0.
0, 1, 3
Let s(q) be the second derivative of -1/2*q**3 + 0 + 7/4*q**2 - 1/24*q**4 + 41*q. Factor s(n).
-(n - 1)*(n + 7)/2
Let r = -1083 + 2181/2. Let m(v) be the first derivative of 1 - r*v**2 + 9/5*v**5 - 6*v + 15/4*v**4 - v**3. Determine n, given that m(n) = 0.
-1, -2/3, 1
Factor -13 - 2*d + 13*d**2 - 16 + 7*d**3 + d**4 + 11 - d.
(d - 1)*(d + 2)*(d + 3)**2
Let z = 3 - -2. Suppose -4*a + 2 = 2*k - 4*k, 0 = -3*k - 2*a + 13. Solve -x**4 + 3*x**z + 3*x**2 - 3*x**k + 3*x**4 - 5*x**4 = 0.
-1, 0, 1
Let j = 1/3394 - -6779/30546. Determine v, given that 0*v**2 + 0*v + 2/9*v**5 + 0 + j*v**3 - 4/9*v**4 = 0.
0, 1
Let h be 7/1 - 572/132. Let -8/3*q + 2/3*q**4 + 4/3*q**2 + h*q**3 - 2 = 0. What is q?
-3, -1, 1
Let i(k) = 8*k**2 + 10*k - 9. Let a(w) = 7*w**2 + 10*w - 6. Let m(l) = 3*a(l) - 2*i(l). Factor m(n).
5*n*(n + 2)
Find d, given that -4/7*d**2 + 1/7*d + 4/7 - 1/7*d**3 = 0.
-4, -1, 1
Let i(w) be the first derivative of w - 7 + 1/4*w**2 - 1/24*w**4 + 0*w**3. Let d(r) be the first derivative of i(r). Find t such that d(t) = 0.
-1, 1
Solve 17/2*c**2 + 3/2*c**3 - 75/2 - 1/3*c**4 - 185/6*c = 0 for c.
-9/2, -1, 5
Let v(l) = 54*l**2 - 24*l + 3. Let s(i) = 108*i**2 - 49*i + 6. Let k be 6/(((-8)/14)/((-10)/35)). Let h(y) = k*s(y) - 5*v(y). Factor h(t).
3*(3*t - 1)*(6*t - 1)
Let y = -11821 + 11824. Determine r, given that 1/2*r**y - 1/2*r**4 + 1/2*r**2 + 0 - 1/2*r = 0.
-1, 0, 1
Let s(y) be the third derivative of -1/40*y**5 + 0*y - 1/160*y**6 - 22*y**2 - 1/32*y**4 + 0*y**3 + 0. Factor s(k).
-3*k*(k + 1)**2/4
Let k(m) be the first derivative of -2*m**5/15 - 7*m**4/6 + 2*m**3/9 + 7*m**2/3 + 136. Factor k(x).
-2*x*(x - 1)*(x + 1)*(x + 7)/3
Let b(k) be the third derivative of k**7/70 - 17*k**6/10 + 396*k**5/5 - 1694*k**4 + 10648*k**3 + 83*k**2. Factor b(o).
3*(o - 22)**3*(o - 2)
Let v be -6 + 8 + (-1 - 0). Suppose 2*s + 5 + 1 = 4*o, -3*s + v = -o. Suppose -1 - 7*p**o + 4*p + 3 + 9*p**2 + 0 = 0. What is p?
-1
Let a(f) be the third derivative of -f**8/2240 - f**7/560 + f**5/80 + f**4/32 + f**3/6 - 31*f**2. Let y(u) be the first derivative of a(u). Factor y(s).
-3*(s - 1)*(s + 1)**3/4
Let a(q) be the third derivative of q**7/105 - 13*q**6/540 - q**5/270 + 5*q**4/108 + 66*q**2. Solve a(r) = 0 for r.
-5/9, 0, 1
Let z - 2*z**3 - 664*z**2 + 3*z**3 - 4*z - 17*z + 672*z**2 = 0. Calculate z.
-10, 0, 2
Let l be 6/21 - (-20)/28. Suppose p - 1 = l. Factor 3*w**4 + 3*w**5 - 3*w**5 + 3*w**3 - 4*w**5 + 5*w**5 + w**p.
w**2*(w + 1)**3
Let c(u) be the third derivative of 0*u**3 + 0 - 2/15*u**5 + 1/6*u**4 + 20*u**2 + 1/30*u**6 + 0*u. Factor c(x).
4*x*(x - 1)**2
Let s(j) be the first derivative of -3*j**5/10 + 77*j**4/8 - 479*j**3/6 - 221*j**2/4 + 169*j + 113. Suppose s(z) = 0. What is z?
