j(z) = 0?
-2, -1, 1
Let d be 0 - 12/18*-6. Let h be (13/d + -3)/(4/8). Factor h - 1/4*z**2 + 1/4*z.
-(z - 2)*(z + 1)/4
Suppose -q - 53 = -5*c - 25, 242 = 4*q + 39*c. Factor 3/4*g**q + 3*g - 9.
3*(g - 2)*(g + 6)/4
Let m be 60/150 + (-2)/5. Let f(t) be the second derivative of 0*t**3 + 0 - 5/21*t**7 - 9/10*t**5 + 3*t - 4/5*t**6 + m*t**2 - 1/3*t**4. Solve f(q) = 0.
-1, -2/5, 0
Let d be (-3)/(-40) + (-10)/(-75). Let c = d + 71/120. Let 24/5*u**3 - c*u + 0 - 14/5*u**4 - 6/5*u**2 = 0. Calculate u.
-2/7, 0, 1
Let n(c) be the first derivative of 0*c - 9/5*c**5 - 5*c**3 + 0*c**2 - 27/4*c**4 - 38 + 1/2*c**6. Factor n(l).
3*l**2*(l - 5)*(l + 1)**2
Let h(q) be the second derivative of q**5/220 - 6*q**3/11 - 44*q - 3. Factor h(f).
f*(f - 6)*(f + 6)/11
Suppose -39 - 3 = -7*q. Determine w so that 0 + 68*w**2 - 2 - 60*w - q = 0.
-2/17, 1
Let h(n) be the first derivative of -n**5/130 + 3*n**4/26 - 7*n - 10. Let a(r) be the first derivative of h(r). Find w such that a(w) = 0.
0, 9
Let j(o) be the third derivative of o**6/24 + 17*o**5/4 + 40*o**4 + 470*o**3/3 - 123*o**2. Suppose j(c) = 0. Calculate c.
-47, -2
Let d(b) be the first derivative of b**7/56 - b**6/36 - 5*b**5/24 + 23*b**3/3 + 15. Let t(n) be the third derivative of d(n). Factor t(s).
5*s*(s + 1)*(3*s - 5)
Let b(v) be the third derivative of -v**6/24 - 13*v**5/4 - v**2 - v. Let b(w) = 0. Calculate w.
-39, 0
Let w = -426 + 429. Let p(n) be the first derivative of 6 - n**4 - 8*n + 2*n**2 + 8/3*n**w. Factor p(o).
-4*(o - 2)*(o - 1)*(o + 1)
Suppose 5*h - 2*q + 0*q - 4 = 0, -3*h - q = -9. Suppose 0 = 3*m - 0*m - 12. Factor 4 - m*c**4 + 18*c**3 + 10*c**4 + 38*c**h + 8*c**3 + 22*c.
2*(c + 1)**2*(c + 2)*(3*c + 1)
Suppose -2*l = 4*m - 8, 1 = -l + m - 1. Let i(q) be the third derivative of l*q + 0 + 0*q**4 + 3*q**2 + 1/210*q**5 + 0*q**3. Determine x, given that i(x) = 0.
0
Let w = -111 - -115. Suppose 18*b = 16*b + w. Factor -5/4*i**b - i + 1/4.
-(i + 1)*(5*i - 1)/4
Let g(a) be the first derivative of a**6/2 - 3*a**5/5 - 9*a**4/4 + a**3 + 3*a**2 + 60. Factor g(h).
3*h*(h - 2)*(h - 1)*(h + 1)**2
Let v(l) = -5*l**2 - 33*l - 14. Let p be v(-6). Let f(r) be the second derivative of -2/7*r**2 - 1/6*r**p + 3/7*r**3 + 0 - 9*r. Find b such that f(b) = 0.
2/7, 1
Suppose 5*p - 3*i + 0*i = 10, -2*i = -3*p + 7. Let l be (-77)/(-44) + p/4. Suppose -x**2 + 0 + 0*x - 1/2*x**4 + l*x**3 = 0. What is x?
0, 1, 2
Let w(b) be the second derivative of 9*b**6/10 - 21*b**5/10 + 13*b**4/12 + b**3/3 - 93*b. Factor w(c).
c*(c - 1)*(3*c - 2)*(9*c + 1)
Suppose -2*u = -14 - 22. Suppose 0 = u*p - 16*p - 10. Factor -115*w**3 + 116*w**3 + 9 + 20*w + 7*w**2 - p*w.
(w + 1)*(w + 3)**2
Suppose 4*i = -0*i - 12, 3*w - 24 = 3*i. Let g(b) = b - 3. Let h be g(w). Let -12 - 12*m - m**h - 7*m**2 + 5*m**2 = 0. What is m?
