/5
Let k(r) be the second derivative of r**5/20 + 5*r**4/4 + 2*r**3 - 14*r**2 - 234*r. Factor k(t).
(t - 1)*(t + 2)*(t + 14)
Suppose -2*i = -341 - 67. Let w = -202 + i. Factor 0*r + 0 - 1/9*r**3 - 1/9*r**w.
-r**2*(r + 1)/9
Let -7 - 28*k - 31*k**2 + 23 + 8*k + 35*k**2 = 0. What is k?
1, 4
Let j(v) be the first derivative of -4/3*v**3 + 4*v**2 - 4*v + 24. Factor j(n).
-4*(n - 1)**2
Let d(r) be the first derivative of r**6/14 - 6*r**5/35 - 9*r**4/14 + 8*r**3/7 + 15*r**2/14 - 18*r/7 - 214. What is x in d(x) = 0?
-2, -1, 1, 3
Let y = -758 - -5312/7. Solve 12/7*f - 4/7 - 13/7*f**2 + y*f**3 - 1/7*f**4 = 0 for f.
1, 2
Let t(g) = -g**2 - 27*g - 33. Let b(a) be the second derivative of a**4/6 + 13*a**3/3 + 17*a**2 + 5*a. Let j(k) = 3*b(k) + 2*t(k). Factor j(i).
4*(i + 3)**2
Suppose 56 = 14*q - 10*q. Suppose -q*p + 18*p = 12. Factor -1/3*d**p - 2/3 + 1/3*d + 2/3*d**2.
-(d - 2)*(d - 1)*(d + 1)/3
Let y(x) be the third derivative of -7*x**5/60 + 13*x**4/12 + 4*x**3/3 - 12*x**2 + 1. Factor y(h).
-(h - 4)*(7*h + 2)
Let t(n) be the first derivative of 0*n + 0*n**4 - 4*n**2 - 12 - 1/60*n**6 + 0*n**3 + 0*n**5. Let d(x) be the second derivative of t(x). Factor d(q).
-2*q**3
Let l(z) be the first derivative of z**3/4 - 27*z**2/8 + 21*z/2 + 107. Solve l(m) = 0.
2, 7
Solve 9/2*x**4 + 111/2*x**3 + 297/2*x**2 + 27 + 249/2*x = 0 for x.
-9, -2, -1, -1/3
Let p be 16/24*27/49. Let u = 394/539 - p. Factor 0*w**3 + u*w**2 - 2/11*w + 2/11*w**5 + 0 - 4/11*w**4.
2*w*(w - 1)**3*(w + 1)/11
Let k(h) = 3*h**4 + 5*h**3 + 2*h**2 + 2*h + 4. Let f(t) = -21*t**4 - 36*t**3 - 15*t**2 - 15*t - 30. Let y(c) = -2*f(c) - 15*k(c). Factor y(n).
-3*n**3*(n + 1)
Let y(s) be the third derivative of -7*s**6/144 + 13*s**5/24 + 335*s**4/144 + 35*s**3/12 - 51*s**2 + 1. Factor y(a).
-5*(a - 7)*(a + 1)*(7*a + 3)/6
Let y(j) be the second derivative of j**6/30 - j**5/5 + j**4/2 - 2*j**3/3 + 7*j**2/2 - 26*j. Let k(b) be the first derivative of y(b). Factor k(w).
4*(w - 1)**3
Let q(s) be the second derivative of -s**4/18 - 10*s**3/9 - 3*s**2 + 40*s. Determine m so that q(m) = 0.
-9, -1
Factor -3 + 17/2*l + l**3 - 11/2*l**2.
(l - 3)*(l - 2)*(2*l - 1)/2
Let w(b) be the first derivative of -b**6/6 + b**5/2 - 5*b**3/3 + 5*b**2/2 + 9*b + 13. Let j(c) be the first derivative of w(c). Let j(z) = 0. Calculate z.
-1, 1
Let n(b) be the second derivative of 3*b**7/14 - 2*b**6/5 - 3*b**5/5 + 3*b**4/2 + b**3/2 - 3*b**2 + 14*b + 3. Suppose n(y) = 0. What is y?
-1, -2/3, 1
Let w(m) = 24*m**4 + 420*m**3 + 594*m**2 + 293*m + 46. Let r(t) = -48*t**4 - 840*t**3 - 1188*t**2 - 587*t - 91. Let n(l) = -2*r(l) - 5*w(l). Factor n(z).
-3*(z + 16)*(2*z + 1)**3
Let y(n) be the second derivative of -3/50*n**5 + 2/5*n**3 - 1/4*n**4 - 12*n + 0 + 9/10*n**2. Suppose y(w) = 0. Calculate w.
