- p**4/12 - p**2. Let n(j) be the second derivative of a(j). Factor n(x).
(x + 1)*(x + 2)**2/2
Let y = -12 + 6. Let p be 2/y*12/(-2). Find s such that 0*s + 0 + 2/3*s**3 + 0*s**p - 2/3*s**4 - 4/3*s**5 = 0.
-1, 0, 1/2
Let f = 5 - 5. Suppose 3*g - g - 6 = f. Find n, given that -4*n**g + 5*n**3 - 2*n**3 = 0.
0
Let z(j) be the second derivative of -j**8/840 - j**7/140 - j**6/60 - j**5/60 - j**3/3 + 2*j. Let x(i) be the second derivative of z(i). What is u in x(u) = 0?
-1, 0
Find w such that 0 + 2/3*w**3 + 0*w**2 + 0*w - 2/3*w**4 = 0.
0, 1
Let s = -5 - -8. Suppose 2*m - 1 - 3 = 0. Factor -2*f**m + 3/2*f**s + 0 + 1/2*f.
f*(f - 1)*(3*f - 1)/2
Let w be 2*4 - (-1 + 3). Solve 9*z**2 + 2*z**4 - 8*z**3 + 8 - 8*z + 3*z**2 - w = 0 for z.
1
Let b = 2893/12900 - 19/86. Let k(q) be the third derivative of 1/75*q**5 + 2*q**2 + 0*q + 1/60*q**4 + b*q**6 + 0*q**3 + 0. What is t in k(t) = 0?
-1, 0
Let x(f) = f**3 - 4*f**2 + 5*f - 2. Let k be x(3). Suppose 5 = k*b - 11. Suppose -6*l**4 - 4*l**b + 14*l**2 - 4*l**3 - 4*l**2 + 4*l = 0. Calculate l.
-1, -2/5, 0, 1
Let d(r) be the first derivative of -2 + r**2 - 1/6*r**3 - 2*r. Determine i so that d(i) = 0.
2
Let x = 35 + -31. Let z(y) be the first derivative of -50/3*y**5 - 68/3*y**2 - 140/3*y**3 + 3 - 16/3*y - 275/6*y**x. Find b, given that z(b) = 0.
-1, -2/5
Factor 0 + 1/7*u**3 + 0*u**2 - 1/7*u.
u*(u - 1)*(u + 1)/7
Factor 131*g**2 + 14*g**2 + 15*g**4 + 81*g**3 - 10*g**2 + 18 - 31*g + 118*g.
3*(g + 1)**2*(g + 3)*(5*g + 2)
Let x(r) = r - 19. Let q be x(19). Let o(t) be the third derivative of 1/20*t**5 + 0*t**4 + 0 - 1/2*t**3 - 4*t**2 + q*t. Factor o(p).
3*(p - 1)*(p + 1)
Suppose 4*f - 12 = 4. Factor -16*o**4 + 36*o**3 - 58 - 24*o**2 + f*o + 58.
-4*o*(o - 1)**2*(4*o - 1)
Let u be (12/(-8))/((-2)/4). Factor u*p**2 - 12 - 13 + 28 - 6*p.
3*(p - 1)**2
Suppose 3*q = 6*r - 2*r - 5, -q = 3*r - 7. Factor 10/11*i + 8/11*i**r + 2/11*i**3 + 4/11.
2*(i + 1)**2*(i + 2)/11
Determine b so that b**4 + 8/3*b - 7/3*b**2 + 4/3 - 17/3*b**3 + 3*b**5 = 0.
-1, -2/3, 1
Let y be (-14)/(-70) + (-27)/(-15). Let 0 - 7/4*u**3 - 1/2*u - 9/4*u**y = 0. Calculate u.
-1, -2/7, 0
Let p(z) be the first derivative of z**8/336 - z**7/210 - z**6/120 + z**5/60 - 3*z**2 + 6. Let g(r) be the second derivative of p(r). What is h in g(h) = 0?
-1, 0, 1
Let x(f) = 4*f**2 - 51*f + 141. Let p(b) = 8*b**2 - 103*b + 281. Let q(j) = -3*p(j) + 7*x(j). Suppose q(d) = 0. Calculate d.
6
Let t(n) be the first derivative of n**3 + 0*n - 3 - n**4 + 1/2*n**2. Determine o so that t(o) = 0.
-1/4, 0, 1
Let i(d) be the first derivative of 3*d**4/4 - 4*d**3 + 6*d**2 + 1. Factor i(c).
3*c*(c - 2)**2
Suppose -4*y = -3*f - 25, 0 = 3*y - y + 3*f + 1. Let j(r) be the first derivative of -1 - 1/4*r**y + 1/3*r**3 + 0*r + 0*r**2. What is g in j(g) = 0?
