - 2)**2*(s - 1)
Let i(w) be the first derivative of -2*w**7/105 + w**6/15 - w**5/10 + w**4/12 + 2*w**3/3 - 9. Let m(x) be the third derivative of i(x). Factor m(v).
-2*(2*v - 1)**3
Let v(r) be the second derivative of -4*r**7/147 - 4*r**6/35 - r**5/14 + 5*r**4/21 + 3*r**3/7 + 2*r**2/7 + 17*r. Suppose v(c) = 0. Calculate c.
-2, -1, -1/2, 1
Let b(k) be the second derivative of k**7/4200 - k**6/600 + k**5/200 - k**4/120 + 7*k**3/6 - 7*k. Let a(d) be the second derivative of b(d). Factor a(r).
(r - 1)**3/5
Let a(u) be the second derivative of u**5/4 - 10*u**4/3 + 65*u**3/6 - 15*u**2 + 18*u. Factor a(h).
5*(h - 6)*(h - 1)**2
Suppose -7 - 13 = -4*h. Let j = 5 + 41. Solve 6*r**2 + j*r**4 - 5*r**5 + 20*r**2 - 9*r**h - 54*r**3 - 4*r = 0.
0, 2/7, 1
Suppose 0 - 4/3*g**2 - 8/3*g**4 + 10/3*g**3 + 0*g + 2/3*g**5 = 0. Calculate g.
0, 1, 2
Let z = 689/258 - 1/258. Let a(s) be the first derivative of 1 + 2*s + 5*s**2 + z*s**3. Suppose a(c) = 0. Calculate c.
-1, -1/4
Let y(n) be the second derivative of 0*n**3 + 0*n**2 + 1/18*n**4 + 0*n**5 - 1/45*n**6 + 0 + 3*n. Suppose y(q) = 0. What is q?
-1, 0, 1
Let m(o) = -2*o - 16. Let w be m(-9). Let p(s) be the first derivative of -s - 1/3*s**3 - s**w + 1. Let p(h) = 0. Calculate h.
-1
Let f(v) = -21*v**2. Let j(w) = -4*w**2 - 3 + 3. Let o(q) = -2*f(q) + 11*j(q). Solve o(z) = 0 for z.
0
Let s = -12/43 + 67/86. Factor -s*x**2 + 3/2*x + 0.
-x*(x - 3)/2
Let u(s) be the first derivative of -3*s**5/10 - s**4/4 + s**3 + 3*s**2/2 + 4*s - 9. Let t(n) be the first derivative of u(n). Determine x so that t(x) = 0.
-1, -1/2, 1
Let b(f) be the second derivative of 1/60*f**6 + 1/3*f**3 + 1/4*f**2 + 1/10*f**5 + 0 - f + 1/4*f**4. Find l, given that b(l) = 0.
-1
Let d = -254/15 + 17. Let n(v) be the second derivative of 1/3*v**4 - d*v**6 + v + 0 - v**2 + 0*v**3 + 0*v**5. Factor n(w).
-2*(w - 1)**2*(w + 1)**2
Determine w so that 0*w - 2/17*w**5 + 0 + 0*w**2 + 4/17*w**4 + 0*w**3 = 0.
0, 2
Let q(y) be the second derivative of 0*y**2 + 0 - y - 1/3*y**3 + 1/6*y**4. Factor q(h).
2*h*(h - 1)
Let a(r) = -r**4 + r**3 - r**2 + r. Let k(z) = 7*z**4 - 12*z**3 - 18*z**2 + 8*z + 15. Let s(q) = 2*a(q) + k(q). Factor s(c).
5*(c - 3)*(c - 1)*(c + 1)**2
Suppose 15