**2*(n + 1)**3/3
Let g = -118 + 123. Let d be ((-252)/80)/(-7) + (-1)/g. Factor -p - 1 - d*p**2.
-(p + 2)**2/4
Let n(q) be the first derivative of -5*q**3/3 - 205*q**2/2 - 190. What is c in n(c) = 0?
-41, 0
Let q be (-8)/6 - (-935)/330. Suppose 0 - 3*t + q*t**2 + 3/2*t**3 = 0. Calculate t.
-2, 0, 1
Let t(s) = 2*s**2 - 25*s + 65. Let f = 39 + -30. Let v be t(f). Factor -13/4*b - b**v - 3/4.
-(b + 3)*(4*b + 1)/4
Suppose -4*s = 2*s. Suppose s*n = -4*n. Factor n*g + g - 5*g**4 + 4*g**4 - g**3 - g**2 + 2*g**4.
g*(g - 1)**2*(g + 1)
Suppose -5*o + 22 = 4*w, -3*w - 2*o + 5 = -4*o. Suppose -6*s = -w*s - 15. Factor 80 - 40*n + s*n**2 + 6*n**2 - 3*n**2 - 3*n**2.
5*(n - 4)**2
Solve -3/7*x**3 + 51/7*x**2 + 3/7*x - 51/7 = 0.
-1, 1, 17
Let w(m) be the third derivative of 0*m**5 + 0*m**3 + 0*m**4 + 5/1008*m**8 - 1/126*m**7 - 6*m**2 + 0 + 0*m**6 + 0*m. Factor w(g).
5*g**4*(g - 1)/3
Let r = 45 + -55. Let c(v) = -3*v**2 - 32*v - 15. Let k be c(r). Factor 2/5*w**2 - 1/5*w**4 - 1/5*w + 2/5*w**3 - 1/5*w**k - 1/5.
-(w - 1)**2*(w + 1)**3/5
Let a be 8662/12780 + 2/9 + 2/4. What is d in -8/5*d + a + 1/5*d**2 = 0?
1, 7
Let b(d) = d**2 - d. Let n(f) = -12*f**2 + 13*f + 3. Let i(c) = -12*c**2 + 13*c + 3. Let q(s) = 6*i(s) - 5*n(s). Let o(z) = -22*b(z) - 2*q(z). Factor o(u).
2*(u - 3)*(u + 1)
Let c(h) = h**2 + 13*h - 6. Let d(i) = i**2 + i. Let k(r) = c(r) - 4*d(r). Factor k(j).
-3*(j - 2)*(j - 1)
Let z(g) be the second derivative of -g**4/48 + g**3/2 - 9*g**2/2 - 5*g. Let z(w) = 0. Calculate w.
6
Let x(k) = 4*k**4 + 36*k**3 - 54*k**2 + 14*k + 39. Let g(t) = 3*t**4 + 18*t**3 - 27*t**2 + 6*t + 18. Let z(h) = -13*g(h) + 6*x(h). Factor z(a).
-3*a*(a - 1)*(a + 2)*(5*a + 1)
Let p(v) be the second derivative of -v**7/6300 + v**6/1350 - v**5/900 - 3*v**3/2 - 10*v. Let c(h) be the second derivative of p(h). Factor c(g).
-2*g*(g - 1)**2/15
Let g(k) be the first derivative of k**9/756 - k**7/70 + k**6/45 + 17*k**3/3 - 18. Let s(c) be the third derivative of g(c). Factor s(z).
4*z**2*(z - 1)**2*(z + 2)
Suppose 0 = -4*u - 8, -2*c - 1 + 7 = u. Determine p, given that 8 - 5*p**2 - 7*p**3 + 23*p**2 - 8*p - 22*p**4 + 23*p**c - 12*p = 0.
1, 2
Let s(q) be the second derivative of -q**6/150 + 3*q**5/50 - 3*q**4/20 + 2*q**3/15 + 17*q. Factor s(n).
-n*(n - 4)*(n - 1)**2/5
Let v(w) = 15*w**5 + 43*w**4 + 27*w**3 + 3*w**2 - 8*w - 3. Let i(j) = 15*j**5 + 44*j**4 + 26*j**3 + 4*j**2 - 9*j - 4. Let k(c) = -3*i(c) + 4*v(c). Factor k(u).
5*u*(u + 1)**3*(3*u - 1)
Let h be (((-31)/(-60))/(-31))/(-1 - 0). Let l(j) be the third derivative of -6*j**2 + 0*j - 1/12*j**4 + 0 - 1/2*j**3 + h*j**5. Determine r so that l(r) = 0.
-1, 3
Let o(p) = p**2 + 7*p - 11. Let q be o(5). Let w be 5*q/35 - 5. Factor 1/5*x**3 + 0*x + 0 + 0*x**w - 1/5*x**4.