-1, 2/3, 13
Let v(c) be the third derivative of 0*c**4 + 2/105*c**5 + 0*c**3 + 0 + 0*c + 1/735*c**7 - 10*c**2 + 1/105*c**6. Factor v(f).
2*f**2*(f + 2)**2/7
Let r be -8 - (-2 - (5 + 5)). Factor 0 + 30/7*q**3 - 2*q**2 - 18/7*q**r + 2/7*q.
-2*q*(q - 1)*(3*q - 1)**2/7
Let k(j) = -7*j**2 + 1. Suppose 5 = 2*m + 15. Let i(r) = 2*r**2 - 1. Let s(t) = t**2. Let v(g) = i(g) + 4*s(g). Let o(p) = m*k(p) - 6*v(p). Factor o(d).
-(d - 1)*(d + 1)
Let v = 50 + -48. Let 72 - 21*t - 6*t**2 - 9*t**2 - 74*t - v = 0. What is t?
-7, 2/3
Suppose 0 = -70*x + 236*x - 830. Factor 2/13*i + 432/13*i**3 + 48/13*i**2 + 2592/13*i**x + 1728/13*i**4 + 0.
2*i*(6*i + 1)**4/13
Let i(b) be the second derivative of 5*b**4/12 + 125*b**3/3 + 245*b**2/2 - 10*b. Factor i(d).
5*(d + 1)*(d + 49)
Suppose 232*o - 106*o - 252 = 0. Determine a so that -1 + 1/2*a**o + 1/2*a = 0.
-2, 1
Let v(d) be the second derivative of -5/18*d**3 - 1/60*d**5 - 1/9*d**4 - 1/3*d**2 + 0 + 8*d. Let v(s) = 0. Calculate s.
-2, -1
Let g(y) = -50*y**2 + 160*y - 135. Let i(f) = 25*f**2 - 80*f + 68. Let o(n) = 4*g(n) + 7*i(n). Factor o(s).
-(5*s - 8)**2
Suppose 0*v - 3*s + 10 = 2*v, 2*s + 36 = 4*v. Suppose 13*o + v*o - 42 = 0. What is w in 0*w**o + 0*w + 2/7*w**5 - 6/7*w**4 + 0 + 4/7*w**3 = 0?
0, 1, 2
Factor -72/5*d + 0 + 3/5*d**3 + 3*d**2.
3*d*(d - 3)*(d + 8)/5
Let q(a) be the first derivative of -a**5/5 + a**4/2 - a**2 + a + 327. Solve q(l) = 0 for l.
-1, 1
Let h(q) = q**3 - 5*q**2 - 2*q + 12. Let m be h(5). What is g in 58*g**m + 38*g**2 - 3*g**4 - 44*g**3 + 7*g**4 + 144*g = 0?
-1, 0, 6
Let f be 24/(-5)*(-120)/36. Factor -25*v - 35*v**3 - 14*v**4 - f*v**4 - 20*v**4 - 55*v**2 + 45*v**4.
-5*v*(v + 1)**2*(v + 5)
Let a(v) be the third derivative of -v**5/90 + 13*v**4/36 + 30*v**2. Let a(m) = 0. Calculate m.
0, 13
Let z(p) be the third derivative of -p**8/840 + 4*p**7/525 + p**6/50 - 8*p**5/75 - 29*p**4/60 - 4*p**3/5 + 92*p**2. Solve z(y) = 0 for y.
-1, 3, 4
Let a = 33 - 30. Factor -t**2 - 3*t**2 - 3*t**2 + 2*t**a + 9*t**2.
2*t**2*(t + 1)
Let o be 18/(-81) - 4/(-36)*38. Let t(y) be the first derivative of -4*y - 9*y**2 - o - 8/3*y**3. Find q, given that t(q) = 0.
-2, -1/4
Let x(p) = -4*p**4 - 33*p**3 + 88*p**2 - 61*p + 17. Let d(v) = v**4 + 11*v**3 - 29*v**2 + 21*v - 6. Let q(l) = -7*d(l) - 2*x(l). Suppose q(f) = 0. What is f?
1, 8
Let o = -2347 + 25961/11. Let c(y) be the first derivative of 72/11*y**3 + 128/11*y - 3 + 27/22*y**4 + o*y**2. Factor c(m).
2*(3*m + 4)**3/11
Let y(u) = -u**2 + 7*u + 3. Let l be y(8). Let p(q) = -2*q + 1. Let j(o) = -5*o**2 - 35*o - 25. Let t(d) = l*p(d) + j(d). Factor t(b).
-5*(b + 2)*(b + 3)
Let l be -6 - (-3)/1 - -28. Suppose 10 = 5*h - l. Factor -19*k - 135*k**3 - 54*k**2 + 14*k**4 - 18*k**2 - 89*k**4 + h*k.
