3*n + 3. Let p(q) = q**2 - 9*q. Let o(u) = -p(u) + 2*x(u). What is h in o(h) = 0?
-1, 2
Let w = 1911 - 5731/3. Suppose 2*f - 1 = 3. Solve -1/3*o**4 + w + o**f + 1/3*o**3 - 5/3*o = 0.
-2, 1
Determine y, given that -4/7*y - 5/7*y**3 - 12/7*y**2 + 0 = 0.
-2, -2/5, 0
Let p(o) = -14*o**4 - 4*o**3 - 8*o**2 + 4*o. Let v(s) = -5*s**4 - s**3 - 3*s**2 + s. Let c(g) = -4*p(g) + 11*v(g). Suppose c(n) = 0. What is n?
-5, -1, 0, 1
Solve 63*t**2 + 637/3*t + 686/3 + 1/3*t**4 + 23/3*t**3 = 0 for t.
-7, -2
Let x(z) be the second derivative of 0 + 6/7*z**2 + 3/14*z**3 - 1/28*z**4 - 24*z. Factor x(o).
-3*(o - 4)*(o + 1)/7
Let p be (-478)/240 + (-16)/120. Let w = p - -35/8. Factor 15/4*y - 3/2*y**2 + w.
-3*(y - 3)*(2*y + 1)/4
Let r(n) = -60*n + 424. Let w be r(7). Let o(z) be the second derivative of 1/2*z**3 + 0 - 4*z - 3/2*z**w + 3*z**2 + 3/20*z**5 + 1/5*z**6. Factor o(b).
3*(b - 1)**2*(b + 2)*(2*b + 1)
Let o(c) = -3*c + 3*c - 2*c + c. Let p(l) = 15*l**3 - 6*l**2 - 9*l + 6. Suppose -2*d - 3*x - 4 = 11, 4 = -4*x. Let h(i) = d*o(i) - p(i). Solve h(t) = 0 for t.
-1, 2/5, 1
Let g(i) be the first derivative of i**4 - 314*i**3/3 + 3120*i**2 - 3042*i - 919. Solve g(j) = 0.
1/2, 39
Let c(t) be the first derivative of 2*t**5/75 - 2*t**4/15 + 16*t**2/15 - 32*t/15 + 32. Factor c(s).
2*(s - 2)**3*(s + 2)/15
Factor 41*n**2 + 12 + 35*n**2 + n**3 + 19*n - 68*n**2.
(n + 1)*(n + 3)*(n + 4)
Let b(g) = -23*g**2 + 7*g - 35. Let q(o) = -8*o**2 + 2*o - 12. Let d(a) = -6*b(a) + 17*q(a). Determine f so that d(f) = 0.
1, 3
Let q(i) be the second derivative of i**5/35 - 5*i**4/21 - 4*i**3/7 - 9*i - 2. Find y, given that q(y) = 0.
-1, 0, 6
Let w be (-30)/4*(-13 - -6)/63. Find y such that -2/3*y**2 - 1/3 - 1/6*y**3 - w*y = 0.
-2, -1
Let m be 21/9 - (-3)/(-9). Determine j, given that -6*j**2 + 3*j**4 - 5*j**4 + 3*j**2 + 5*j**m = 0.
-1, 0, 1
Find f, given that -12/7*f**2 + 4/7*f**3 - 2/7 + 9/7*f = 0.
1/2, 2
Let -9/2*i - 2 + 0*i**3 + 1/4*i**4 - 11/4*i**2 = 0. What is i?
-2, -1, 4
Let i(u) be the first derivative of -3*u**4/4 + 2*u**3 + 27*u**2/2 - 54*u - 69. Suppose i(k) = 0. Calculate k.
-3, 2, 3
Let t = -5970 - -11943/2. Factor 3/2*n**2 + 3/2*n**3 - 3/2*n - t.
3*(n - 1)*(n + 1)**2/2
Let x(n) be the second derivative of -5/36*n**4 + 0 - 5/9*n**3 + 0*n**2 - 8*n. Factor x(b).
-5*b*(b + 2)/3
What is m in 23/6*m - 4 + 1/6*m**2 = 0?
-24, 1
Let v be 3/9 - 10/(-6). What is n in 3*n - 9*n - v*n**2 + 8*n = 0?
0, 1
Let n = -144313/3 + 48105. Factor n*k**4 + 10*k**2 + 6*k + 0 + 14/3*k**3.
2*k*(k + 1)*(k + 3)**2/3
Let f(p) be the third derivative of -p**5/120 - p**4/8 - 5*p**3/12 - 187*p**2. Determine z so that f(z) = 0.
-5, -1
Let y(l) = -5*l**2 - 48*l - 22. Let h(t) = t**2 + t + 1. Let a(b) = 3*h(b) + y(b). Let v be a(-22). Factor 3/5*x**2 + 1/5*x**v + 1/5 + 3/5*x.