-x**3*(x - 1)/5
Let q(h) be the second derivative of 5*h**4/12 - 530*h**3/3 + 28090*h**2 - 10*h + 9. Factor q(z).
5*(z - 106)**2
Let x(w) = -11*w + 22. Let k be x(10). Let l = k + 266/3. Factor -2/3*o + l*o**3 - 1/3*o**4 + 0 + 1/3*o**2.
-o*(o - 2)*(o - 1)*(o + 1)/3
Let k(p) be the third derivative of p**6/5 - 37*p**5/5 + 145*p**4/16 - 9*p**3/2 - 9*p**2. Find v, given that k(v) = 0.
1/4, 18
Let n(d) be the first derivative of d**9/5292 + d**8/2940 - d**7/1470 - d**6/630 + 4*d**3/3 - 6. Let v(c) be the third derivative of n(c). Factor v(j).
4*j**2*(j - 1)*(j + 1)**2/7
Let t(n) be the second derivative of -n**4/24 - 37*n**3/3 - 1369*n**2 + 671*n. Find k, given that t(k) = 0.
-74
Let f(v) be the third derivative of -v**6/660 - v**5/55 + 4*v**4/33 + 107*v**2. Factor f(g).
-2*g*(g - 2)*(g + 8)/11
Factor 139*l**2 - 1444*l + 13*l**2 + 5*l**3 - 19*l**3 + 10*l**3.
-4*l*(l - 19)**2
Let j(l) be the second derivative of -2*l**4/3 + 4*l**3 - 53*l**2/2 + l. Let n(b) = -b**2 - 1. Let d(w) = -j(w) + 5*n(w). Factor d(r).
3*(r - 4)**2
Let y be 4 + ((-7)/(-28) - 2/(-8)). Let c be 8 - 4*5/4. Factor -c + 21/2*m - y*m**2.
-3*(m - 2)*(3*m - 1)/2
Let i(b) be the third derivative of -5/24*b**4 - 1/2*b**5 + 0*b + 5*b**3 + 3*b**2 + 0 + 1/24*b**6. Factor i(y).
5*(y - 6)*(y - 1)*(y + 1)
Let l(s) = 8 + 5*s + s - 5*s + 1. Let w be l(-7). Factor -21*i**3 + 1 + 14*i**3 + 6*i**3 - i**w + i.
-(i - 1)*(i + 1)**2
Let l(d) = 4*d**2 + 14*d - 18. Let h(s) = -4*s**2 - 15*s + 19. Let u(a) = -6*h(a) - 5*l(a). Factor u(g).
4*(g - 1)*(g + 6)
Factor 5*c**2 + 30*c + c**4 + 15*c**2 + 7*c**3 - 15*c + 2*c**3 - 3*c.
c*(c + 1)*(c + 2)*(c + 6)
Suppose 4*u = y + 31, u + 14 = 3*u - 2*y. Suppose 4*q - u - 48 = 0. Suppose 3*l**2 + q + 0*l**2 - 18*l + 13 + 0*l**2 = 0. Calculate l.
3
Let x = -6/47 + 95/376. Let d(s) be the second derivative of 0*s**2 + 0 + 1/20*s**6 - 5*s + 0*s**5 + 1/56*s**7 - 1/8*s**4 - x*s**3. Solve d(j) = 0.
-1, 0, 1
Let k(m) = 8*m**2 - 8*m + 5. Let g be 1*-2 + 15 + -8. Let o(s) = s + 8*s**2 - 5*s - 2*s**2 - 2*s**2 + 3. Let y(x) = g*o(x) - 3*k(x). Solve y(l) = 0 for l.
0, 1
Let t(g) = g**3 + 17*g**2 - 20*g - 36. Suppose 75 + 51 = -7*n. Let x be t(n). Factor x + 1/2*j**2 + j - 1/2*j**3.
-j*(j - 2)*(j + 1)/2
Let k(x) be the first derivative of -x**3/12 + 9*x**2/8 - 7*x/2 - 138. Suppose k(o) = 0. Calculate o.
2, 7
Let j(r) = 5*r**2 - 10*r + 8. Let g be j(4). Factor -g*n**2 + n**3 + 2*n**3 - 12*n**3 - 256 - 192*n + 5*n**3.
-4*(n + 4)**3
Find w, given that 6*w**2 + 248/9 + 80/3*w - 2/9*w**3 = 0.
-2, 31
Let r(b) = 973*b - 2916. Let a be r(3). Factor 0 - 3/2*s**2 + 0*s - 3/2*s**4 - a*s**3.
-3*s**2*(s + 1)**2/2
Let h be (-284)/5 + (-4)/(-2). Let y = 55 + h. Let -1/5*n**2 + y*n + 0 = 0. What is n?
0, 1
Let q(m) = 5*m**4 + 16*m**3 + m**2 - 22*m. Let i(o) = 11*o**4 + 32*o**3 + 2*o**2 - 45*o. Let y(h) = 4*i(h) - 10*q(h). Solve y(w) = 0.
