
Suppose 5*a - a - z = 15, 2*a - 4*z = 18. Let o(c) be the first derivative of -8/9*c - 16/9*c**2 - 1/6*c**4 - 26/27*c**a - 2. Factor o(q).
-2*(q + 2)**2*(3*q + 1)/9
Let r be (3/16)/(9/6). Let m(p) be the second derivative of -1/16*p**4 - 1/80*p**5 + p + 0 - r*p**3 - 1/8*p**2. Factor m(i).
-(i + 1)**3/4
Suppose 0 = 2*p - 5*p - 12. Let r = p - -7. Find l, given that -5 + 3 + r*l + l - 2*l**2 = 0.
1
Let m(w) be the third derivative of -w**8/336 - w**7/35 - w**6/30 + w**5/10 + 5*w**4/24 - 6*w**2. Factor m(z).
-z*(z - 1)*(z + 1)**2*(z + 5)
Let k(c) be the first derivative of c**3/6 + 3*c**2/2 + 9*c/2 - 8. Factor k(d).
(d + 3)**2/2
Suppose -4 = 4*d - 5*w, -4*d - 3*w + 5 = -23. Determine u, given that u + u**4 - u**3 + 1 + d*u**4 - 3*u**4 - 3*u**2 = 0.
-1, -1/2, 1
Let m(x) be the second derivative of 0 + x + 0*x**3 + 1/30*x**6 - 1/20*x**5 + 1/42*x**7 - 1/12*x**4 + 0*x**2. Factor m(j).
j**2*(j - 1)*(j + 1)**2
Factor 3/7*t**4 - 9/7*t**2 + 3/7*t + 6/7 - 3/7*t**3.
3*(t - 2)*(t - 1)*(t + 1)**2/7
Let s(x) be the first derivative of -1/2*x**2 - 1 + 1/33*x**3 + 0*x + 1/66*x**4 + 1/330*x**5. Let t(c) be the second derivative of s(c). Factor t(h).
2*(h + 1)**2/11
Let x(d) be the second derivative of -4*d**7/7 + 13*d**6/15 + 4*d**5/5 - 7*d**4/6 - 2*d**3/3 - 6*d. Solve x(k) = 0.
-2/3, -1/4, 0, 1
Let y(r) = -r**2 - r. Let q(g) = -2*g**3 - 12*g**2 - 10*g. Let k(z) = -q(z) + 8*y(z). Suppose k(a) = 0. Calculate a.
-1, 0
Let h = -391/3 - -131. Factor h*s + 10/3*s**3 + 16/3*s**2 - 4/3.
2*(s + 1)**2*(5*s - 2)/3
Suppose -4*g - f = -6, f = g + 3*f + 2. Let d(p) = -p**2 + 8*p - 5. Let k be d(7). What is i in -k*i**2 - 4*i**3 - 10*i + 2 + 2*i**3 + 2 + 10*i**g = 0?
1, 2
Let b(r) = r**3 - 11*r**2 + 12*r - 15. Let o be b(10). Let n(i) be the third derivative of 1/240*i**o + 0 + 1/24*i**4 - i**2 + 1/6*i**3 + 0*i. Factor n(l).
(l + 2)**2/4
Let l(w) = -4*w**5 + 32*w**4 - 52*w**3 + 56*w**2 - 24*w. Let r(t) = -t**4 - t**2 + t. Let c(d) = l(d) + 8*r(d). Factor c(j).
-4*j*(j - 2)**2*(j - 1)**2
Suppose 3 - 7 = -2*h. Suppose -3 = -2*i + 3. Let 1/4*z + 0 + 1/2*z**h + 1/4*z**i = 0. What is z?
-1, 0
Let i(t) be the third derivative of -t**7/1260 + t**6/720 + t**5/360 - t**4/144 + 29*t**2. Find n such that i(n) = 0.
-1, 0, 1
Let g = -1097/9 - -367/3. What is l in -g*l**2 + 0 + 2/9*l + 2/9*l**3 = 0?
0, 1
Let b be 2 - 0 - 7565/(-15). Let n = b + -499. Find h such that -n*h - 26/3*h**2 + 10*h**4 + 22/3*h**3 - 4/3 = 0.
-1, -2/5, -1/3, 1
Let b be (-13)/(-26) + (-9)/30. Suppose 0 = i - 1, -5*m + 21 = -m + 5*i. Suppose 1/5*f**2 + 0 + 0*f - 4/5*f**3 + 4/5*f**5 - b*f**m = 0. Calculate f.
-1, 0, 1/4, 1
Factor -8*k**4 + 10*k**4 + k**3 + k**5 + 0*k**5.
k**3*(k + 1)**2
Let q = 0 - -2. Suppose 0*z + q = z. Let 1 - 4*u + 7/4*u**z = 0. Calculate u.
