/9
Let z(n) be the second derivative of -n**6/720 - n**5/180 + n**2 - 8*n. Let m(q) be the first derivative of z(q). Solve m(j) = 0.
-2, 0
Let a be 1 + 4/(-8) + ((-168)/(-63) - 2). Let 1/3*n**2 + a*n**3 - 3/2*n**4 + 0 + 0*n = 0. What is n?
-2/9, 0, 1
Let t(f) be the third derivative of f**5/90 - 7*f**4/36 - 2*f**3 - 2*f**2 - 125*f. Factor t(n).
2*(n - 9)*(n + 2)/3
Solve -4/3*t + 8/3*t**2 - 5/3*t**3 + 0 + 1/3*t**4 = 0.
0, 1, 2
Let d = -128 - -194. Suppose 18*i - d = -4*i. Factor -9/7*v**i + 9/7*v - 6/7 + 6/7*v**2.
-3*(v - 1)*(v + 1)*(3*v - 2)/7
Let f(a) be the third derivative of 0 + 25*a**2 + 1/18*a**5 + 1/3*a**3 - 7/36*a**4 + 0*a - 1/180*a**6. Factor f(k).
-2*(k - 3)*(k - 1)**2/3
Let c(s) be the first derivative of 6*s**5/7 + s**4 - 16*s**3/7 - 30*s**2/7 - 2*s - 101. Determine z, given that c(z) = 0.
-1, -1/3, 7/5
Let g(o) be the first derivative of 4/5*o**5 - 4*o**3 - o**4 + 10*o**2 - 8*o + 31. Factor g(w).
4*(w - 1)**3*(w + 2)
Let k(h) = -21*h**2 - 165*h - 170. Let m(o) = -10*o**2 - 82*o - 84. Let z(p) = 6*k(p) - 13*m(p). Factor z(d).
4*(d + 1)*(d + 18)
Let z(w) be the third derivative of -w**8/120960 - w**7/30240 + w**6/2160 - 11*w**5/60 + 13*w**2. Let i(l) be the third derivative of z(l). Factor i(s).
-(s - 1)*(s + 2)/6
Let p(k) be the second derivative of 0 - 4*k + 1/480*k**6 + k**2 + 1/24*k**3 - 1/96*k**4 - 1/240*k**5. Let z(n) be the first derivative of p(n). Factor z(c).
(c - 1)**2*(c + 1)/4
Suppose -21*l + 19*l = -14. Let -13*s**4 + 22*s**2 - 30 + 42*s**4 - 14*s**4 + 55*s**3 - 55*s - l*s**2 = 0. Calculate s.
-3, -1, -2/3, 1
Factor -4/3*b**3 - b**2 + 4/3*b + 4/3 - 1/3*b**4.
-(b - 1)*(b + 1)*(b + 2)**2/3
Let d(z) = -4*z**2 + 3*z. Let v(i) = -7*i**2 + 5*i. Let f be -1 + 9*2/3. Let u(c) = f*d(c) - 3*v(c). Suppose u(t) = 0. What is t?
0
Let h(a) = 50*a**2 + 322*a + 50. Let x(f) = f**2 + f - 1. Let s(l) = -h(l) + 6*x(l). Factor s(c).
-4*(c + 7)*(11*c + 2)
Let z(x) = 28*x**2 - 7*x - 4. Let u(p) = 54*p**2 - 15*p - 9. Let d(f) = -4*u(f) + 9*z(f). Factor d(m).
3*m*(12*m - 1)
Let 7/9*u**3 + 64/9 + 20/3*u**2 + 16*u = 0. What is u?
-4, -4/7
Let m(h) be the second derivative of h**5/30 - 2*h**4/9 - 4*h**3/9 + 16*h**2/3 + 88*h - 1. Find b, given that m(b) = 0.
-2, 2, 4
Find m such that -6/11*m**3 + 0*m**2 + 0 + 6/11*m = 0.
-1, 0, 1
Let u(q) be the first derivative of -2*q**3 - 2*q**2 + 2*q - 73. What is k in u(k) = 0?
-1, 1/3
Let p(g) be the second derivative of -1/34*g**4 - 1/17*g**2 - 24*g + 0 - 1/170*g**5 - 1/17*g**3. Solve p(z) = 0.
-1
Let a(t) be the third derivative of -1/315*t**7 + 2/9*t**3 + 1/1008*t**8 + 0 - 1/90*t**5 + 0*t + 5*t**2 - 1/45*t**6 + 7/72*t**4. What is k in a(k) = 0?
-1, 1, 4
Let l(s) be the first derivative of 2*s**5 - 45*s**4/4 + 70*s**3/3 - 45*s**2/2 + 10*s - 176. Solve l(x) = 0 for x.
