
Let u(l) = 4*l**3 - 4*l. Suppose -2*n = n - 24. Let w = -5 - -4. Let z(q) = q**2 - 1. Let j(d) = n*z(d) + w*u(d). Factor j(v).
-4*(v - 2)*(v - 1)*(v + 1)
Let r(a) = -2*a**5 - a**4 + a - 1. Let v(l) = -5*l**5 + 26*l**4 - 166*l**3 - 420*l**2 - 223*l - 2. Let u(h) = 10*r(h) - 5*v(h). Factor u(w).
5*w*(w - 15)**2*(w + 1)**2
Let v(s) be the second derivative of 0 + 1/9*s**4 + 9*s + 4/9*s**3 - 2*s**2. Let v(y) = 0. What is y?
-3, 1
Let c(h) be the second derivative of -h**6/1080 - h**5/180 - h**4/72 - h**3 - 18*h. Let q(r) be the second derivative of c(r). Find n such that q(n) = 0.
-1
Suppose -14 = -d + 3*q, 7*q + 4 = -4*d + 4*q. Determine c, given that 8/11 + 2/11*c**d + 8/11*c = 0.
-2
Let a = 45121 + -45049. Determine q so that -308*q + 242 - 68/11*q**3 + 2/11*q**4 + a*q**2 = 0.
1, 11
Let c(j) be the second derivative of 35*j**4/12 - 10*j**3 - 10*j**2 + 231*j. Factor c(p).
5*(p - 2)*(7*p + 2)
Let y(q) be the third derivative of q**8/84 - 2*q**6/15 + 2*q**5/15 + q**4/2 - 4*q**3/3 - 23*q**2. Factor y(b).
4*(b - 1)**3*(b + 1)*(b + 2)
Let r(a) be the first derivative of -a**4/8 + a**3/3 + 6*a**2 - 157. Factor r(v).
-v*(v - 6)*(v + 4)/2
Let l = 4031/10115 + 3/2023. Let s be ((-2)/(-8))/(5/4). Factor -l*z - s*z**2 + 0.
-z*(z + 2)/5
Let d(f) = -2*f**3 + 14*f**2 - 12*f. Let p(s) = -s**2 + s. Let u be (23 - 11)/(2/(-2)). Let c = u + 32. Let o(g) = c*p(g) + 2*d(g). Factor o(m).
-4*m*(m - 1)**2
Let n(s) be the first derivative of s**4/6 + 8*s**3/9 - 11*s**2/3 + 4*s + 166. Solve n(r) = 0 for r.
-6, 1
Let z(y) be the second derivative of 0 + 6*y + 0*y**2 + 0*y**3 + 1/54*y**4. Factor z(s).
2*s**2/9
Let z(f) be the first derivative of -f**5/4 + 5*f**3/6 - 27*f + 19. Let r(q) be the first derivative of z(q). Factor r(i).
-5*i*(i - 1)*(i + 1)
Let r be 14*((-18)/45 - (-272)/630). Suppose 0 + 14/9*v**2 + r*v = 0. Calculate v.
-2/7, 0
Factor -12*u**2 - 200 + 204 + 8*u**2.
-4*(u - 1)*(u + 1)
Let h be -2 + 11/((-44)/(-488)). Let v = h + -117. Factor 27/2 - 15/2*f**2 - 9/2*f - 3/2*f**v.
-3*(f - 1)*(f + 3)**2/2
Let m(q) be the third derivative of q**8/2856 - q**7/1785 - q**6/204 + q**5/102 + q**4/51 - 4*q**3/51 + 52*q**2. Let m(x) = 0. Calculate x.
-2, -1, 1, 2
Let k = 1738 + -1736. Let u(o) be the first derivative of 0*o - 1/6*o**3 + 1/16*o**4 + 0*o**k - 10. Factor u(r).
r**2*(r - 2)/4
Let p(g) be the third derivative of -g**8/1680 - g**7/280 - g**6/180 - 2*g**3/3 + 12*g**2. Let s(x) be the first derivative of p(x). Solve s(v) = 0.
-2, -1, 0
Let d(b) be the second derivative of b**4/16 + 13*b**3/8 - 21*b**2/4 - 126*b. Factor d(j).
3*(j - 1)*(j + 14)/4
Suppose 92/3*n + 30 + 2/3*n**2 = 0. Calculate n.
-45, -1
Suppose 0 = -89*m - 10*m - 1 + 1. Determine n so that n**2 + m + 0*n + 1/2*n**3 = 0.