-3, -1/2, 1
Solve -164/13*x**2 + 506/13*x - 340/13 - 2/13*x**3 = 0 for x.
-85, 1, 2
Let h(n) = -2*n + 24. Let y be h(11). Factor -5*o**3 - 2 + 1 + 10*o**y - 5*o**4 + 1.
-5*o**2*(o - 1)*(o + 2)
Let z = 917 - 914. Let o(w) be the first derivative of 0*w**z + 0*w + 0*w**5 + 1/36*w**6 + 1/12*w**2 - 1/12*w**4 - 2. Factor o(i).
i*(i - 1)**2*(i + 1)**2/6
Let n(l) be the second derivative of l**4/12 + 5*l**3 + 2*l + 12. Factor n(c).
c*(c + 30)
Find j such that -22 + 52 - 139*j + 77*j + 60*j**3 + 4*j**2 + 2*j**5 - 34*j**4 = 0.
-1, 1, 15
Suppose -2*c - 4 = 2*v, -2*v - 4*c = -0*v + 12. Factor -2*j + 18*j + 4*j**v + 8 + 4.
4*(j + 1)*(j + 3)
Let x(h) be the third derivative of h**8/1848 + h**7/1155 - 3*h**6/220 + h**5/30 - h**4/33 - 194*h**2. Solve x(n) = 0.
-4, 0, 1
Let i(t) = t**3 - 13*t - 10. Let y be i(-3). Let r(o) be the first derivative of -6 + 0*o + 0*o**y - 1/6*o**3. Determine z so that r(z) = 0.
0
Let l(u) = -u - 3. Let w be l(-6). Let j be w*(-1 - (-6)/4). Determine b, given that -3/2*b**5 + 3*b - 3*b**2 - j*b**3 - 3/4 + 15/4*b**4 = 0.
-1, 1/2, 1
Factor -2*f**5 - 260*f + f**5 + 0*f**5 + 60*f - 7*f**4 - 1584 + 235*f**2 - 416 + 29*f**3.
-(f - 4)**2*(f + 5)**3
Let t = 315 - 311. Let a(c) be the first derivative of 0*c**2 - 1/18*c**3 + 0*c + 5 + 0*c**t + 1/30*c**5. What is y in a(y) = 0?
-1, 0, 1
Let o(b) = -20*b**3 - 15*b**2 + 15*b + 30. Let m(t) = -t**3 - t**2 + t + 2. Let n(f) = 15*m(f) - o(f). Factor n(u).
5*u**3
Suppose -6*z + 7 = -17. Let t(x) be the third derivative of -1/24*x**z + 2*x**2 + 0*x + 0 + 0*x**3 - 1/120*x**5. Factor t(s).
-s*(s + 2)/2
Let b = -40 + 45. Find h, given that 11 + b - h**2 - 2*h**2 - 1 + 12*h = 0.
-1, 5
Let v(u) = 15*u**4 - 40*u**3 + 20*u**2 - 11*u. Let n(l) = 3*l**4 - 8*l**3 + 4*l**2 - 2*l. Let k(x) = 11*n(x) - 2*v(x). Determine q, given that k(q) = 0.
0, 2/3, 2
Let b(m) be the second derivative of 6*m + 0 - 2/21*m**7 - 2/15*m**6 + 1/3*m**4 + 1/5*m**5 + 0*m**2 + 0*m**3. Factor b(z).
-4*z**2*(z - 1)*(z + 1)**2
Let l = -21 + 47. Find n, given that l*n - 41*n - 158 - 5*n**2 + 33 - 35*n = 0.
-5
Let t(m) = -229*m + 689. Let p be t(3). Solve 0 - 18/7*y**3 - 22/7*y**p - 4/7*y = 0.
-1, -2/9, 0
Let w = 735 + -732. Determine z, given that -z + 0 - 1/4*z**w - z**2 = 0.
-2, 0
Let z(i) = -4*i - 8. Let h(d) = 3*d + 7. Let n(b) = -5*h(b) - 4*z(b). Let j be n(7). Factor -7*m**j + 21*m**5 + m**4 - 5*m**3 - 23*m**5 + m**3.
-2*m**3*(m + 1)*(m + 2)
Let i(s) = -s**3 + s**2 - 13*s + 21. Let t be i(11). Let h be (-6 - t/225)*(-5)/3. Solve -4/15*o**4 + h*o**3 + 0 - 2/15*o + 4/15*o**2 = 0 for o.
-1, 0, 1/2, 1
Suppose 12*c**4 + 4*c**2 + 256*c**5 - 121*c**5 + 12*c**3 - 131*c**5 = 0. What is c?
-1, 0
Let v(c) be the second derivative of -3*c**5/100 + 3*c**4/2 + c**3/10 - 9*c**2 - 30*c. Find t such that v(t) = 0.
