). Let 0*t**2 - s*t + 8 + t**2 + 8*t - 6*t = 0. What is t?
2, 4
Suppose -3/5*o**2 + 3/5 + 0*o = 0. What is o?
-1, 1
Suppose -4*m = v - 8, 5*m - 5 = -2*v + 5. Let g be m + (47/(-44) - (-26)/(-143)). Solve 3/4*o + g*o**2 + 0 = 0.
-1, 0
Let s(x) be the first derivative of 980*x**3/3 + 70*x**2 + 5*x + 49. What is i in s(i) = 0?
-1/14
Let 0 + 0*s + 0*s**2 - 1/4*s**3 = 0. Calculate s.
0
Let b be 3465/10500 + 4/(-50). Let l(r) be the first derivative of 0*r + 1/6*r**6 - 5 - 2/5*r**5 + 0*r**2 - b*r**4 + 2/3*r**3. Solve l(p) = 0.
-1, 0, 1, 2
Let i(b) = 31*b + 349. Let s be i(-11). Let y(c) be the second derivative of 1/50*c**5 + 0 - 1/10*c**4 - s*c + 1/5*c**3 - 1/5*c**2. Let y(a) = 0. What is a?
1
Let c(t) = -t - 2. Let g(j) = -5*j**2 + 60*j - 20. Let v(m) = 10*c(m) - g(m). Let v(i) = 0. What is i?
0, 14
Suppose -5*u = 5*h + 25, -h - h - 15 = 3*u. Suppose h = 2*f + 2*s + s + 9, 4*s = -5*f - 5. Solve 0 - 2/3*n**2 - 1/3*n**f + 1/3*n**5 + 2/3*n**4 + 0*n = 0.
-2, -1, 0, 1
Let b(x) be the third derivative of -1/120*x**5 + 0*x - 7*x**2 + 0*x**3 + 0*x**4 + 1/240*x**6 + 0. What is l in b(l) = 0?
0, 1
Let z(a) = 10*a**3 + 10*a**2 + 12*a - 6. Let r(f) = -8*f**3 - 9*f**2 - 11*f + 5. Let q(y) = -6*r(y) - 5*z(y). Let q(u) = 0. Calculate u.
-1, 0, 3
Suppose 348 = 233*y - 59*y. Factor -1/3*l**y - l + 0.
-l*(l + 3)/3
Suppose 24 = 28*w - 32. Let h(k) be the second derivative of -5*k + 2/15*k**5 - 4/9*k**3 + 1/45*k**6 + 0 - 4/3*k**w + 1/6*k**4. Factor h(a).
2*(a - 1)*(a + 1)*(a + 2)**2/3
Let k be (-12)/6 - (-159)/72. Let u(x) be the second derivative of k*x**4 + 0 - 1/40*x**5 - 2/3*x**3 - 2*x + x**2. Determine v so that u(v) = 0.
1, 2
Let q = -12036 - -12039. Factor 0 + 3/2*x + 3/4*x**q - 9/4*x**2.
3*x*(x - 2)*(x - 1)/4
Suppose 0 = 5*n + 7*m - 3*m - 64, 0 = 3*n - 3*m - 33. Let t be (2 - 3)*(n/10)/(-1). Factor 2/5*o**2 + t*o + 4/5.
2*(o + 1)*(o + 2)/5
Let n = -12 - -7. Let w(f) = -9*f**3 + 4*f**2 + 13*f + 5. Let x(j) be the first derivative of j**4/4 - j**2/2 - j - 2. Let q(b) = n*x(b) - w(b). Factor q(o).
4*o*(o - 2)*(o + 1)
Suppose -18 = -3*j + 2*d, 0*j = -4*j - d + 35. Let 65*i**2 + 60*i + 14*i**4 + j*i**3 + 10*i**4 - 19*i**4 + 20 + 22*i**3 = 0. Calculate i.
-2, -1
Let l(j) = -j**2 - 12*j + 36. Let q be l(-15). Let z be -96*((-4)/q)/(-2). Determine a, given that -16/3 - 64/3*a**3 + z*a - 7*a**4 - 8/3*a**2 = 0.
-2, 2/7, 2/3
Let m(s) be the third derivative of s**7/630 - s**6/720 + s**2 + 106. Factor m(h).
h**3*(2*h - 1)/6
Let a(o) be the second derivative of -3*o**5/80 + 15*o**4/16 - 63*o**3/8 + 147*o**2/8 - 21*o + 1. Find z such that a(z) = 0.
1, 7
Suppose -5*o + v + 10 = 4*v, 3*o - 4*v = 6. Solve 5*d**3 + 12*d**4 + 4*d**5 - d**3 - 2*d**3 - 12*d**o - 8*d + 2*d**3 = 0.