-2, 0
Let h(j) = -2*j**2 + 5*j - 2. Let k be h(2). Suppose 4*z - 21 = -3*m, 15*m - 10*m + 2*z - 21 = k. Factor -1/4*x**m + 0 + 1/4*x + 0*x**2.
-x*(x - 1)*(x + 1)/4
Let p(b) be the third derivative of b**5/270 - 16*b**4/27 + 1024*b**3/27 + b**2 - 43. Suppose p(u) = 0. What is u?
32
Find g, given that 2/3*g**3 + 0 - 4*g + 10/3*g**2 = 0.
-6, 0, 1
Let t(m) = 2*m**2 - 7. Let s(z) = -z**2 - 4*z + 10. Let v be s(-5). Let l(u) = -2*u**2 + 8. Let b(a) = v*l(a) + 6*t(a). Factor b(n).
2*(n - 1)*(n + 1)
Let c(t) = -t**2 - t. Let i(w) be the third derivative of -w**5/60 + w**3/6 + 8*w**2. Let n(b) = -5*c(b) + 10*i(b). Suppose n(r) = 0. Calculate r.
-1, 2
Let q(d) be the first derivative of d**5/120 - d**4/18 + 5*d**3/36 - d**2/6 - 7*d - 1. Let j(g) be the first derivative of q(g). Find h, given that j(h) = 0.
1, 2
Let n(x) = 13*x**2 + 14*x + 1. Let y(w) = 11*w**2 + 13*w + 2. Let b(v) = 5*n(v) - 6*y(v). Let b(p) = 0. Calculate p.
-7, -1
Let g be -4*(1 - (4 + -2)). Let y be 3*2 + (-2691)/(-351). Find u such that -98/3*u**4 - g*u + 49*u**3 - y*u**2 + 4/3 = 0.
-2/7, 2/7, 1/2, 1
Let h(o) be the second derivative of -3*o**6/2 + 105*o**5/4 + 190*o**4/3 + 130*o**3/3 - 211*o. Factor h(z).
-5*z*(z - 13)*(3*z + 2)**2
Find o such that 178/13*o + 94/13*o**3 + 242/13*o**2 + 36/13 - 6/13*o**4 = 0.
-1, -1/3, 18
Let p(d) = 7*d + 1. Let k be p(3). Let j = 8 - 5. Find z, given that 10*z**3 + 0*z**2 + 3*z + z + 40*z**4 - k*z**2 + 4*z**j = 0.
-1, 0, 1/4, 2/5
Let f = -913 + 915. Let q(s) be the first derivative of -1/4*s**3 - 7 + 3/8*s**f + 0*s. Find r such that q(r) = 0.
0, 1
What is k in -90*k**2 - 6/11*k**5 - 90/11*k**4 - 42*k**3 + 0 - 756/11*k = 0?
-7, -3, -2, 0
Let i be 7/(0 - (-5)/(-10)). Let p be (-9)/27 - i/6. Find k such that k**2 - 2 - 9*k + p + 11*k = 0.
-2, 0
Let z(c) be the first derivative of c**7/840 + c**6/90 + c**5/40 - c**3 + 8. Let u(q) be the third derivative of z(q). Factor u(b).
b*(b + 1)*(b + 3)
Let v(l) be the third derivative of 28561*l**8/1176 - 68107*l**7/735 - 4056*l**6/35 - 5876*l**5/105 - 44*l**4/3 - 16*l**3/7 + 222*l**2. What is z in v(z) = 0?
-2/13, 3
Let s(v) be the second derivative of 0 - 1/3*v**2 + 1/36*v**4 - 1/18*v**3 - v. Solve s(q) = 0.
-1, 2
Let x(g) = 66*g**3 + 686*g**2 + 1406*g - 414. Let s(z) = 13*z**3 + 137*z**2 + 281*z - 83. Let m(k) = 14*s(k) - 3*x(k). Factor m(h).
-4*(h + 4)*(h + 5)*(4*h - 1)
Suppose 5*c - 2*c = 0. Solve -4*k**2 - k + c*k + 5*k**2 = 0 for k.
0, 1
Suppose -113*q + 49*q**2 - 29*q**3 + 326*q**2 + 3*q + 64*q**3 = 0. Calculate q.
-11, 0, 2/7
Let k(f) be the second derivative of -f**5/30 - 2*f**4/9 - 4*f**3/9 - 330*f. Find p such that k(p) = 0.
-2, 0
Let m(p) be the second derivative of p**7/105 - p**6/20 + 3*p**5/50 + p**4/30 - 5*p + 2. Suppose m(y) = 0. Calculate y.
-1/4, 0, 2
Let f(w) be the first derivative of -2*w**3/3 - 6*w**2 - 10*w + 85. Determine q, given that f(q) = 0.
