
Let p(o) be the first derivative of o**6/180 - o**5/45 - o**4/36 + 2*o**3/9 + 3*o**2/2 + 2. Let q(b) be the second derivative of p(b). Factor q(t).
2*(t - 2)*(t - 1)*(t + 1)/3
Let q = 1/48 - -7/48. Let y(v) be the second derivative of 0 - 1/4*v**2 - q*v**4 + v - 5/12*v**3. Let y(t) = 0. Calculate t.
-1, -1/4
Let s = -13 + 1. Let a be ((-6)/(-4))/((-9)/s). Factor 6*z**a - 8*z - 2*z**3 + 2 + 2*z + 0.
-2*(z - 1)**3
Let c(w) = w**2 - 1. Let u(l) = 17*l**2 + 21*l + 4. Let f(m) = 2*c(m) - u(m). Factor f(a).
-3*(a + 1)*(5*a + 2)
Let p be (6/4)/(3/20). Suppose 5*x - p = -0*x. Factor 2/3*w + 0 + 1/3*w**3 + w**x.
w*(w + 1)*(w + 2)/3
Let q(p) be the first derivative of 40/3*p**2 + 26/3*p**4 + 2 + 5/18*p**6 + 136/9*p**3 + 16/3*p + 37/15*p**5. Determine r so that q(r) = 0.
-2, -1, -2/5
Suppose 2*q + 2*q = 8. Solve -6*w**q - 10*w - 7 + 3 + 0 = 0.
-1, -2/3
Let x(d) be the second derivative of -d**4/6 - 2*d**3/3 - d**2 - 7*d. Solve x(n) = 0.
-1
Let q(p) be the second derivative of p**6/75 + 3*p**5/25 + 13*p**4/30 + 4*p**3/5 + 4*p**2/5 - 7*p. Let q(a) = 0. What is a?
-2, -1
Let k(m) be the second derivative of 2*m**7/7 - 14*m**6/15 - 3*m**5/5 + 11*m**4/3 - 8*m**2 - 9*m. Determine i so that k(i) = 0.
-1, -2/3, 1, 2
Find i, given that -15*i**3 - 4 + 2*i**5 + 7*i**2 + 16*i**3 - 3*i**4 - i**5 - 2*i**5 = 0.
-2, -1, 1
Let s(t) be the third derivative of t**6/420 + 3*t**5/70 + 2*t**4/7 + 16*t**3/21 - 35*t**2 + 1. Solve s(i) = 0.
-4, -1
Let x(i) be the third derivative of -i**6/240 + i**5/40 - 2*i**3/3 + 5*i**2. Let g(o) be the first derivative of x(o). Factor g(b).
-3*b*(b - 2)/2
Let t(l) be the third derivative of l**6/150 + l**5/25 - 6*l**2 - 3. Factor t(o).
4*o**2*(o + 3)/5
Suppose -k = q - 11 - 2, 2*q - k = 11. Suppose 3*g = 4 + q. Factor -a**g - a**2 - a**3 + a**3 - 2*a**3.
-a**2*(a + 1)**2
Let t(z) be the first derivative of -3*z**4/16 + 7*z**3/4 - 6*z**2 + 9*z - 13. Factor t(u).
-3*(u - 3)*(u - 2)**2/4
Let p = 6 + -1. Let 11*o - p*o - o**3 - 5*o = 0. Calculate o.
-1, 0, 1
Let p(z) be the third derivative of 1/588*z**8 - 1/245*z**7 - 1/105*z**6 + 0*z**3 + 0 + 1/42*z**4 + 0*z + 1/70*z**5 - z**2. Find c such that p(c) = 0.
-1, -1/2, 0, 1, 2
Let v(k) = 3*k - k - 3*k - 1. Let w be v(-3). Let 0 - 2/5*x - 2/5*x**w = 0. Calculate x.
-1, 0
Suppose 4*o - o = -2*n + 17, 0 = -2*n + o + 5. Let t be (6/16)/(6/n). Factor -t*v**2 + 0*v + 1/4.
-(v - 1)*(v + 1)/4
Suppose 0*i - i = 0. Let y(p) be the third derivative of -1/315*p**7 + 0 + 1/36*p**4 + i*p + 2*p**2 - 1/180*p**6 + 0*p**3 + 1/90*p**5. Let y(b) = 0. What is b?
-1, 0, 1
Let k = -34/15 + 7/3. Let p(x) be the first derivative of 1/5*x**2 - k*x**3 - 1/5*x + 2. Factor p(u).
-(u - 1)**2/5
Let n be 12*-1*10/6. Let r be (8/n)/((-2)/10). Suppose -1/2*q**r + 0 + 1/4*q**3 + 1/4*q = 0. What is q?
