
Let y = 116 + -115. Let x be (1 + -1 + y)*(2 - 2). Factor x + 0*d + 1/3*d**2.
d**2/3
Determine b, given that -4/5*b**2 + 2/15*b**4 + 0*b**3 - 2/5 + 16/15*b = 0.
-3, 1
Let t(g) be the second derivative of -g**5/10 - g**4/24 + g**3/3 + g**2/4 + 6*g - 12. Find n such that t(n) = 0.
-1, -1/4, 1
Let m(f) = -3 - 6*f - 4 + 2 - 7. Let k be m(-2). What is t in 0 + 0*t**3 + 1/7*t**2 + k*t - 1/7*t**4 = 0?
-1, 0, 1
Let t(o) be the first derivative of -o**5/28 + o**4/14 + o**3/14 + 33*o**2/2 - 28. Let c(a) be the second derivative of t(a). Solve c(m) = 0.
-1/5, 1
Factor -77/4*l**2 - 74*l - 73 - 1/4*l**3.
-(l + 2)**2*(l + 73)/4
Let f(z) be the second derivative of -z**6/60 + z**4/8 - z**3/6 - 96*z + 2. Factor f(r).
-r*(r - 1)**2*(r + 2)/2
Let -28*c - 10*c**2 + 6*c**4 - 12*c**2 - 45*c**2 - 114*c**3 + 38*c**3 - 43*c**2 = 0. What is c?
-1, -1/3, 0, 14
Let j(r) = 17*r**3 + 83*r**2 + 1368*r - 1444. Let q(x) = 2*x**3 + x**2. Let m(p) = -5*j(p) + 40*q(p). Factor m(c).
-5*(c - 1)*(c + 38)**2
Determine w, given that -11*w**2 - 2*w**3 + 19 - 4*w**3 - 30 + 8*w - 2*w**3 - w**4 + 23 = 0.
-6, -2, -1, 1
Let q(s) be the second derivative of 5/7*s**2 - 1/21*s**3 + 1/70*s**5 - 5/42*s**4 - 4*s + 0. Determine w, given that q(w) = 0.
-1, 1, 5
Let u(l) be the third derivative of l**6/30 - l**5/5 + l**4/3 + 44*l**2 + l. Factor u(v).
4*v*(v - 2)*(v - 1)
Let m(d) be the first derivative of d**6/600 + d**5/100 + d**4/40 - 5*d**3/3 - 6. Let z(g) be the third derivative of m(g). Solve z(l) = 0 for l.
-1
Let h(b) be the first derivative of -1/27*b**3 + 2/9*b**2 - 1/27*b**4 + 1/90*b**5 - 9*b - 1. Let w(x) be the first derivative of h(x). Let w(i) = 0. What is i?
-1, 1, 2
Let v(u) be the first derivative of 1/3*u**6 - 6 - 4/3*u**3 + u**2 + 2*u + 2/5*u**5 - u**4. Factor v(s).
2*(s - 1)**2*(s + 1)**3
Suppose o + 6 = 3*h, -13 = -2*h - 3*o + 2. Solve -h*i + i**3 - 3*i - i**3 + 9*i**2 - 3*i**3 = 0 for i.
0, 1, 2
Let q(v) = -65*v**3 + 3105*v**2 - 77945*v + 144025. Let p(x) = 11*x**3 - 518*x**2 + 12991*x - 24004. Let s(l) = -35*p(l) - 6*q(l). Factor s(w).
5*(w - 49)**2*(w - 2)
Let x(y) be the first derivative of -5*y**4 + 2*y**5 + 5/6*y**6 + 9 - 40/3*y**3 + 0*y**2 + 0*y. Factor x(m).
5*m**2*(m - 2)*(m + 2)**2
Let l(g) be the first derivative of 1/35*g**5 + 5 - 4/21*g**3 + 0*g**2 - 1/21*g**4 - 5*g. Let x(m) be the first derivative of l(m). Factor x(h).
4*h*(h - 2)*(h + 1)/7
Suppose -2*z - 3*z + 10 = 0. Let 5*n**5 - 10*n**z - 5*n + 7*n**3 + 10*n**4 - 16*n**3 + 9*n**3 = 0. What is n?