0, 1
Let g(x) be the third derivative of -8*x**7/105 - 13*x**6/45 - 5*x**5/12 - 7*x**4/24 - x**3/9 + 11*x**2. Let g(w) = 0. What is w?
-1, -2/3, -1/4
Solve 0 - 16/9*u**4 - 2*u - 44/9*u**3 - 2/9*u**5 - 16/3*u**2 = 0 for u.
-3, -1, 0
Factor -1/2 + 0*x + 1/2*x**2.
(x - 1)*(x + 1)/2
Suppose -5*z - 24 = -3*o, o - 4*z + 5*z = 0. Let p(h) be the third derivative of -1/6*h**o + h**2 - 1/48*h**4 + 0*h + 1/120*h**5 + 0. Factor p(d).
(d - 2)*(d + 1)/2
Let g(v) = -31*v - 3*v**2 + 9 - 2*v**2 + 10*v**2. Let b(l) = -l**2 + 6*l - 2. Let k(w) = -33*b(w) - 6*g(w). Factor k(u).
3*(u - 2)**2
Let b(q) be the third derivative of -q**6/720 + q**5/120 - q**3/9 - 2*q**2. Factor b(x).
-(x - 2)**2*(x + 1)/6
Let y(r) be the first derivative of -r**4/18 + 4*r**3/9 - 4*r**2/3 + 2*r + 3. Let u(z) be the first derivative of y(z). Factor u(h).
-2*(h - 2)**2/3
Suppose -s + 2*s + 2 = 0. Let k(a) = 10*a**2 - 10*a - 11. Let l(v) = v**2 - v - 1. Let i(j) = s*k(j) + 22*l(j). Factor i(z).
2*z*(z - 1)
Solve 2/3*v - 2/3*v**3 + 0 - 1/3*v**2 + 1/3*v**4 = 0 for v.
-1, 0, 1, 2
Let s = -12 + 14. Suppose -2*b = s*z - 14, 2*b = z - 5*z + 20. Factor -1/4*v**z + 1/4 + 3/4*v**2 - 3/4*v.
-(v - 1)**3/4
Let -120*z + 181 + 211 + 328 + 9*z**2 - 4*z**2 = 0. Calculate z.
12
Let n(k) = -85*k**3 + 265*k**2 - 95*k - 85. Let q(y) = -7*y**3 + 22*y**2 - 8*y - 7. Let x(j) = -3*n(j) + 35*q(j). Factor x(d).
5*(d - 2)*(d - 1)*(2*d + 1)
Let g(s) be the third derivative of -s**9/45360 + s**8/10080 - s**7/7560 - s**4/6 - s**2. Let w(o) be the second derivative of g(o). Factor w(n).
-n**2*(n - 1)**2/3
Factor 8/11 + 8/11*b - 70/11*b**2.
-2*(5*b - 2)*(7*b + 2)/11
Let r(n) be the first derivative of -n**6/40 + 17*n**5/80 - 5*n**4/8 + n**3/2 - 5*n**2/2 - 4. Let f(l) be the second derivative of r(l). Factor f(k).
-3*(k - 2)**2*(4*k - 1)/4
Let k(w) be the second derivative of w**7/84 - w**6/20 + 3*w**5/40 - w**4/24 - 10*w. Let k(r) = 0. Calculate r.
0, 1
Suppose -o + 3 = 2*o. Suppose 2*n - 3*x + 6 = -0*n, 5*n - 4*x = -o. Factor 1/4 - 1/4*f**2 - 1/4*f**n + 1/4*f.
-(f - 1)*(f + 1)**2/4
Let f(c) = 6*c**4 + 80*c**3 + 74*c**2 - 94*c - 80. Let p(g) = g**4 + 16*g**3 + 15*g**2 - 19*g - 16. Let v(z) = 3*f(z) - 14*p(z). Factor v(q).
4*(q - 1)*(q + 1)*(q + 2)**2
Let h = 9 - 1. Suppose h*o - 2*o**2 - 9 - 2 + 3 = 0. What is o?
2
Solve 0 + 0*t**3 + 2/11*t**5 + 2/11*t**4 + 0*t + 0*t**2 = 0 for t.
-1, 0
Let s(t) be the first derivative of -11/9*t**3 + 4/3*t**2 + 2 + 4/3*t + 1/4*t**4. Factor s(n).
(n - 2)**2*(3*n + 1)/3
Let k = 25 + -25. Let n(q) be the third derivative of -1/480*q**6 + 0 + k*q**4 - 1/240*q**5 - 2*q**2 + 0*q**3 + 0*q. Suppose n(u) = 0. Calculate u.
-1, 0
Let q be 3/(3*-2) - 46/(-12). Solve 8/3*g**3 + q*g**2 + 0 + 2/3*g = 0.
-1, -1/4, 0
Factor 7*g**4 - 28*g**5 + 25*g**2 + 16*g + 29*g**5 - 2 + 19*g**3 + 6.