0, 1
What is p in -6/13*p**3 - 2/13*p**4 + 6/13*p + 4/13 - 2/13*p**2 = 0?
-2, -1, 1
Let f(r) be the third derivative of 0 - 2*r**2 - 1/600*r**6 + 0*r + 0*r**3 + 1/300*r**5 + 0*r**4. Factor f(x).
-x**2*(x - 1)/5
Let w = 2/5803 - -5563/696360. Let l(t) be the third derivative of -1/24*t**4 + 1/12*t**3 + 0 + 0*t + w*t**5 - 2*t**2. Solve l(c) = 0.
1
Let n(r) be the first derivative of 2/9*r**5 + 1/9*r**2 - 2 - 13/18*r**4 - 4/9*r + 2/3*r**3. Let n(t) = 0. What is t?
-2/5, 1
Suppose -16 = -0*u - 4*u. Let 0*i + 8*i**5 + 3*i + 28*i**u + i + 36*i**3 + 20*i**2 = 0. What is i?
-1, -1/2, 0
Suppose 25*q**4 + 25*q**3 - 35*q**5 - 12*q + 20*q**3 + 2*q - 25*q**2 = 0. What is q?
-1, -2/7, 0, 1
Let m(f) = -f**2 - f - 1. Let l(y) = 17*y**2 - 39*y + 29. Let k(s) = l(s) + 5*m(s). Factor k(t).
4*(t - 3)*(3*t - 2)
Let n(x) = -x**3 + 4*x**2 - 3*x - 4. Let b(c) = 9*c**3 - 33*c**2 + 24*c + 33. Let l(i) = 4*b(i) + 33*n(i). Find k such that l(k) = 0.
-1, 0, 1
Let d(i) = -i**3 + 8*i**2 - 4*i + 2. Let z be d(7). Factor 2*c**4 + 23*c + c**5 + c**3 - z*c.
c**3*(c + 1)**2
Let q = 130 + -385/3. Factor 1/3*b**4 + q*b**3 + 2/3 + 7/3*b + 3*b**2.
(b + 1)**3*(b + 2)/3
Find u, given that -1 + 1/3*u**2 - 2/3*u = 0.
-1, 3
Suppose -400 = -6*z - 388. Factor -8/7*p**z - 2/7*p + 0.
-2*p*(4*p + 1)/7
Let t = 20214/31 + -652. Let u = 288/341 + t. Factor 4/11*b + u*b**2 + 0.
2*b*(5*b + 2)/11
Find a, given that -20/7*a + 1/7*a**4 + 2/7*a**3 - a**2 - 12/7 = 0.
-2, -1, 3
Let v(j) be the second derivative of -j**4/8 + j**3 - 3*j**2 + 7*j. Determine x, given that v(x) = 0.
2
Let c(y) be the second derivative of 3/10*y**5 + 1/3*y**6 + 0*y**3 - 4*y - 1/3*y**4 + 0 + 0*y**2. Factor c(b).
2*b**2*(b + 1)*(5*b - 2)
Suppose -1/8*j**2 + 0 + 1/8*j**3 + 0*j = 0. Calculate j.
0, 1
Let j(a) be the first derivative of -4*a**5/5 + 5*a**4 - 12*a**3 + 14*a**2 - 8*a - 27. Find t, given that j(t) = 0.
1, 2
Let v be (4 + (27/(-6) - -1))*1. Let u(s) be the first derivative of -1/12*s**3 + v*s - 1/8*s**2 + 3. Factor u(l).
-(l - 1)*(l + 2)/4
What is m in 3 + 7*m**2 - m**2 - 3*m**2 - 6*m = 0?
1
Suppose -12 = -2*z - 2. Let m(w) = w**4 + w**3 + w**2 - 1. Let y(g) = 3*g**4 + 4*g**3 + 6*g**2 - 5. Let a(j) = z*m(j) - y(j). Factor a(c).
c**2*(c + 1)*(2*c - 1)
Let o(f) = -7*f**4 + 4*f**3 + 5*f**2 + f - 3. Let k(q) = -3*q**4 + 2*q**3 + 2*q**2 - 1. Let h(g) = 5*k(g) - 2*o(g). Suppose h(v) = 0. What is v?
-1, 1
Let z(p) be the second derivative of 3*p**5/20 + 3*p**4/4 + 3*p**3/2 + 3*p**2/2 - 8*p. Suppose z(f) = 0. What is f?
-1
Suppose -3*z - 16 = -2*n - 2*n, -2*n = -3*z - 8. Factor 0*u + 1/3*u**2 + 1/3*u**3 + z.
u**2*(u + 1)/3
Suppose -76 + 76 + 2*d**4 = 0. Calculate d.
0
Let f = 1594/5 - 317. Let u = 37/15 - f. Factor -u*k + 0 + 4/3*k**2 - 2/3*k**3.
