 1
Let i(d) be the third derivative of 0 - 13/168*d**4 + 43*d**2 + 0*d + 1/420*d**5 + 0*d**3. Let i(z) = 0. What is z?
0, 13
Suppose 9 = -2*t - t. Let l be (2/6)/(t/(-18)). Factor -24*y**3 - 19*y**l + 21*y**2 - 2 + 24*y**2.
-2*(y - 1)*(3*y - 1)*(4*y + 1)
Suppose -5*l + 3*j = j + 56, 36 = -3*l + 2*j. Let v(k) = -1 - k + 4 - 2. Let t(i) = -i**3 + 2*i**2 + 5*i - 5. Let o(z) = l*v(z) - 2*t(z). Factor o(h).
2*h**2*(h - 2)
Let t(p) be the first derivative of -p**5/5 - 3*p**4 - 11*p**3/3 + 74. Find v such that t(v) = 0.
-11, -1, 0
Suppose 5*j + 3*y = -0*y + 137, -59 = -2*j + 3*y. Factor 0*f**4 - 12*f + j*f**4 + 20*f**3 + 4*f**2 + 24*f**3.
4*f*(f + 1)**2*(7*f - 3)
What is k in 5719/3*k + 3698/3 + k**3 + 260/3*k**2 = 0?
-43, -2/3
Let d(o) = 2*o**3 - 4*o**2 - 4*o + 12. Let t(l) = 2*l**3 - 3*l**2 - 5*l + 11. Let f(a) = -5*d(a) + 6*t(a). Let f(q) = 0. What is q?
-3, 1
Let o(u) be the second derivative of -u**4/12 + u**3/3 - u**2/2 - 162*u. Find p, given that o(p) = 0.
1
Let b(d) be the second derivative of 0*d**2 - 1/21*d**7 + 2/3*d**3 + 0 - 1/15*d**6 + 5/6*d**4 - 10*d + 3/10*d**5. Factor b(i).
-2*i*(i - 2)*(i + 1)**3
Let i(y) be the second derivative of -y**7/210 - 11*y**6/150 - 23*y**5/50 - 23*y**4/15 - 44*y**3/15 - 16*y**2/5 - 11*y - 4. Factor i(k).
-(k + 1)*(k + 2)**3*(k + 4)/5
Suppose -6*n + n = 3*x - 1, 0 = -2*n - 3*x - 5. What is q in -n*q**3 - 35*q**2 + 1 - 26 + 7*q**3 + 55*q = 0?
1, 5
Suppose 3*p + 30 = -4*s, 2*p + s + 11 = p. Let t be 7/p*(-3 + (5 - 2)). Factor 0*i**3 + 3/4*i**4 + 0*i + t - 3/4*i**2.
3*i**2*(i - 1)*(i + 1)/4
Let i be (-14)/21 - (-1)/(-3). Let t be 6/3 + (-3)/i. Factor -2*l**2 - 2*l**4 - 2*l**3 + 4*l**4 + 0*l**5 - 3*l**t + 5*l**5.
2*l**2*(l - 1)*(l + 1)**2
Let h(i) be the third derivative of -i**8/6720 + i**6/240 + i**5/4 - 6*i**2. Let f(a) be the third derivative of h(a). Factor f(x).
-3*(x - 1)*(x + 1)
Suppose -18050/9 - 380/9*a - 2/9*a**2 = 0. What is a?
-95
Let r(s) be the first derivative of 26/3*s**3 + 48*s**2 + 1/2*s**4 + 12 + 72*s. Solve r(d) = 0.
-6, -1
Let p be -12*8/276*14/(-132). Let s = p + 10/69. Find f such that -2/11*f**3 - 6/11*f - s - 6/11*f**2 = 0.
-1
Factor 3*v**5 - 24*v**4 + 14*v + 13*v - 56*v**2 + 66*v**3 - 16*v**2.
3*v*(v - 3)**2*(v - 1)**2
Let t(u) be the first derivative of -37538*u**3/33 + 548*u**2/11 - 8*u/11 + 50. Factor t(b).
-2*(137*b - 2)**2/11
Let v = 135671/10854 + 2/5427. Suppose -v - 5*w - 1/2*w**2 = 0. Calculate w.
-5
Let b(t) = -t**2 - 14*t + 2. Let y be b(-14). Factor -22 - 5*f**3 - 10 + 96*f + 0*f**3 - 32*f**y - 19*f**3 + 10*f**4.
2*(f - 2)**2*(f + 2)*(5*f - 2)
Factor 856*f**2 + 4*f**4 + 4035 + 865 - 64*f**3 - 32*f**3 - 3360*f.