(x + 1)**3/5
Let q(k) be the first derivative of k**6/6 - 12*k**5/5 + 27*k**4/2 - 36*k**3 + 81*k**2/2 + 17. What is i in q(i) = 0?
0, 3
Let p(m) = -3*m**5 + m**4 + m**2 + 1. Let w(n) = -4*n**5 - 24*n**4 + 24*n**3 - 4*n**2 - 4. Let u(d) = -4*p(d) - w(d). Factor u(i).
4*i**3*(i + 2)*(4*i - 3)
Let u = 1149/1042 + -7/2605. Factor 17/5*s + u + 3/10*s**2.
(s + 11)*(3*s + 1)/10
Factor -58*t + 57*t**2 + 330*t**3 - 167*t**3 + 49 - 167*t**3 - 152*t.
-(t - 7)**2*(4*t - 1)
Let t(h) be the second derivative of -5*h**4/4 - 11*h**3/2 + 18*h**2 - 85*h. Factor t(k).
-3*(k + 3)*(5*k - 4)
Solve -5/3*d + 1/3*d**2 + 4/3 = 0.
1, 4
Let d be (-2)/4*(9 + -19). Let j(f) be the first derivative of -f**3 + 99/2*f**2 + 9/5*f**d - 39/4*f**4 - 2 + 54*f. Factor j(r).
3*(r - 3)**2*(r + 1)*(3*r + 2)
Let r(s) be the first derivative of s**6/2 - 18*s**5/5 + 33*s**4/4 - 2*s**3 - 18*s**2 + 24*s + 76. Let r(j) = 0. Calculate j.
-1, 1, 2
Let x(o) be the second derivative of -o**5/100 + 242*o. Factor x(r).
-r**3/5
Let z(v) be the second derivative of 1/6*v**3 + 1/60*v**4 + 2/5*v**2 + 0 - 5*v. Determine c, given that z(c) = 0.
-4, -1
Let c = 53543/69 + -776. Let x = c - -74/345. Factor -3/5*s + x*s**3 + 0*s**2 - 2/5.
(s - 2)*(s + 1)**2/5
Let y(j) be the third derivative of -22*j**2 - 5/12*j**4 + 0*j + 0 + 1/12*j**5 + 5/6*j**3. Factor y(x).
5*(x - 1)**2
Let q(s) be the first derivative of 2*s**5/75 - s**4/6 + 2*s**3/15 + 3*s**2/5 - 264. Factor q(a).
2*a*(a - 3)**2*(a + 1)/15
Let q be -4*(0 + -1 + (-1)/(-2)). Factor -15*s**2 + s**3 + q*s**3 + 3*s**2.
3*s**2*(s - 4)
Suppose -5*m + 3 = -5*h - 27, m - 2 = -3*h. Factor 4*u**4 - 4 + m*u + 3*u - u**3 - 7*u**3.
4*(u - 1)**3*(u + 1)
Let f be 155/50 - -4*24/(-32). Let g(y) be the first derivative of 1/12*y**6 + 0*y - 11 + 0*y**2 - 1/8*y**4 + f*y**5 - 1/6*y**3. Factor g(l).
l**2*(l - 1)*(l + 1)**2/2
Let i be ((-2)/(-39))/((17 + -3)/42). Factor -i*w**4 + 0 - 6/13*w**2 + 6/13*w**3 + 2/13*w.
-2*w*(w - 1)**3/13
Let j(d) be the first derivative of -2*d**3 - 4 + 3/8*d**2 + 0*d. Determine w so that j(w) = 0.
0, 1/8
Factor -176/7 - 92/7*a - 2/7*a**2.
-2*(a + 2)*(a + 44)/7
Let d(x) be the second derivative of -x**7/42 + 2*x**6/15 - x**5/5 - x**4/6 + 5*x**3/6 - x**2 + 21*x + 2. Factor d(z).
-(z - 2)*(z - 1)**3*(z + 1)
Suppose 0 = 3*d + 15, -5*t = -3*d + 14 - 59. Let p = 7 - -1. What is j in -p*j**4 + 5*j**2 - 2*j**5 - 3*j**2 + 8*j - j**2 + 7*j**2 - t*j**3 = 0?
-2, -1, 0, 1
Solve -8*l + 0 - 2/9*l**2 = 0.
-36, 0
Let m(c) = -c + 2. Let f be m(-3). Suppose f*a - 4*a = 3. Suppose -a + 15/2*t - 9/2*t**2 = 0. What is t?
2/3, 1
Let n(b) = 2 + 383*b - 382*b - 2. Let r(a) = -a**4 - 3*a**3 + 4*a**2 - 7*a. Let y(o) = 21*n(o) + 3*r(o). Factor y(h).