-5, -1
Suppose 19 - 27 = -2*p. Factor -m**4 - 5*m**2 - 3*m**p - 2*m - 16*m**3 + 3*m**4 + 12*m**3.
-m*(m + 1)**2*(m + 2)
Let o(y) = y**3 + 3*y**2 - 5*y + 2. Let j be o(-4). Suppose -4 = x + 3*v, -7*x + j*x - 5*v = 8. What is u in 0*u + 0 - 2/9*u**x = 0?
0
Let 6 - 27*v**5 - 3*v**3 - 12 + 30*v**5 - 36*v + 18 + 33*v**2 - 9*v**4 = 0. What is v?
-2, 1, 2
Let b(a) be the second derivative of a**4/24 + 7*a**3/24 - 9*a**2/8 - 10*a + 6. What is c in b(c) = 0?
-9/2, 1
Suppose -2*m + h = 5 - 13, -5*m + 3*h + 20 = 0. Suppose 8/17*c**m - 12/17*c**3 + 8/17*c**2 - 2/17*c + 0 - 2/17*c**5 = 0. Calculate c.
0, 1
Let z(s) = s**2 + 1. Let h(p) = -2*p**2 + 3*p - 7. Let t(u) = h(u) - 4*z(u). Let j(i) = -i**2 - i + 1. Let b(f) = 5*j(f) - t(f). Suppose b(c) = 0. What is c?
4
Let o(i) be the second derivative of i**7/231 + 5*i**6/33 + 83*i**5/55 + 16*i**4/11 - 96*i**3/11 + i - 1. Solve o(t) = 0 for t.
-12, -2, 0, 1
Let h be 21/(-49) + (-361)/(-532). Solve 0*s + 7/2*s**5 + 0*s**2 + h*s**3 + 15/8*s**4 + 0 = 0.
-2/7, -1/4, 0
Factor 0 + 0*m**2 + 1/4*m + 1/4*m**5 + 0*m**4 - 1/2*m**3.
m*(m - 1)**2*(m + 1)**2/4
Factor -4*t**2 - 56 + 124 + 11*t - 75*t.
-4*(t - 1)*(t + 17)
Let y(g) = -19*g**2 + 1. Let h be y(-1). Let i(t) = t**3 + 19*t**2 + 17*t - 14. Let s be i(h). What is k in 4/7*k + 4/7*k**s - 10/7*k**2 + 0 + 2/7*k**3 = 0?
-2, 0, 1/2, 1
Let b(w) = 239*w**2 - 286*w + 74. Let j(z) be the third derivative of -4*z**5 + 95*z**4/8 - 25*z**3/2 - 28*z**2. Let p(u) = -5*b(u) - 6*j(u). Factor p(o).
5*(7*o - 4)**2
Let x(o) be the third derivative of -1/60*o**5 + 2*o**2 + 0*o - 3/2*o**3 + 1/4*o**4 + 0. Let x(c) = 0. What is c?
3
Let z(v) be the second derivative of 1/2*v**4 + v**2 + 0 + v**3 + 1/10*v**5 - 10*v. Solve z(r) = 0.
-1
Let a(z) be the second derivative of 0 - 4/3*z**3 + 9/2*z**2 + 22*z - 1/12*z**4. Factor a(h).
-(h - 1)*(h + 9)
Suppose 0 = -52*j + 55*j - 6, -4*b = -4*j. Factor g - 1/3*g**b - 2/3.
-(g - 2)*(g - 1)/3
Let y(l) be the first derivative of -l**6/25 - 4*l**5/25 - l**4/5 + l**2/5 - 26*l - 13. Let n(h) be the first derivative of y(h). Factor n(i).
-2*(i + 1)**3*(3*i - 1)/5
Let m(x) be the first derivative of -5*x**5/28 + 5*x**4/21 - 2*x**3/21 + 8*x + 10. Let b(d) be the first derivative of m(d). Factor b(g).
-g*(5*g - 2)**2/7
Let f(o) = o**3 + 14*o**2 + 43*o - 10. Let b be f(-5). Let t(c) be the first derivative of 0*c**3 + 0*c**2 - 6 + b*c - 1/16*c**4. Solve t(j) = 0 for j.
0
Suppose -4*d + 8 = -h, 4*h = -d + 2*h + 2. Let q(n) be the first derivative of -3/5*n**5 + 0*n + n**3 - 3/2*n**d + 3/4*n**4 - 4. Solve q(a) = 0.
-1, 0, 1
Let d(h) be the second derivative of -h**9/3920 + 3*h**8/15680 + h**7/1176 