-1, 1, 30
Let v(g) be the first derivative of -g**4/18 - g**3/9 + 3*g + 11. Let z(x) be the first derivative of v(x). Factor z(l).
-2*l*(l + 1)/3
Let q be ((-5)/(-25))/(4/(-90))*6/(-15). Solve 21/5*m - 6/5 - q*m**2 = 0.
1/3, 2
Let r(p) = -p**2 - p + 7. Let l(f) = -f**2 - f + 4. Let n = -51 + 46. Let w(o) = n*l(o) + 2*r(o). Factor w(m).
3*(m - 1)*(m + 2)
Let i(t) be the first derivative of 25 + 36/5*t**5 + 0*t + 144*t**3 + 1/3*t**6 + 0*t**2 + 54*t**4. Factor i(d).
2*d**2*(d + 6)**3
Suppose -5*f + 4*f + 2 = 0. Suppose f*y = -y + 6. Suppose -n + 8*n + n**y - 3*n - n = 0. Calculate n.
-3, 0
Let k(f) be the second derivative of -f**7/84 - f**6/15 - 3*f**5/40 + 303*f. Factor k(b).
-b**3*(b + 1)*(b + 3)/2
Suppose 5*k + 5*n = -35, 3*k + 4 = 3*n + 13. Let l be (-3 + 4)/((-1)/k). Factor 3/2*s**3 + 0 + 1/6*s - s**l.
s*(3*s - 1)**2/6
Let l(q) be the third derivative of -q**5/60 + 3*q**4/2 - 64*q**3/3 + 76*q**2 - 4*q. Factor l(t).
-(t - 32)*(t - 4)
Let k(h) be the third derivative of -h**5/150 - 131*h**4/30 - 17161*h**3/15 - 2*h**2 + 119*h. Solve k(u) = 0 for u.
-131
Let w be (1 - 11/9) + (-47)/(-9). Factor -d**5 - 25*d - 55*d**3 - 4*d**5 + 5*d**3 + 50*d**2 + 25*d**4 + w.
-5*(d - 1)**5
Let f be (-8)/36*-1*9. Let a(p) be the first derivative of 8/27*p**3 - 14/45*p**5 - 6 + 2/3*p**4 + 0*p + 0*p**f. Let a(g) = 0. What is g?
-2/7, 0, 2
Let w = 9 + -5. Let 3*p**w + 4*p**2 + p**2 + p**2 - 9*p**4 + 3*p**5 - 3*p = 0. Calculate p.
-1, 0, 1
Let f(q) be the first derivative of -q**5/15 + 5*q**4/6 - 4*q**3 + 28*q**2/3 - 32*q/3 + 711. Factor f(z).
-(z - 4)*(z - 2)**3/3
Let r(m) = 27*m + 9*m**2 + 0*m**3 + m**3 - 6*m**3 + 15 + 9*m**3. Let o(d) = 2*d**3 + 4*d**2 + 14*d + 8. Let j(u) = 7*o(u) - 4*r(u). Let j(c) = 0. Calculate c.
-2, -1
Let d = -95 + 98. Let q be (d/(-27))/((-4)/312). Factor 0 + 18*v**3 - 46/3*v**4 + 14/3*v**5 - q*v**2 + 4/3*v.
2*v*(v - 1)**3*(7*v - 2)/3
Let d(f) be the first derivative of f**6/72 - f**5/60 - f**4/8 + f**3/9 + f**2/3 - 324. Solve d(a) = 0 for a.
-2, -1, 0, 2
Suppose t = 29 - 25. Suppose -2*n - t*p = -7*p - 16, -3*p + 40 = 2*n. Suppose 35*k + 45*k - 5*k**2 - n - 7 + 25*k**4 + 1 - 115*k**3 + 35*k**5 = 0. Calculate k.
-2, -1, 2/7, 1
Determine r, given that 24*r + 97*r**2 - 88*r**2 + 12 - 6*r**3 + 0*r**4 - 3*r**4 = 0.
-2, -1, 2
Let j(a) = -a**3 - 4*a**2 + 4*a + 10. Let v be j(-4). Let s be v/21 - 6/(-7). Factor -s + 2*x + 8/7*x**2.
2*(x + 2)*(4*x - 1)/7
Factor 6*y + 108*y**2 - 6*y + 12*y + 135*y**3.
3*y*(3*y + 2)*(15*y + 2)
Suppose 23 = 3*w + 11. What is s in 5*s**3 + 3*s**w + 100*s**2 + 15*s**3 - 2*s**4 = 0?
-10, 0
Let d(n) = -5*n**3 + 246*n**2 + 492*n + 4. Let j(k) = 5*k**3 - 245*k**2 - 485*k - 5. Let b(w) = -5*d(w) - 4*j(w). Factor b(x).
5*x