4*(f - 7)**2*(f - 5)**2
Let u(v) be the third derivative of 10*v**2 + 1/50*v**5 + 0*v + 2/15*v**3 + 0 + 1/12*v**4. Find q, given that u(q) = 0.
-1, -2/3
Let l(t) be the first derivative of t**2/2 + 4*t - 9. Let v be l(0). Factor -1/3*b + 0*b**3 + 0 + 1/2*b**2 - 1/6*b**v.
-b*(b - 1)**2*(b + 2)/6
Let h be (2 - 1 - 4) + (-5)/(-1). Factor 6/5*c**3 + 0*c**h + 0 - 8/5*c**4 + 0*c - 14/5*c**5.
-2*c**3*(c + 1)*(7*c - 3)/5
Let n(p) = -p**2 + 14*p - 11. Let f(m) = -m**2 - m. Let l(c) = -6*f(c) - n(c). Let s(q) = 2*q**2 - 2*q + 3. Let j(h) = -6*l(h) + 22*s(h). Factor j(g).
2*g*(g + 2)
Let y(m) = 15*m**2 - m + 1. Let c be y(1). Let n be 3/c + (-2)/10. Factor -3*r**3 - 2*r**2 - 2*r**3 + n*r**2 + 0*r**3.
-r**2*(5*r + 2)
Let b(y) = -42*y**3 - 2*y**2 - 2*y - 8. Let d be b(-2). Factor 111*r - 450*r - 237*r - d*r**2 - 256.
-4*(9*r + 8)**2
Let a(j) = 10*j - 2. Let d(w) = -7*w + 1. Let v(x) = 5*a(x) + 8*d(x). Let k be v(-1). Let -3*t**k - 15*t**2 + 0*t**2 + 19*t**3 + 6*t - 7*t**3 = 0. Calculate t.
0, 1, 2
Let i(f) be the second derivative of -f**4/6 - 64*f**3/3 - 1024*f**2 - 125*f - 1. Factor i(d).
-2*(d + 32)**2
Let u = -13 + 13. Suppose 5*y = 5*q, 5*q - 17 - 3 = u. Factor -5/7*w**2 + 1/7*w**5 - 2/7*w - 3/7*w**3 + 1/7*w**y + 0.
w*(w - 2)*(w + 1)**3/7
Let b(p) be the second derivative of 0 - 1/240*p**5 - 1/24*p**4 - 3*p**2 - 5*p - 1/8*p**3. Let j(f) be the first derivative of b(f). What is x in j(x) = 0?
-3, -1
Let w = -6 - -11. Let g(b) = -b**3 + 8*b**2 + b - 40. Let z be g(6). Find u such that -w + 6 + z*u**2 + u - u**3 - 39*u**2 = 0.
-1, 1
Let f(c) be the second derivative of -2*c**6/15 - 2*c**5/5 + 4*c**3/3 + 2*c**2 - 2*c + 19. Factor f(k).
-4*(k - 1)*(k + 1)**3
Let q be -1 + 2/4 - 9519/(-1002). Find r, given that 0*r - q*r**3 + 6*r**2 + 0 + 9/2*r**4 - 3/4*r**5 = 0.
0, 2
Let y(r) be the second derivative of r**5/30 + r**4/6 + r**3/3 + 8*r**2 + 5*r. Let i(v) be the first derivative of y(v). Factor i(l).
2*(l + 1)**2
Let x(h) = -3*h**4 - h**2 - h. Let q(t) = -2*t**4 - 33*t**3 + 285*t**2 - 193*t - 512. Let c(b) = -3*q(b) + 3*x(b). Factor c(d).
-3*(d - 16)**2*(d - 2)*(d + 1)
Let c(k) be the third derivative of -k**7/490 + 3*k**6/280 - k**5/140 - 3*k**4/56 + k**3/7 + 2*k**2 - 19*k. Determine b, given that c(b) = 0.
-1, 1, 2
Let v(g) be the third derivative of 1/21*g**7 + 0*g - 2/15*g**5 - 3/40*g**6 - 1/3*g**3 + 0 + 3/8*g**4 - 4*g**2. Solve v(f) = 0.
-1, 2/5, 1/2, 1
Factor 53/3*w - 1/3*w**3 - 9 - 25/3*w**2.
-(w - 1)**2*(w + 27)/3
Let c(d) be the third derivative of d**6/1260 - d**4/84 - 7*d**3/3 + 5*d**2. Let h(t) be the first derivative of c(t). Factor h(i).
2*(i - 1)*(i + 1)/7
Let r be 58/232 + (-2 - 45/(-12)). Let q(g) be the first derivative of 18/7*g - 15/7*g**r - 3 - 16/21*g**3 + 8/7*g**4. Factor q(k).