(g + 1)**3*(g + 2)**2
Let s(d) = -d**2 + d - 1. Let c(n) = 4*n**2 - 2*n + 1. Let a(g) = g - 1. Let v be a(4). Let y(p) = v*s(p) + c(p). Factor y(x).
(x - 1)*(x + 2)
Let d(c) be the first derivative of 0*c**3 - 4 - 1/2*c**2 + 1/12*c**4 - 2/3*c. Factor d(r).
(r - 2)*(r + 1)**2/3
Suppose 0 = l - 2*f + 2, -35 = -l - 4*l - 5*f. Factor 4/3*z**l - 8/3*z + 0*z**2 - 4/3 + 8/3*z**3.
4*(z - 1)*(z + 1)**3/3
Let s(h) be the first derivative of -h**6/120 - h**5/60 + h**4/24 + h**3/6 + h**2 - 3. Let j(t) be the second derivative of s(t). Factor j(o).
-(o - 1)*(o + 1)**2
Let w be (-28)/(-48)*(-1)/(-7). Let i(s) be the second derivative of 0 + w*s**4 - 1/20*s**5 + 0*s**3 + s + 0*s**2. Suppose i(j) = 0. Calculate j.
0, 1
Solve 44 - 34 - 13*q**3 + 2*q**5 + 42*q + 18*q**4 + 65*q**3 + 68*q**2 = 0.
-5, -1
Let l(i) = i**2 - 5*i - 3. Let h be l(6). Let r = -1 + h. Factor 2*c**3 + r*c**2 - 2*c**2 - c - c**5.
-c*(c - 1)**2*(c + 1)**2
Let u = -1409/4 - -354. Let -1/2 - 5/4*w**3 - u*w - 1/4*w**4 - 9/4*w**2 = 0. What is w?
-2, -1
Let x(s) = -s**3 - 9*s**2 - 9*s - 11. Let l be x(-8). Let q be (-6)/9 + (-17)/l. Let 3*y**q - y**4 - 2*y**3 - 4*y**2 + 4*y**2 = 0. Calculate y.
-2/3, 0, 1
Let i(d) = -3*d**3 + 27*d**2 - 87*d + 81. Let v(w) = 6*w**3 - 54*w**2 + 173*w - 162. Let g(a) = -11*i(a) - 6*v(a). Suppose g(b) = 0. What is b?
3
Let i(d) be the first derivative of d**7/3360 + d**6/288 + d**5/60 + d**4/24 - d**3/3 - 1. Let h(m) be the third derivative of i(m). Factor h(u).
(u + 1)*(u + 2)**2/4
Let y(t) be the first derivative of 100*t**6/51 - 10*t**5/17 - 58*t**4/17 + 58*t**3/51 + 16*t**2/17 - 8*t/17 - 2. Suppose y(b) = 0. What is b?
-1, -2/5, 1/4, 2/5, 1
Suppose -3*m - 4*o = m - 24, -m + 3*o = 2. Let b = -1 + m. Determine y, given that y + 0*y**b - 5*y**2 - 2*y**3 + 3*y**2 + 1 + y**4 + y**5 = 0.
-1, 1
Suppose -3*g - 18 = -4*t, -4*t + 5*g = -5*t + 16. Solve -1/2*j**4 + 2*j**5 + 0 + 11/2*j**2 - j - t*j**3 = 0.
-2, 0, 1/4, 1
Suppose 2*i + 6 = 2*v, 9*v - 6 = 4*v - 4*i. Factor 1/5*z**v + 2/5 + 3/5*z.
(z + 1)*(z + 2)/5
Let o(c) = -2*c**3 - 2*c - 1. Let h be o(-1). Let g(q) be the second derivative of -1/48*q**4 - q + 0 - 1/12*q**h - 1/8*q**2. Factor g(d).
-(d + 1)**2/4
Suppose a = 4*t + 14, 2*a + 2*a = -2*t + 2. Factor -2*u + 5*u**2 + 2*u**3 - 3*u**4 - u**4 - 3*u**2 + a*u**4.
-2*u*(u - 1)**2*(u + 1)
Let f(h) be the second derivative of -4*h**6/15 - 13*h**5/10 - 5*h**4/2 - 7*h**3/3 - h**2 - 6*h. Factor f(s).
-2*(s + 1)**3*(4*s + 1)
Factor -12*l + 7 + 17 + 12 + l**2.
(l - 6)**2
Let g = 1 - -2. Let u be -1*(-8 + g - 0). Factor 0*k + 1/4*k**u + 1/4*k**4 + 0 + 0*k**3 + 0*k**2.
k**4*(k + 1)/4
Suppose z - 36*k = -35*k - 3, -3*k + 9 = 0. Determine o so that 4/3