1/2, 1, 2
Let j(f) be the second derivative of 4/5*f**2 + 18*f + 1/100*f**5 + 0 - 1/30*f**4 - 2/15*f**3. Suppose j(x) = 0. Calculate x.
-2, 2
Let w(c) = c**3 - 11*c**2 - 11*c - 7. Let s be w(12). What is t in -s + 2*t**2 + 1 - 4*t**2 + 2 + 4*t = 0?
1
Let s be 8 + -22 + (-1 - -5). Let h be (2/(-5))/(1/s). Solve -2/15*u**2 - 2/15*u**3 + 2/15*u**h + 2/15*u + 0 = 0 for u.
-1, 0, 1
Find y, given that 18*y - 2*y - 64*y**3 + 11*y + y - 4 - 32*y**2 = 0.
-1, 1/4
Let i = 38/25 - 27/100. Factor i*x**2 + 5/4*x - 5/4*x**3 + 0 - 5/4*x**4.
-5*x*(x - 1)*(x + 1)**2/4
Let s(x) = 237*x**2 - 23*x - 156*x - 120*x**3 + 99 - 16*x + 30*x**4 - 45*x. Let u(d) = d**5 - d**2 + 1. Let j(h) = -s(h) + 3*u(h). Determine b so that j(b) = 0.
2
Let q be 5/2*(-15 + (-1479)/(-85)) - 0. Find l such that q*l**4 - 3/2*l + 3 - 9*l**2 - 9/2*l**5 + 6*l**3 = 0.
-1, -2/3, 1
Let j = 2214 - 2210. Factor 0 + 0*q**2 + 2/7*q**j + 4/7*q**3 - 6/7*q**5 + 0*q.
-2*q**3*(q - 1)*(3*q + 2)/7
Suppose -8 = 7*z - 1. Let c be 4*(z + 3/2)*1. Factor -1/2*q**c + 2/3*q - 1/6.
-(q - 1)*(3*q - 1)/6
Let 6 + 3*o - 3*o**3 + 14 + 36*o**2 - 56 = 0. Calculate o.
-1, 1, 12
Let l(u) be the second derivative of 0*u**2 + 0 - 11/24*u**6 - 25/168*u**7 - 7*u + 0*u**3 + 7/10*u**5 - 1/4*u**4. Find j such that l(j) = 0.
-3, 0, 2/5
Let g(v) be the second derivative of 4*v - 1/80*v**5 + 1/48*v**4 + 1/6*v**3 - 1/2*v**2 + 0. Factor g(z).
-(z - 2)*(z - 1)*(z + 2)/4
Suppose 3*m + 5*z - 36 = 0, -163*m + 5*z - 48 = -167*m. Factor 10/3*v**3 - m*v**2 - 1/3*v**4 + 18*v - 9.
-(v - 3)**3*(v - 1)/3
Let f = -7/5 - -19/10. Let i(m) be the first derivative of -f*m + 1/2*m**2 - 7 - 1/6*m**3. Determine k, given that i(k) = 0.
1
Let y(x) be the third derivative of -x**5/40 - x**4/16 + 119*x**2. Find u, given that y(u) = 0.
-1, 0
Suppose -11 = -3*l + 7. Suppose 0 = 3*o + 6*v - 2*v - l, 0 = -4*o + 3*v + 8. Determine z, given that 12*z - 5 - 6*z**2 + 0*z**2 - 6*z**o + 2 = 0.
1/2
Factor 4/3 - 8*k - 7*k**3 + 37/3*k**2 + 4/3*k**4.
(k - 2)**2*(k - 1)*(4*k - 1)/3
Let m(k) = -8*k + 107. Let n be m(21). Let v = -61 - n. Factor -2/9*z**3 + 2/9*z**4 + v*z**2 + 0*z + 0.
2*z**3*(z - 1)/9
Let v(g) = -26*g**5 + 11*g**4 + 41*g**3 - 26*g - 11. Let w(r) = -9*r**5 + 4*r**4 + 14*r**3 - 9*r - 4. Let j = 3 + 1. Let m(y) = j*v(y) - 11*w(y). Factor m(p).
-5*p*(p - 1)**2*(p + 1)**2
Let i be ((-42)/(-49))/(1/7). Let s be 10/15 - (-14)/i. Factor -4*b - 14*b**2 + 2*b**4 + 0*b**4 - 5*b**4 - 3*b**4 - 16*b**s.
-2*b*(b + 1)**2*(3*b + 2)
Suppose -4*x = -3*i - 88, x - 5*x = -2*i - 56. Let q be i/(-14) - 2/7. Factor 4 - 42*p + p**2 + 48*p + p**4 - 6*p**3 - 3*p**q - 3*p**4.
-2*(p - 1)*(p + 1)**2*(p + 2)
Let m(p) be the second derivative of -8*p - 5/28*p**4 - 4/7*p**3 + 1 - 3/140*p**5 - 6/7*p**2. Factor m(y).