2*(k + 1)*(4*k - 3)**2/7
Let n(f) = 3*f**2 + 6*f + 12. Let m = 14 - 5. Let i(j) = -45 - 19*j - 2 - m*j**2 + 11 + 0*j. Let y(d) = -6*i(d) - 17*n(d). Factor y(b).
3*(b + 2)**2
Let t(w) be the third derivative of 1/168*w**8 + 0*w + 0 - 1/15*w**6 + 0*w**4 - 2/105*w**7 + 46*w**2 + 0*w**3 + 4/15*w**5. Solve t(k) = 0 for k.
-2, 0, 2
Let h(b) be the third derivative of -b**7/1260 - b**6/36 + b**4/24 + b**3/6 - 6*b**2 - 2. Let z(v) be the second derivative of h(v). Factor z(u).
-2*u*(u + 10)
Suppose -7*r = -65*r. Determine w so that 0*w**2 - 1/3*w + r + 1/3*w**3 = 0.
-1, 0, 1
Let p(u) be the first derivative of u**4/12 + 7*u**3/3 + 24*u**2 + 108*u - 380. Factor p(h).
(h + 6)**2*(h + 9)/3
Let s be 7252/3773 - (-12)/(-105)*10/4. Factor 4*h**2 + s - 16/11*h**3 - 48/11*h + 2/11*h**4.
2*(h - 3)**2*(h - 1)**2/11
Let c = -34373 - -34376. Factor 1/4*v**5 + 2*v**2 - 1/2*v**4 - 1/2*v**c - 7/4*v + 1/2.
(v - 1)**4*(v + 2)/4
Let s(k) = k**3 + k**2 - 5*k + 5. Let y be s(-3). Factor -y + 5*n**2 - 11 + 3 + 5*n.
5*(n - 1)*(n + 2)
Let c(o) be the third derivative of 5*o**6/72 + 7*o**5/18 + 35*o**4/72 - 5*o**3/9 - 153*o**2. Factor c(a).
5*(a + 1)*(a + 2)*(5*a - 1)/3
Let r(u) be the third derivative of u**7/42 - 5*u**6/12 + 25*u**5/12 + 126*u**2. Let r(n) = 0. Calculate n.
0, 5
Let f = -16277/6 - -2713. Solve -9/2 + 9/2*t + f*t**3 - 3/2*t**2 = 0.
3
Factor -1/2*r**3 + 0 - 24*r + 8*r**2.
-r*(r - 12)*(r - 4)/2
Let v = -229 + 229. Suppose 5*n = 3*j, v = -3*j + 8*n - 5*n. Determine f so that j*f + 0*f**2 + 6/17*f**3 - 2/17*f**4 + 0 = 0.
0, 3
Factor -35*f - 60 + 2*f - 3*f**2 + 4*f**3 - 15*f - f**3.
3*(f - 5)*(f + 2)**2
Let t(x) = -18*x**4 + 158*x**3 - 102*x**2 - 34*x - 2. Let m(z) = -z**4 + z**3 + z**2 + z - 1. Let w(c) = 2*m(c) - t(c). Determine k so that w(k) = 0.
-1/4, 0, 1, 9
Let s(k) be the second derivative of -7744*k**4/9 + 352*k**3/9 - 2*k**2/3 + 360*k. Factor s(m).
-4*(88*m - 1)**2/3
Determine a, given that 6*a**3 + 0*a**3 + 41*a + 127*a - 3*a**3 + 240 + 24*a**2 + 15*a**2 = 0.
-5, -4
Let p(z) be the second derivative of z**7/5040 + z**6/1440 - z**4 + 12*z. Let i(b) be the third derivative of p(b). Factor i(j).
j*(j + 1)/2
Let q(o) be the second derivative of -3/2*o**3 - 1/60*o**5 - 2*o**2 + 0 + 2*o - 1/4*o**4. Let x(l) be the first derivative of q(l). Factor x(m).
-(m + 3)**2
Let x(u) be the third derivative of u**8/420 + u**7/1050 - u**6/25 + 13*u**5/150 - u**4/30 - u**3/10 + 8*u**2 - 7*u. Determine n so that x(n) = 0.
-3, -1/4, 1
Let t(q) be the third derivative of -q**8/1680 - 2*q**7/525 - q**6/120 - q**5/150 - q**2 - q. Solve t(z) = 0.
-2, -1, 0
Let r(d) = -7*d - 1. Let k be r(-1). Let b(s) = -6*s**2 + 257*s + 45. Let t be b(43). Find p, given that 4/3*p**4 - 8/3*p + 0*p**t + 0 + k*p**3 - 2*p**5 = 0.
-1, 0, 2/3, 2
Let a be 21/9 + (-14)/(-21). Solve -5*r**a + 2*r + r**4 - 2*r + 4*r**3 = 0 for r.
0, 1
Let