-5, -4/3, 0, 1
Let a(l) = 25*l**2 + 50*l + 125. Let f(c) = c**2. Suppose 2 - 4 = -2*k. Let p(x) = k*a(x) - 20*f(x). Find m, given that p(m) = 0.
-5
Let q = -1679 + 3501/2. Let y = -70 + q. Determine z, given that 3*z**3 + 5/2*z**4 + 0 + 3/4*z**5 + y*z**2 + 1/4*z = 0.
-1, -1/3, 0
Suppose 0 = w + 5, 0 = -5*i - 2*w + 7*w + 85. Solve -24 + 7442*v + 28*v**2 - i*v**2 - 4*v**3 - 7446*v = 0.
-1, 2, 3
Let i = 7485 - 7481. Let -8/19*l**2 + 6/19*l**5 + 20/19*l**i + 14/19*l**3 - 8/19*l + 0 = 0. Calculate l.
-2, -1, 0, 2/3
Let x be ((-12)/5*-1)/(2/5). Factor 0*q**2 - q**3 - 5*q + 12 + x*q + q**2 - 13.
-(q - 1)**2*(q + 1)
Suppose -359*h + 4*d = -361*h + 8, 4*h - 2*d = 6. Let -h*m**2 + 1/2*m**3 + 0 + 1/2*m + 3*m**4 = 0. What is m?
-1, 0, 1/3, 1/2
Suppose 14 = 9*y - 2*y. Suppose 3*k + 9 + 5 = f, 4*k = y*f - 20. Determine n, given that n - 2 - 12*n - 3*n**f - 1 + 17*n = 0.
1
Let y(d) be the third derivative of -13*d**2 - 1/6*d**4 + 0*d + 1/15*d**5 + 0 + 0*d**3. Factor y(a).
4*a*(a - 1)
Let m = -280 - -286. Let j(q) be the second derivative of 2/15*q**3 + 0 + 0*q**4 - 1/25*q**5 + 1/75*q**m + 5*q - 1/5*q**2. Factor j(c).
2*(c - 1)**3*(c + 1)/5
Let f = -126/5 + 27. Let n = -1473/20 - -297/4. Factor -9/5*y**3 + 0 - 3/5*y + f*y**2 + n*y**4.
3*y*(y - 1)**3/5
Let c be (-1)/(-2)*((-168)/60)/(-7). Suppose c*y**2 + 3/5*y**3 + 3/5*y**4 + 0 + 1/5*y**5 + 0*y = 0. Calculate y.
-1, 0
Factor 0 - 1/4*n**4 - 1/4*n**3 + 3*n + 2*n**2.
-n*(n - 3)*(n + 2)**2/4
Factor o**2 - 11 + 13 + 26*o**2 - 2 + 3*o**3.
3*o**2*(o + 9)
Solve -9*m**2 + 2*m - 14*m + 4*m**2 + 7*m**2 = 0 for m.
0, 6
Let k(m) be the second derivative of 0 + 7/27*m**3 - 14*m - 4/27*m**4 + 1/9*m**2. Find y, given that k(y) = 0.
-1/8, 1
Let b(t) be the third derivative of -50625*t**8/784 + 85725*t**7/98 + 5940*t**6/7 + 2406*t**5/7 + 538*t**4/7 + 72*t**3/7 + 32*t**2. Factor b(d).
-3*(d - 9)*(15*d + 2)**4/7
Suppose x - 18 = 4*y, 0 = -x + y + 12 - 0. Suppose -3*k + p + x = 0, -k + 1 = p - 1. Find b such that 1/6*b**k + 1/6*b + 0 - 1/3*b**2 = 0.
0, 1
Let x = 1109 - 1106. Let j(c) be the first derivative of 0*c + 10 + 2/21*c**x + 1/7*c**2. Let j(q) = 0. What is q?
-1, 0
Let l be 3 + -8 + (-1100)/(-221). Let u = l - -4907/1989. Factor -14/9*s**5 - u*s**3 + 0*s + 32/9*s**4 + 4/9*s**2 + 0.
-2*s**2*(s - 1)**2*(7*s - 2)/9
Let d(h) be the first derivative of h**3/4 - 27*h/4 - 89. Factor d(c).
3*(c - 3)*(c + 3)/4
Factor 0*q**3 - 45*q**5 + 18*q**4 + 81*q + 42*q**5 - 2*q**3 - 108*q**2 + 162 - 4*q**3.
-3*(q - 3)**3*(q + 1)*(q + 2)
Let q(z) be the third derivative of -z**8/196 + 2*z**7/147 + z**6/15 - 2*z**5/105 - 11*z**4/42 - 2*z**3/7 + 35*z**2. Let q(a) = 0. What is a?
-1, -1/3, 