-2
Let f(i) be the second derivative of -5*i**4/12 + 530*i**3/3 - 28090*i**2 + 304*i. What is r in f(r) = 0?
106
Let b = -1147/387 - 19/129. Let d = -22/9 - b. Solve -4/3*w**4 + 4/3*w**2 - d*w + 0 + 0*w**3 + 2/3*w**5 = 0.
-1, 0, 1
Let f(a) be the second derivative of a**7/840 - a**6/72 + 7*a**5/120 - a**4/8 - 14*a**3/3 + 2*a. Let t(m) be the second derivative of f(m). Solve t(d) = 0.
1, 3
Let k(f) be the first derivative of f**4/20 - 6*f**3/5 - 19*f**2/10 - 85. Determine i so that k(i) = 0.
-1, 0, 19
Suppose -32*q = -19808 + 19712. Solve 0 - 3/8*t**q + 3*t**2 - 6*t = 0 for t.
0, 4
Let a(s) = s**3 - 16*s**2 + 65*s - 12. Let n be a(7). Factor 0 + 3/7*q**3 - 5/7*q**4 - 1/7*q + 2/7*q**5 + 1/7*q**n.
q*(q - 1)**3*(2*q + 1)/7
Let b(g) be the second derivative of -g**6/90 - g**5/60 + g**4/18 - 72*g. Factor b(f).
-f**2*(f - 1)*(f + 2)/3
Let c(t) be the third derivative of -1/9*t**5 - 8/9*t**3 - 1/90*t**6 + 0*t - 4/9*t**4 + 0 - 37*t**2. Factor c(a).
-4*(a + 1)*(a + 2)**2/3
Suppose -2*d - d + 30 = 0. Let n(t) = t**3 - 11*t**2 + 11*t - 5. Let q be n(d). Factor q - 1 - 3*g**2 - g**3 + 2*g**3.
(g - 2)**2*(g + 1)
Suppose 6*j - 2*j - 2*v - 134 = 0, 4*j - 5*v - 131 = 0. Let x = j + -24. Factor x*h - 5*h - 3*h**2 - 14*h.
-3*h*(h + 3)
Let w(i) be the third derivative of i**6/120 + 28*i**5/15 + 392*i**4/3 + i**2 - 31*i. Determine v so that w(v) = 0.
-56, 0
Let d be 15 + (150/(-10) - -4). Let w(s) be the third derivative of 0 - 10*s**2 - 1/30*s**5 + 1/12*s**d + 0*s + 2/3*s**3. Factor w(q).
-2*(q - 2)*(q + 1)
Let w(k) = -4*k - 3. Let x be w(-13). Let f be 12/(-48) - x/(-68). Factor f*y - 8/17 - 2/17*y**2.
-2*(y - 2)**2/17
Let y(w) = -7*w**4 - 18*w**3 + 13*w**2 + 48*w - 38. Let d(j) = -85*j**4 - 215*j**3 + 155*j**2 + 575*j - 455. Let x(f) = -2*d(f) + 25*y(f). Factor x(g).
-5*(g - 1)**2*(g + 2)*(g + 4)
Let o(c) be the third derivative of -9*c**2 - 81/28*c**4 + 0 + 9/70*c**5 + 0*c + 243/7*c**3 - 1/420*c**6. Factor o(d).
-2*(d - 9)**3/7
Factor -18*p - 50*p**3 - 36*p**3 + 77*p**3 - 33*p**2.
-3*p*(p + 3)*(3*p + 2)
Suppose -3*p - 24 = -30. Factor 3*q**3 - 8*q**p - q**5 + 7*q**2 - 4*q + 2*q + q**4 + 0*q**4.
-q*(q - 2)*(q - 1)*(q + 1)**2
What is j in 30*j + 18*j - 161 + 113 - 12*j**3 + 3*j**4 = 0?
-2, 2
Let n(x) be the second derivative of -1/18*x**4 - 16*x + 0 + 1/9*x**3 + 2/3*x**2. Factor n(w).
-2*(w - 2)*(w + 1)/3
Let c(i) be the second derivative of -6*i + 1/20*i**5 + 0*i**4 + 0*i**2 + 0 + 0*i**3 - 1/60*i**6. Factor c(b).
-b**3*(b - 2)/2
Let q(v) be the first derivative of -v**4/50 - 2*v**3/75 + 4*v**2/25 + 8*v/25 + 38. Find u such that q(u) = 0.
-2, -1, 2
Let q(d) be the second derivative of -d**7/420 + d**6/180 + d**5/10 + 5*d**3 - 11*d. Let k(z) be the second derivative of q(z). Suppose k(l) = 0. Calculate l.