-1, 0, 1
Let j = 36 + -29. Let z(g) = 11*g**2 + 2*g + 1. Let w be z(-1). Find h such that 0 - 5*h**2 + 2 - w*h + j*h = 0.
-1, 2/5
Let i(f) be the third derivative of -1/1512*f**8 + 0*f + 0*f**3 - 1/27*f**4 + 0 + 2*f**2 + 1/180*f**6 - 2/945*f**7 + 2/135*f**5. Determine t so that i(t) = 0.
-2, 0, 1
Let l(n) = 105*n + 366. Let m(i) = 26*i + 91. Let p(k) = 5*l(k) - 21*m(k). Let j be p(-4). Let 8/3*z - 8/3*z**2 + 0 + 2/3*z**j = 0. Calculate z.
0, 2
Let g = -91 + 87. Let v be (g - 50/(-15)) + 3. Factor -r**2 + 5/3*r**4 - 2/3 - 7/3*r + v*r**3.
(r - 1)*(r + 1)**2*(5*r + 2)/3
Let d(r) be the second derivative of 0 + 0*r**2 - 1/40*r**5 - 18*r + 0*r**3 - 1/24*r**4. Factor d(z).
-z**2*(z + 1)/2
Let d(u) be the third derivative of u**5/300 - 7*u**4/120 + u**3/3 - 63*u**2. Factor d(p).
(p - 5)*(p - 2)/5
Suppose -14*z + 17 + 11 = 0. Factor 62*q**z + 5*q**4 + 10*q**3 - 10*q + 70*q**2 - 137*q**2.
5*q*(q - 1)*(q + 1)*(q + 2)
Let l(u) = -u - 1. Let k(i) = -4*i**3 - 4*i**2 + 25*i - 7. Let n be (-8 + 4 + 3)*5. Let z(b) = n*l(b) - k(b). Factor z(q).
4*(q - 1)**2*(q + 3)
Let i = -9 - -13. Let h(f) = -f**3 + 14*f**2 - 41*f + 10. Let t be h(10). Determine d, given that -6/5*d**3 + 3/5*d**i + 3/5*d**2 + t + 0*d = 0.
0, 1
Let h(r) = r**2 + 9*r + 24. Let i be h(-8). Determine g, given that i*g + 41*g**2 + 8*g - 6 + 9*g**2 + 18*g**3 - 2 = 0.
-2, -1, 2/9
Suppose -56*z + 1 = -52*z - 5*q, -3*z - 2*q = -18. Factor 0*x - 2/5*x**3 + 1/5*x**z + 0 + 1/5*x**2.
x**2*(x - 1)**2/5
Suppose -4*r = -5*z - 23, -4*r + 4*z = -3*r - 3. Let a(o) be the first derivative of 0*o + r - 1/22*o**4 + 0*o**2 - 2/33*o**3. Factor a(f).
-2*f**2*(f + 1)/11
Let w(v) be the first derivative of 2*v**3 - 3*v**2/2 - 3*v - 17. Let f(c) = -c**2 + 1. Let x(m) = -35*f(m) - 5*w(m). Factor x(n).
5*(n - 1)*(n + 4)
Let h be -8 + 5 - (-5 - 1). Let -9*s**3 - 12*s**h - 37*s**2 + 26*s**3 + 7*s**2 = 0. Calculate s.
0, 6
Let o = -2839 - -8519/3. Find l, given that -l - o*l**2 + 2/3 + l**3 = 0.
-1, 2/3, 1
Suppose 2/3*i**3 + 122/3*i**2 - 512/3*i + 520/3 = 0. What is i?
-65, 2
Let d(n) = 12*n**2 + 7*n - 8. Let k(c) = 60*c**2 + 36*c - 40. Suppose 2*u + 9 = -u. Let j(v) = u*k(v) + 16*d(v). Factor j(x).
4*(x + 1)*(3*x - 2)
Let v(l) = l**2 + l. Let f(z) = -z**2 - 7*z. Let u = 12 - 18. Let g be -9*((-10)/u - 2). Let q(t) = g*v(t) + f(t). Factor q(h).
2*h*(h - 2)
Suppose 67 = -20*j + 103*j - 265. What is u in 2/3*u**2 + 0 + 0*u - 1/6*u**5 + 0*u**3 - 1/2*u**j = 0?