-3*(y + 1)*(y + 2)**2/7
Let y(o) be the third derivative of -1/32*o**4 - 41*o**2 + 0*o**7 + 0 + 0*o - 1/80*o**6 + 1/30*o**5 + 0*o**3 + 1/1344*o**8. Factor y(k).
k*(k - 1)**3*(k + 3)/4
Let o(d) be the third derivative of -d**7/350 - d**6/50 + 19*d**5/100 - 7*d**4/20 + d**2 + 38*d. Determine n, given that o(n) = 0.
-7, 0, 1, 2
Let b(d) = -5*d**2 + 129*d - 2175. Let v(w) = -29*w**2 + 775*w - 13051. Let a(n) = 34*b(n) - 6*v(n). Factor a(s).
4*(s - 33)**2
Let r(x) = -5*x - 27. Let a be r(-8). Factor -a*f + f + 27*f**3 - 475*f**2 - 21*f**4 + 511*f**2.
-3*f*(f - 2)*(f + 1)*(7*f - 2)
Let y(s) be the first derivative of -s**6/9 - 11*s**5/15 - 13*s**4/12 - 4*s**3/9 + 280. Let y(t) = 0. Calculate t.
-4, -1, -1/2, 0
Suppose 781/2*b**2 + 50*b**4 + 9/2 - 87*b + 290*b**3 = 0. Calculate b.
-3, 1/10
Let q(j) = -3*j**2 + j**2 - 3*j + 2*j. Let g(k) = -4*k**2 - 6*k**2 - 6*k + 0*k**2. Let b(c) = -3*g(c) + 16*q(c). Factor b(a).
-2*a*(a - 1)
Let f = 1 - -3. Suppose -3*q + 6*q - 12 = 0. Suppose -32*b**3 + 28*b**3 - 4*b**5 - 12*b**q + f*b**4 = 0. What is b?
-1, 0
Let l(s) be the third derivative of 20*s**2 + 0*s**3 + 1/210*s**5 + 1/42*s**4 - 1/420*s**6 + 0 + 0*s. Factor l(q).
-2*q*(q - 2)*(q + 1)/7
Suppose 21 = 4*k - 3. Let p(b) = -9*b**2 - 5*b - 25. Let l(c) = -4*c**2 - 3*c - 12. Let u be ((-336)/9)/(-8)*(-2 + -1). Let r(v) = k*p(v) + u*l(v). Factor r(y).
2*(y + 3)**2
Factor -h**2 - 81*h - 3*h**2 + 2*h**2 - h**2.
-3*h*(h + 27)
Suppose -5*r = 4*m - 33, 0*m = m - 5*r + 23. Let o be 4*1*m/(28/2). Determine b so that 0*b - o*b**4 - 6/7*b**3 + 0 + 4/7*b**2 + 6/7*b**5 = 0.
-1, 0, 2/3, 1
Let y(g) be the second derivative of -g**5/60 + 17*g**4/36 - 8*g**3/9 - 4*g + 19. Factor y(x).
-x*(x - 16)*(x - 1)/3
Suppose -32 = 5*q - 7, -m = 3*q - 390. Let j = m - 183. Factor 218 - 4*y**3 + 6*y**3 + 4*y**2 - j - 2*y.
2*(y - 1)*(y + 1)*(y + 2)
Let j(x) be the third derivative of -x**8/672 - x**7/140 + x**5/30 + 4*x**2 + 26*x. Suppose j(l) = 0. What is l?
-2, 0, 1
Factor -54/5*x**2 - 594/5 - 378/5*x + 2/5*x**3.
2*(x - 33)*(x + 3)**2/5
Suppose 4*r + 0*h - 6 = -h, -2*h - 6 = -r. Let m = -18 - -18. Factor 2*z**3 + 4*z - 3*z**2 + m*z**2 - 3*z**r.
2*z*(z - 2)*(z - 1)
Let x be (-20)/90 - 58/21 - -3. Let y(j) be the second derivative of -1/3*j**2 + 1/9*j**4 + 6*j + x*j**7 - 1/45*j**6 + 0 + 1/9*j**3 - 1/15*j**5. Factor y(z).
2*(z - 1)**3*(z + 1)**2/3
Let s(x) be the third derivative of x**6/60 + x**5/12 + x**4/6 + 5*x**3/3 - 4*x**2. Let f(n) be the first derivative of s(n). Let f(c) = 0. What is c?
-1, -2/3
Let a(u) be the second derivative of 0*u**2 + 0 - 1/40*u**6 - 1/12*u**3 + 1/80*u**5 + u + 1/16*u**4 + 1/168*u**7. Find l, given that a(l) = 0.
-1, 0, 1, 2
Suppose 4*o - 7*o = -9. Factor 6*d**4 - d**4 - o*d**2 - 10*d - 12