-2, -1, 0, 1
Let v be (5 - (1 - 4)) + -4. Factor v*p**2 + 0*p**4 - 3*p**4 - 2 - 2*p**4 + 3*p**4.
-2*(p - 1)**2*(p + 1)**2
Let n(k) = 2*k**2 + k. Let p(z) = z**3 + 17*z**2 - 27*z + 15. Let g(y) = -10*n(y) + 5*p(y). Factor g(j).
5*(j - 1)**2*(j + 15)
Suppose 6*n + 8*n - 24 = 4. Let -12/11*u**n - 6/11 + 2/11*u**4 + 0*u**3 - 16/11*u = 0. Calculate u.
-1, 3
Let x(m) = m**3 - 30*m**2 - 229*m - 74. Let v be x(-6). Factor 0 - 1/2*h**3 - 1/3*h - 5/6*h**2 + 1/6*h**5 + 1/6*h**v.
h*(h - 2)*(h + 1)**3/6
Let 167*q**2 - 126546*q - 43966*q + 21337*q + 42250 - 35*q**3 + 4393*q**2 = 0. What is q?
2/7, 65
Let w be -1*(3 - 0) - -34. Suppose -4*i + w = 11. Factor 2*b + 3*b**4 - 3*b - 6*b**3 - b - 6*b**2 - i*b**4.
-2*b*(b + 1)**3
Determine h so that 148*h**3 - 22*h + 4*h**4 - 117 + 4*h**3 - 47 - 249*h**2 + 510*h - 231*h**2 = 0.
-41, 1
Let u(o) be the first derivative of -o**4/2 + 10*o**3/3 - 3*o**2 - 18*o - 40. Find x, given that u(x) = 0.
-1, 3
Let 4*h**4 - 4*h + 28/3*h**2 + 77/3*h**3 + 0 = 0. Calculate h.
-6, -2/3, 0, 1/4
Factor 45/4*w - 1/4*w**3 + 3/4*w**2 + 81/4.
-(w - 9)*(w + 3)**2/4
Let c(x) be the first derivative of 1/3*x**2 + 1/9*x**3 - 1/12*x**4 + 26 + 0*x. Find h, given that c(h) = 0.
-1, 0, 2
Let r(d) = d**3 - 13*d**2 - 7*d - 6. Let w be r(11). Let x be w/(-91) - (-8)/(-14). What is q in -q**2 + q**2 + 5*q**5 + 2*q**4 - x*q**5 = 0?
-1, 0
Let v be (-4 - (-148)/40) + (-112)/(-160). What is i in -4/5*i**2 + 4/5 - v*i + 2/5*i**3 = 0?
-1, 1, 2
Suppose 37 + 74*d + 40 - 77 + 3*d**3 - 113*d**2 = 0. What is d?
0, 2/3, 37
Solve 0 - 2/7*d**3 + 16/7*d**2 - 30/7*d = 0 for d.
0, 3, 5
Let g be 2 + ((-45)/(-10))/(-3). Let f be (2/9 - (-256)/144) + -2. Find w, given that -2*w + f + 0*w**2 + g*w**3 = 0.
-2, 0, 2
Let t(l) be the first derivative of 26 + 1/6*l**3 + 3/8*l**4 - 3/4*l**2 - l + 1/10*l**5. Factor t(n).
(n - 1)*(n + 1)**2*(n + 2)/2
Let f = 49/15 - 107/45. Factor -f*v - 8/9 + 2/9*v**3 + 2/9*v**2.
2*(v - 2)*(v + 1)*(v + 2)/9
Suppose -2*i = 5*i. Let z(k) be the second derivative of i + 0*k**3 - 5*k - 3/20*k**6 - 1/24*k**4 - 3/20*k**5 + 0*k**2. Factor z(h).
-h**2*(3*h + 1)**2/2
Suppose 587*b = 755*b. Let -2/7*m**4 + 10/7*m**5 + 2/7*m**2 + b - 10/7*m**3 + 0*m = 0. What is m?
-1, 0, 1/5, 1
Let m(u) be the third derivative of -u**5/20 + 25*u**4/28 - u**3/2 + 273*u**2. What is v in m(v) = 0?
1/7, 7
Let q(u) = -4*u**3 - u**2 - 2*u - 1. Let y be q(-1). Let m(d) be the third derivative of 0*d - 1/20*d**6 + 0*d**3 + 0 - 1/6*d**y - d**2 + 1/6*d**5. Factor m(o).
-2*o*(o - 1)*(3*o - 2)
Let u(a) = 7*a**5 - a**4 - a**3 + a**2. Let g(q) = 260*q**4 + 285*q**3 - 1065*q**2 - 1440*q - 320. Let f(j) = g(j) + 5*u(j). Find n, given that f(n) = 0.