-3*h**2*(h - 1)*(h + 4)
Let h = 81 + -72. Let f(r) = 3*r**3 - 2*r**2 - 3*r. Let y(g) = 13*g**3 - 9*g**2 - 13*g. Let c be (-1)/1 - (-3)/(-3). Let w(s) = c*y(s) + h*f(s). Factor w(a).
a*(a - 1)*(a + 1)
Let q be 117/195*(-10)/(-2). What is v in -4/13 + 14/13*v - 8/13*v**q + 10/13*v**2 = 0?
-1, 1/4, 2
Let i(q) be the second derivative of q**7/6 - 4*q**6/3 + 51*q**5/20 - 5*q**4/6 - 4*q**3/3 + 321*q. What is p in i(p) = 0?
-2/7, 0, 1, 4
Factor -200/13 + 40/13*h - 2/13*h**2.
-2*(h - 10)**2/13
Factor 196/3*f - 40/3*f**3 + 0 - 8/3*f**4 + 14/3*f**2.
-2*f*(f - 2)*(2*f + 7)**2/3
Suppose 104/9*b + 12 - 4/9*b**2 = 0. What is b?
-1, 27
Let w(c) be the first derivative of c**5/90 - c**4/36 - 2*c**3/9 + 3*c**2 - 5. Let t(s) be the second derivative of w(s). Factor t(r).
2*(r - 2)*(r + 1)/3
Let w(h) = -h**2 - 8*h + 10. Let s be w(-9). Let l(f) = 3*f**2 + 15 - 6*f - 3 - 2 - s. Let t(m) = -m**2. Let o(u) = -l(u) - 2*t(u). Find a, given that o(a) = 0.
3
Let w = -119 - -167. Determine d so that -w + 5*d**2 - 7*d + 2*d + 38 = 0.
-1, 2
Let g(a) = 1 + 0*a - 2*a**2 - 55 - 58*a. Let c be g(-28). Factor c*p + 3/2 + 1/2*p**2.
(p + 1)*(p + 3)/2
Let h = -515/2 + 773/3. Solve 2/3*d + h*d**2 + 2/3 = 0 for d.
-2
Suppose -54*f = -56*f + 14. Let o(c) = c**3 - 8*c**2 + 5*c + 18. Let t be o(f). What is p in 0*p**t + 0 - 2/11*p**5 + 0*p**2 + 4/11*p**3 - 2/11*p = 0?
-1, 0, 1
Let d = 405 + -845/2. Let k = -17 - d. Let 1/4*x**4 - x**5 - k*x**2 + 1/4 + 2*x**3 - x = 0. What is x?
-1, 1/4, 1
Let d(x) be the first derivative of -28/3*x**3 + 17*x**2 + 0*x**4 - 1/3*x**6 + 8/5*x**5 - 31 - 12*x. Factor d(z).
-2*(z - 3)*(z - 1)**3*(z + 2)
Let x(l) be the second derivative of l**7/1470 + l**6/280 - l**4/42 - 3*l**2 + 8*l. Let n(m) be the first derivative of x(m). Factor n(o).
o*(o - 1)*(o + 2)**2/7
Let c(u) be the third derivative of u**7/42 + u**6/6 - 7*u**5/4 + 146*u**2. Solve c(l) = 0.
-7, 0, 3
Let n = 0 + 8. Let w(d) = d**3 - 9*d**2 + 7*d + 11. Let s be w(n). Solve 4*q - s*q**3 + 0*q**3 - q**3 + 4 - 4*q**2 = 0.
-1, 1
Suppose 5*o - 26 - 14 = 0. Factor 8*w**2 + 17*w**3 - w - 19*w + 4*w**5 - 16*w**4 - w**3 + o.
4*(w - 2)*(w - 1)**3*(w + 1)
Let y be 6/(-11)*11/(-21). Factor -4/7*o - 6/7 + y*o**2.
2*(o - 3)*(o + 1)/7
Let a be 2/(-16) + (-2460)/(-4320). Let b(d) be the first derivative of 5/6*d**2 - 3 + 2/3*d + a*d**3 + 1/12*d**4. Factor b(j).
(j + 1)**2*(j + 2)/3
Let u(n) be the second derivative of n**7/14 - n**6/20 - 3*n**5/20 + n**4/8 - 2*n + 10. What is c in u(c) = 0?
-1, 0, 1/2, 1
Let h(j) = j**2 - 3*j + 4. Suppose x = 5*c - 3 + 1, 0 = -2*c + 2. Let w be h(x). Let 2*b**2 + 30 - w*b - 30 = 0. What is b?
0, 2
Factor 84*b - 8*b**2 + 38*b**2 - 60 - 11*b**2 - 10*b**2.
3*(b + 10)*(3*b - 2)
Let c(p) be the third derivative of 2*p**7/105 + 31*p**6/30 - 32*p**5/15 + p**2 -