-2*k*(k - 1)**2/3
Suppose 0 = 10*z - 14*z + 12. Let i(t) be the first derivative of 0*t - 1/8*t**2 - 1/20*t**5 + 1/12*t**z + 1/16*t**4 + 2. Factor i(a).
-a*(a - 1)**2*(a + 1)/4
Let g(o) be the first derivative of o**4/48 - o**3/12 + 6*o - 3. Let j(u) be the first derivative of g(u). Find w, given that j(w) = 0.
0, 2
What is b in 0 - 6*b**2 + 4/3*b = 0?
0, 2/9
Let v(i) be the third derivative of -i**5/30 + i**4/6 - i**3/3 - 8*i**2. Factor v(g).
-2*(g - 1)**2
Let d(t) = t**4 - t**3 - 1. Let j(b) = b**5 - 7*b**4 + 9*b**3 + 6*b**2 - 9*b + 1. Let r(c) = d(c) + j(c). Factor r(m).
m*(m - 3)**2*(m - 1)*(m + 1)
Let f(q) be the second derivative of -q**4/18 - 2*q**3/27 + q**2/9 + 14*q. Factor f(r).
-2*(r + 1)*(3*r - 1)/9
Let p(y) = -3*y. Let a be p(-1). Suppose i = 5*i - a*s, 3*i = s. Find v, given that 2/5*v - 2*v**2 + i + 18/5*v**4 + 6/5*v**3 = 0.
-1, 0, 1/3
Factor s**4 + 3 - 6*s - 2 + 6*s - 2*s**2.
(s - 1)**2*(s + 1)**2
Factor 1/5*m**4 - 12/5 - 7/5*m**2 - 2/5*m**3 + 4*m.
(m - 2)**2*(m - 1)*(m + 3)/5
Let w(i) be the third derivative of i**8/2184 + i**7/1365 - i**6/780 - i**5/390 - 5*i**2. Factor w(z).
2*z**2*(z - 1)*(z + 1)**2/13
Solve -6/17*g**3 + 4/17*g**2 + 0 + 0*g + 2/17*g**4 = 0 for g.
0, 1, 2
Let m be ((-2)/72)/((-3)/6). Let j(z) be the first derivative of -2/45*z**5 + 0*z + 2/27*z**3 - m*z**4 - 2 + 1/9*z**2. Determine u, given that j(u) = 0.
-1, 0, 1
Factor -1/4*i - 1/2 + 1/4*i**2.
(i - 2)*(i + 1)/4
Let i = 2/193 - -185/772. Let m = 1/12 + i. Factor -r**4 + 2/3*r**3 - r + m*r**5 + 2/3*r**2 + 1/3.
(r - 1)**4*(r + 1)/3
Let r(l) be the second derivative of -l**6/3 - l**5/10 - 22*l. Solve r(y) = 0 for y.
-1/5, 0
Let k(u) be the second derivative of -3/4*u**4 - 3/2*u**2 + 3/2*u**3 + 0 + u + 3/20*u**5. Factor k(b).
3*(b - 1)**3
Let 21/2*r**3 + 3*r**2 + 0 + 0*r = 0. Calculate r.
-2/7, 0
Let p = 11 + -11. Let r be (p + (-2)/(-18))*6. Find m such that r*m - 2/3*m**2 + 4/3 = 0.
-1, 2
Factor -10/11*c**3 + 0 - 2/11*c**5 + 4/11*c**2 + 0*c + 8/11*c**4.
-2*c**2*(c - 2)*(c - 1)**2/11
Let i = -6 - -9. Let m be (4 - i)*-1 + 2. Let p(b) = -b + 1. Let a(o) = 3*o**3 - 9*o**2 - o + 1. Let c(w) = m*a(w) - p(w). Factor c(z).
3*z**2*(z - 3)
Suppose p + 1 = r, p - r + 2 = r. Let a(y) be the first derivative of -4/3*y**3 + 0*y**2 + 1 + p*y - 6/5*y**5 + 5/2*y**4. Factor a(v).
-2*v**2*(v - 1)*(3*v - 2)
Let j = -191/3 - -65. Factor 2/3*t - 2/3*t**3 + j - 4/3*t**2.
-2*(t - 1)*(t + 1)*(t + 2)/3
Let d(z) = 4*z**3 - 2*z**2 - 2*z. Let i(o) be the second derivative of -13*o**5/20 + o**4/2 + 7*o**3/6 + 3*o. Let n(p) = 7*d(p) + 2*i(p). What is j in n(j) = 0?
0, 1
Let w be ((-71)/(-24) - 3)*-2. Let l(s) be the third derivative of 0 - 1/16*s**4 - w*s**3 + 0*s - 2*s**2 - 1/60*s**5. Factor l(u).
-(u + 1)*(2*u + 1)/