2/7, 2
Let d = 0 - 0. Let u be 19/42 - (-5)/(-30). Factor -u*o**3 - 4/7*o**4 + 0*o + d*o**2 + 0.
-2*o**3*(2*o + 1)/7
Let k(d) be the first derivative of d**7/840 - 2*d**3/3 - 4. Let h(b) be the third derivative of k(b). Factor h(z).
z**3
Let b(u) be the second derivative of 0*u**2 - 1/30*u**4 - 1/15*u**3 - 2*u + 0. Factor b(g).
-2*g*(g + 1)/5
Suppose 3*x + 23 = 5*w, -w + 8 = 4*x + 2*w. Let u be 3*x - 42/(-12). Let 0 + 0*q**4 - 1/4*q**5 + 0*q**2 - 1/4*q + u*q**3 = 0. Calculate q.
-1, 0, 1
Let o(k) be the second derivative of k**6/285 + k**5/95 - 2*k**4/57 - 8*k**3/57 - 16*k + 1. Find c, given that o(c) = 0.
-2, 0, 2
Let w(v) be the third derivative of -v**7/15120 + v**6/4320 + v**5/360 - 5*v**4/24 + v**2. Let j(b) be the second derivative of w(b). Factor j(i).
-(i - 2)*(i + 1)/6
Let p(z) be the first derivative of z**4/12 + 4*z**3/9 + 2*z**2/3 - 7. Let p(u) = 0. What is u?
-2, 0
Let i(l) be the first derivative of l**4 + 4*l**3/3 - 11. Factor i(m).
4*m**2*(m + 1)
Find c such that -4*c**4 + 26 + c**2 - 3*c**3 - 26 = 0.
-1, 0, 1/4
Let c be ((3/(-84))/(-1))/(14/168). Find z such that 6/7 - c*z**3 - 15/7*z + 12/7*z**2 = 0.
1, 2
Let c(r) = r**2 - r + 1. Let i(k) = 2*k**4 + 18*k**3 + 57*k**2 + 51*k + 3. Let b(y) = -3*c(y) + i(y). Factor b(v).
2*v*(v + 3)**3
Let t(w) = w**3 + 7*w**2 + 6*w + 3. Let u be t(-6). Let i(v) = -v + 4. Let f be i(-3). Let 2*q**4 - 3*q**3 - 8*q**u + f*q**3 + 2*q**2 = 0. Calculate q.
0, 1
Let v(x) = 4 + 4 - 20*x + 19*x. Let d be v(8). Suppose 2/3*a**4 + 10/3*a**2 + d + 4/3*a + 8/3*a**3 = 0. Calculate a.
-2, -1, 0
Let o(m) be the first derivative of 0*m + 1 - 44/5*m**5 + 0*m**2 - 5/3*m**6 - 16/3*m**3 - 14*m**4. Suppose o(n) = 0. What is n?
-2, -2/5, 0
Let i(p) be the second derivative of p**4/42 - 10*p**3/21 + 25*p**2/7 - 13*p. Factor i(l).
2*(l - 5)**2/7
Factor 0*x**3 + 0 + 24*x**2 - 3/2*x**5 - 6*x**4 + 24*x.
-3*x*(x - 2)*(x + 2)**3/2
Let u(g) be the third derivative of -g**5/30 + g**4/2 + 16*g**3/3 - 34*g**2. Determine f, given that u(f) = 0.
-2, 8
Let a(t) = -t**4 + t - 1. Let o(c) = -14*c**2 - 4*c**2 + 6*c - 4*c**2 - 2*c**4 + 2*c**2 + 16*c**3 + 2. Let y(d) = 2*a(d) + o(d). Factor y(f).
-4*f*(f - 2)*(f - 1)**2
Suppose -4*v = -4*w + 20, -4*w - w = 4*v - 25. Suppose -r + 0 + 2 = v. Factor 1/2*y**r + 0 + 1/2*y.
y*(y + 1)/2
Let o(b) = -2*b**2 + 37*b + 22. Let q be o(19). Let -4/11*d**4 + 0 + 2/11*d**5 + 0*d + 2/11*d**q + 0*d**2 = 0. Calculate d.
0, 1
Let x(o) be the second derivative of -o**6/120 + o**5/80 + o**4/48 - o**3/24 - 22*o. Suppose x(f) = 0. Calculate f.
-1, 0, 1
Factor 1/5*s**2 - 2/5*s + 1/5.
(s - 1)**2/5
Suppose q = 4*i - 3*q - 8, -22 = -3*i - 5*q. Let r = -2 + 6. Let 2*v**2 - i*v + 4*v + 30*v**3 - r*v = 0. What is v?
-2/5, 0, 1/3
Let b = 4 - 2. Determine m so that 3*m**2 + m**2 - m**b = 0.