-4, -1, -2/7, 2
Let m(y) = 4*y**4 + 16*y**3 - 48*y**2 - 36*y + 64. Let d(c) = -c**4 - 6*c**3 + 16*c**2 + 12*c - 21. Let a(s) = 10*d(s) + 3*m(s). Determine b so that a(b) = 0.
-1, 1, 3
Let w(q) = 3*q**2 - q + 7. Let u be 5/1*(-8)/10. Let i(x) = -x**2 - 2. Suppose -54 - 2 = 4*h. Let y(g) = h*i(g) + u*w(g). Determine v, given that y(v) = 0.
-2, 0
Suppose 38*p + 77 = 45*p. Let q(d) be the first derivative of d**6 - 6 - 4*d + 13*d**4 + p*d**2 - 28/5*d**5 - 16*d**3. Suppose q(u) = 0. What is u?
2/3, 1
Let v(y) be the first derivative of 3*y**3/7 + 87*y**2/7 - 120*y/7 + 345. Factor v(w).
3*(w + 20)*(3*w - 2)/7
Let p(n) be the first derivative of -n**3 + 0*n + 3/4*n**4 - 3/2*n**2 + 5 + 3/5*n**5. Factor p(l).
3*l*(l - 1)*(l + 1)**2
Let f be 2*2/(12/30). Suppose f = 8*o - 6. Suppose 0 - 4/3*c + 2/3*c**o = 0. Calculate c.
0, 2
Let f be (2 - 3)*12/4 - -3. Suppose f*v + 4 = 2*v. Solve 16/9 - 4/9*c**v - 2/9*c**3 + 8/9*c = 0.
-2, 2
Let z(b) be the first derivative of b**8/1344 + b**7/210 + b**6/96 + b**5/120 + 13*b**2 + 4. Let a(l) be the second derivative of z(l). Let a(m) = 0. What is m?
-2, -1, 0
Let z(u) be the second derivative of 9*u**7/28 + 33*u**6/40 + 51*u**5/80 + u**4/8 + 33*u - 1. Find a such that z(a) = 0.
-1, -2/3, -1/6, 0
Let t be ((-3705)/390)/(2 + -21). Solve t*y - 1/2*y**3 + 1/6*y**2 + 1/6*y**4 - 1/3 = 0.
-1, 1, 2
Determine a so that 9*a + 2*a + 12*a - 15*a - 2*a**3 = 0.
-2, 0, 2
Let o be (-76 + 78)/((1 - 3)/(-2)). Solve 32/3*l - 1/3 - 256/3*l**o = 0.
1/16
Suppose 2*g - 10 = -2*a + 14, 4*g + 8 = 0. Suppose 19*p - 26*p = -a. Determine i so that 0 - 4/3*i - 4/3*i**p + 4/3*i**4 + 4/3*i**3 = 0.
-1, 0, 1
Determine d so that -14*d**2 + 8/5 - 136/5*d = 0.
-2, 2/35
Factor -25*j**2 - 11*j - 3 + 24*j**2 + 7*j.
-(j + 1)*(j + 3)
Let d = 9 - 6. Let -9*r - 12*r**2 + 4*r**3 - 7*r**d + 0*r**3 = 0. Calculate r.
-3, -1, 0
Let s(p) = p**3 + 12*p**2 + 10*p - 16. Let d be s(-11). Let l = d + 8. Determine t so that -24*t - t**4 - 8 - 12*t**l + t**4 - 26*t**2 - 2*t**4 = 0.
-2, -1
Let f(h) be the first derivative of 7/20*h**5 + 1 + 1/10*h**6 + 4*h + 0*h**2 + 2/9*h**3 + 4/9*h**4. Let d(j) be the first derivative of f(j). Factor d(q).
q*(q + 1)*(3*q + 2)**2/3
Suppose 2*u - 6 = -2. Suppose q = -q. Suppose -4*n**3 + 2*n**4 - u*n**2 + q*n**2 + 5*n - n = 0. What is n?
-1, 0, 1, 2
Let k(b) = b**2 + 7*b + 2. Let x be k(-7). Factor -115*u**2 + 229*u**2 - 110*u**x + 32*u - 36.
4*(u - 1)*(u + 9)
Let r(i) = 2*i**2 + 84*i + 796. Let s(h) = h - 1. Let y(t) = -r(t) + 4*s(t). Factor y(j).
-2*(j + 20)**2
Let d(g) be the third derivative of -g**5/12 - 10*g**4/3 - 70*g**3/3 - 2*g**2 + 168. Suppose d(h) = 0. Calculate h.
-14, -2
Let y be (-12)/10 + (-2 + 7)/25. Let n be 0 - y - 4/(-28). Find c, given that 8/7*c**2 + 2/7 + n*c = 0.
-1/2
Let v = -2969 - -2973. Suppose 0*b + 2/7*b**v - 12/7*b**3 + 18/7*b**2 + 0 = 0. What is b?
0, 3
Let q(s) be 