-3*k*(k + 1)*(5*k + 2)**2
Let q(s) be the third derivative of -5*s**8/336 + 274*s**7/21 - 18769*s**6/4 + 2571353*s**5/3 - 1761376805*s**4/24 + 510*s**2. Factor q(t).
-5*t*(t - 137)**4
Let v(h) = -h**3 - 5*h**2 - 5*h - 4. Let u be v(-4). Suppose u = 5*k - k - 8. Factor -c**4 + 0*c**4 - 4*c**k + 0*c**4 + 3*c**2 + 2*c**3.
-c**2*(c - 1)**2
Let k(h) be the second derivative of h**5/5 - 8*h**4 + 30*h**3 - 44*h**2 - 103*h. Factor k(d).
4*(d - 22)*(d - 1)**2
Let d(v) be the third derivative of v**6/120 - v**5/15 - v**4/24 + 2*v**3/3 + 108*v**2. Factor d(z).
(z - 4)*(z - 1)*(z + 1)
Let k(q) be the third derivative of q**9/40320 + q**8/6720 + q**7/3360 - q**5/6 - 13*q**2. Let h(c) be the third derivative of k(c). Factor h(x).
3*x*(x + 1)**2/2
Factor 4*h**2 - 7/2*h - h**3 + 1 + 1/2*h**5 - h**4.
(h - 1)**4*(h + 2)/2
Factor 5/4*m**5 + 7/4*m**3 + 0*m + 11/4*m**4 + 0 + 1/4*m**2.
m**2*(m + 1)**2*(5*m + 1)/4
Let z(a) be the second derivative of a**7/147 - 4*a**6/35 + 23*a**5/35 - 10*a**4/7 + 25*a**3/21 + a - 8. Factor z(y).
2*y*(y - 5)**2*(y - 1)**2/7
Suppose 0 = -4*r - 2*o + 7*o - 31, 0 = 3*r - 2*o + 25. Let b be (r - -5)*3/(-4). Let d**5 + 10*d**3 - 10*d**3 + 6*d**3 - 4*d**5 - b*d = 0. Calculate d.
-1, 0, 1
Suppose -1650*l = -1645*l - 10. Factor 1/2*b**4 + b**3 + 1/2*b**l + 0*b + 0.
b**2*(b + 1)**2/2
Let s(m) be the third derivative of -10*m**2 + 0 + 0*m**3 - 1/15*m**6 + 0*m + 1/105*m**7 - 1/6*m**4 + 1/6*m**5. Factor s(u).
2*u*(u - 2)*(u - 1)**2
Let f(s) = -s**2 - 1. Let u(l) = 3 + 16*l - 15*l + 5. Let a be u(-5). Let w(g) = 9*g**2 - 3*g + 10. Let z(x) = a*w(x) + 24*f(x). Factor z(t).
3*(t - 2)*(t - 1)
Let g(i) = -i**2 + 5*i - 3. Let q be g(4). Let v = -76 + 80. Factor -q - 2*w**2 - 2*w**2 - 9*w + v*w.
-(w + 1)*(4*w + 1)
Let p(g) be the third derivative of -1/240*g**5 + 0 + 0*g**3 + 0*g**6 - 16*g**2 + 0*g + 1/840*g**7 + 0*g**4. Factor p(w).
w**2*(w - 1)*(w + 1)/4
Let f be -5*(-4)/20*65/130. Suppose 1/4*r**4 + r**3 - 1/2*r + 1/4 - 1/2*r**2 - f*r**5 = 0. Calculate r.
-1, 1/2, 1
Let c(o) = -o - 3. Let i be c(-3). Find g, given that -22*g + 31*g + 3*g**2 + i*g**2 = 0.
-3, 0
Suppose 0 = 4*w - 3*u - 51, 3*w - 39 = u + 2*u. Let v be w/30 - (-4)/(-10). Determine d so that -4*d + 2*d**2 - 5*d**2 + d**2 + v*d**2 = 0.
-2, 0
Find d, given that 2/11*d**4 - 38/11*d**2 + 8/11*d**3 + 0 + 28/11*d = 0.
-7, 0, 1, 2
Let q = -1/13945 - -111563/41835. Find y, given that -q + 2/3*y**2 + 2*y = 0.
-4, 1
Find w, given that 54*w**2 - 41*w - 57*w**2 + 33 + 11*w = 0.
-11, 1
Let l(v) = v**3 - v**2 + 1. Let z(i) = 8*i**3 - 7*i**2 - i + 5. Let d(x) = -x + 6. Let u be d(3). Let p(t) = u*z(t) - 15*l(t). Factor p(b).
3*b*(b - 1)*(3*b + 1)
Let u be ((-20)/45)/(5/(-60)). Factor u*s + 32/3 + 2/3*s**2.
2*(s + 4)**2/3
Suppose -257 = 6*w + 1039. Let b = w - -219. Suppose -3/4*l**4 - 11/