-2, 0, 3
Let b(g) be the first derivative of -2 - 1/2*g**2 + 2/3*g**3 + 0*g. Let b(y) = 0. What is y?
0, 1/2
Let l(b) be the first derivative of 15*b**4/4 - 50*b**3/3 - 20*b**2 + 220. Determine x, given that l(x) = 0.
-2/3, 0, 4
Let f(g) be the second derivative of g**5/80 + g**4/16 - 5*g**3/12 + 115*g. Factor f(h).
h*(h - 2)*(h + 5)/4
Solve -1232/3*q**3 - 331/2*q**4 - 332*q**2 - 40/3 - 112*q + 21*q**5 = 0.
-2/3, -1/2, -2/7, 10
Let b(p) = p**2 + p. Let f(j) = -8*j**2 - 52*j - 144. Let x(g) = 4*b(g) + f(g). Factor x(n).
-4*(n + 6)**2
Let h(t) be the second derivative of 5*t**4/12 + 5*t**3/3 - 15*t**2/2 - 72*t. What is s in h(s) = 0?
-3, 1
Let a(t) be the second derivative of -t**5/10 + 13*t**3/3 + 12*t**2 + 28*t. Factor a(c).
-2*(c - 4)*(c + 1)*(c + 3)
Let z(t) be the second derivative of -t**5/140 - t**4/14 - t**3/14 + 5*t**2/7 + 2*t - 52. Factor z(u).
-(u - 1)*(u + 2)*(u + 5)/7
Let g(p) be the first derivative of -5*p**4/12 - 5*p**3/6 + 5*p**2 - 23*p + 2. Let c(o) be the first derivative of g(o). Factor c(b).
-5*(b - 1)*(b + 2)
Factor -10*v - 20/3*v**3 + 55/3*v**2 + 0 - 5/3*v**4.
-5*v*(v - 1)**2*(v + 6)/3
Let n be 173/(-346)*(-2)/5. Factor 2/5 - 1/5*x**2 + n*x.
-(x - 2)*(x + 1)/5
Suppose -j + 34 = 29. Let 9*l**4 + 13*l**j + 16*l**2 - 19*l**5 + 15*l**4 + 36*l**3 + 10*l**5 = 0. What is l?
-4, -1, 0
Let i(l) be the third derivative of -25*l**8/224 - l**7/2 + 9*l**6/20 + 27*l**5/20 - 27*l**4/16 + 6*l**2. Determine x so that i(x) = 0.
-3, -1, 0, 3/5
Let p = -4153 - -12463/3. What is c in -p*c**2 + 0 + c**4 + 0*c + 4/3*c**3 = 0?
-2, 0, 2/3
Determine w, given that 12*w**4 + 302/15*w**3 + 4/15 + 68/15*w**2 - 10/3*w = 0.
-1, 1/10, 2/9
Let d(v) be the first derivative of v**5/10 + 51*v**4/8 + 104*v**3 - 169*v**2 + 222. Determine t so that d(t) = 0.
-26, 0, 1
Let -20/3*y**3 - 7/3*y**2 - 2/3 + 11/3*y = 0. What is y?
-1, 1/4, 2/5
Let x(t) be the second derivative of 1/10*t**3 - 3/100*t**5 + t + 1/30*t**4 - 1/5*t**2 - 12. Find y, given that x(y) = 0.
-1, 2/3, 1
Let y(r) = r**2 - 6. Let p be y(0). Let f = p - -8. Factor 12 - 4*x - 19*x**2 + 15*x**f - 4*x.
-4*(x - 1)*(x + 3)
Let m = 21 - 16. Factor -8*l + 1 + 0 - 4*l**2 - m.
-4*(l + 1)**2
Solve 192/7*j - 30/7*j**4 - 6/7*j**5 + 96/7 - 24/7*j**3 + 96/7*j**2 = 0.
-2, -1, 2
Let a(v) be the second derivative of -v**5/5 + 10*v**4/3 - 64*v**3/3 + 64*v**2 + 33*v. Factor a(l).
-4*(l - 4)**2*(l - 2)
Suppose -1700*k = -1693*k - 14. Factor k*l + 2/3*l**3 + 2*l**2 + 2/3.
2*(l + 1)**3/3
Factor 11/5*n + 12/5 - 1/5*n**2.
-(n - 12)*(n + 1)/5
Let d(y) = -15*y - 12. Let m = 42 + -43. Let o be d(m). Let 1/3*x**o - 2/3*x**2 + 1/3*x + 0 = 0. Calculate x.
0, 1
Let g be 12/8 + (-9)/6. Suppose -3*m = -g*m - 6. Find v such that -3*v**m + 3*v 