0
Let a(i) = 6*i**5 + 4*i**4 + 4. Let y(q) = -q**2 + 5*q - 1. Let v be y(4). Let x(f) = -5*f**5 - 3*f**4 - 3. Let g(n) = v*a(n) + 4*x(n). Factor g(o).
-2*o**5
Let d(n) be the first derivative of -1/4*n**2 + 0*n + 3 + 1/6*n**3. Find h such that d(h) = 0.
0, 1
Let g(i) be the third derivative of 1/80*i**6 + 0*i**3 + 0*i + 0 - 1/40*i**5 - 4*i**2 + 0*i**4. Determine r, given that g(r) = 0.
0, 1
Let d(v) = -14*v**3 + 10*v**2 - 3*v + 7. Suppose 5*j + 14 = -21. Let b(p) = -2*p + 4*p - 5*p**2 - 1 - 3 + 7*p**3. Let r(z) = j*b(z) - 4*d(z). Factor r(q).
q*(q - 1)*(7*q + 2)
Let n(j) be the first derivative of -1/3*j - 4 - 56/15*j**5 - 25/3*j**4 - 37/6*j**3 - 25/12*j**2. Solve n(f) = 0.
-1, -2/7, -1/4
Let -18/7 + 12/7*j - 2/7*j**2 = 0. What is j?
3
Let f(m) be the first derivative of m**6/9 - 44*m**5/75 + 19*m**4/15 - 64*m**3/45 + 13*m**2/15 - 4*m/15 - 2. Factor f(j).
2*(j - 1)**4*(5*j - 2)/15
Let h(p) be the third derivative of -4*p**2 - 2/45*p**3 - 1/36*p**4 + 0*p + 1/180*p**6 + 0 + 1/225*p**5. Factor h(l).
2*(l - 1)*(l + 1)*(5*l + 2)/15
Suppose -3 = 3*f - 3*x, -5*x + 16 = -x. Let 2*z + 0 - 2*z - 2*z + 2*z**f + 2 - 2*z**2 = 0. What is z?
-1, 1
Let m(r) be the second derivative of -r**7/336 - r**6/240 - 7*r - 1. Factor m(j).
-j**4*(j + 1)/8
Let x(o) be the first derivative of 3*o**4/4 - 9*o**2/2 + 6*o + 10. Let x(r) = 0. Calculate r.
-2, 1
Determine x so that 4*x**2 - 4 - 8*x**3 + 0*x**2 + 4*x**4 + 4 = 0.
0, 1
Let s(z) = -9*z**3 - 136*z**2 - 320*z - 166. Let q(m) = 19*m**3 + 271*m**2 + 640*m + 331. Let a(n) = -6*q(n) - 11*s(n). Factor a(w).
-5*(w + 4)**2*(3*w + 2)
Factor 0*v + 0 - 2/11*v**3 + 2/11*v**2.
-2*v**2*(v - 1)/11
Let t be 15/52 + 6/(-12). Let d = t - -6/13. Factor 0 + 0*l - d*l**2 - 1/2*l**3 - 1/4*l**4.
-l**2*(l + 1)**2/4
Let h(j) be the third derivative of 0*j - 1/540*j**6 + 4/27*j**3 - 2/27*j**4 + 1/54*j**5 + 4*j**2 + 0. Suppose h(n) = 0. Calculate n.
1, 2
Let v = 1/52 + 49/156. Solve -v*c**2 + c + 2/3*c**4 - 1/3 - c**3 = 0.
-1, 1/2, 1
Let p(r) = 8*r**2 + 8*r - 5. Let s(q) = 12*q**2 + 12*q - 8. Let v(m) = -8*p(m) + 5*s(m). Factor v(z).
-4*z*(z + 1)
Let h be -3 + -3 + (11 - 1). Factor -2*b + 8*b - 4*b**2 - 2 - 8*b**3 + 6*b**h + 2*b.
2*(b - 1)**2*(b + 1)*(3*b - 1)
Let n(f) be the second derivative of f**7/630 - f**6/90 - f**5/10 + f**4/6 - f. Let m(r) be the third derivative of n(r). Factor m(w).
4*(w - 3)*(w + 1)
Factor 2*x**3 + 423*x**4 + x**2 - 851*x**4 + 425*x**4.
-x**2*(x - 1)*(3*x + 1)
Let k = -42 - -62. Determine d so that 48*d**2 + 21*d**3 + 53*d - k*d + 0 + 6 = 0.
-1, -2/7
Let i(k) be the third derivative of k**6/120 + k**5/12 - 5*k**4/24 + 4*k**3/3 + 2*k**2. Let c be i(-6). Factor y + y**4 + 0 + 0 - y**c - y**3.
y*(y - 1)**2*(y + 1)
Le