-2, 0, 1
Let j = -18 + 20. Let u = 97 + -39. Solve -k**3 - 58 + u + k**j = 0 for k.
0, 1
Let i(h) = 3*h**2 + 17*h + 8. Let x be i(-6). Suppose -4 = -5*a + 2*g, -x = -a - 3*g - g. Factor 4/3*p + 10/3*p**a + 0.
2*p*(5*p + 2)/3
Let p(n) be the first derivative of -n**5/5 + 14*n**4 - 18*n**3 - 28*n**2 + 55*n - 759. Let p(g) = 0. Calculate g.
-1, 1, 55
Let -18/19*j**3 - 32/19 - 166/19*j**2 - 180/19*j = 0. Calculate j.
-8, -1, -2/9
Suppose 3267/5 + 3/5*c**2 + 198/5*c = 0. What is c?
-33
Let h be ((-2)/(-8))/((204/16)/17). Suppose -1/2*k**2 + 1/2*k + h - 7/6*k**3 - 1/2*k**4 = 0. Calculate k.
-1, 2/3
Let u(t) = t**3 + 5*t**2 - 9*t - 7. Let n be u(-6). Suppose -13 = -3*z + n. Solve -2*x**2 + 6*x**3 + 3*x**3 + z*x**2 + x**3 - 24*x + 8 = 0.
-2, 2/5, 1
Let w = -10198 + 10202. Factor 0 + 12/5*l**w - 2/5*l**5 + 24/5*l**2 - 26/5*l**3 - 8/5*l.
-2*l*(l - 2)**2*(l - 1)**2/5
Factor -10/21*d + 4/7 - 2/21*d**2.
-2*(d - 1)*(d + 6)/21
Let k be 1*-3 - (-54)/16. Let n(i) be the first derivative of 5 - k*i**2 - 1/4*i**3 - 1/16*i**4 - 1/4*i. Factor n(j).
-(j + 1)**3/4
Suppose -12*o + 96 + 24 = 0. Let f be (258/(-60) - -5) + (-2)/o. Solve -l - f*l**3 - 3/2*l**2 + 0 = 0 for l.
-2, -1, 0
Let 10*d**3 + 51*d + 152 + 3*d - 343*d - 374*d**2 + 47*d + 10*d = 0. Calculate d.
-1, 2/5, 38
Let i be 10 + -7 + (-1 - 0). Suppose 0*l - 4*l - i*a + 4 = 0, 2*l = -2*a. Factor h**4 + 1 + 3*h**4 + 6*h**l - 4*h - 4*h**3 - 3*h**4.
(h - 1)**4
Suppose 3*c = 5*x + 2 - 18, 0 = 2*c + x - 11. Let m(z) be the second derivative of -1/42*z**4 + 1/7*z**2 - 1/21*z**3 + 1/70*z**5 + c*z + 0. Factor m(n).
2*(n - 1)**2*(n + 1)/7
Let o(a) = 7*a**4 - 10*a**3 + a**2 + 26*a. Let f(x) = -3*x**4 + 3*x**3 - 9*x. Let k(l) = -8*f(l) - 3*o(l). Factor k(g).
3*g*(g - 1)*(g + 1)*(g + 2)
Let t(d) be the third derivative of 0*d + 0*d**4 + 7*d**2 + 1/2*d**3 + 0 - 1/240*d**6 + 1/80*d**5. Let f(w) be the first derivative of t(w). Factor f(j).
-3*j*(j - 1)/2
Let i be 39/91 + ((-6)/(-7))/(-2). Let s(y) be the third derivative of 0*y + 0*y**3 + i - 1/18*y**4 - 1/90*y**5 - y**2. Factor s(h).
-2*h*(h + 2)/3
Let 9 + 12*p**2 + 6*p - 2*p**3 - 22*p - 1 + 0*p**2 - 2*p**2 = 0. What is p?
1, 2
Let o(l) be the first derivative of l**3/3 - 7*l**2 + 49*l - 173. Factor o(z).
(z - 7)**2
Let o(d) be the third derivative of d**6/1260 - 5*d**3/6 + 3*d**2. Let t(i) be the first derivative of o(i). Suppose t(j) = 0. What is j?
0
Let a(x) = -43*x - 169. Let z be a(-4). Factor -8/5 + 4/5*l**z - 16/5*l**2 + 4*l.
4*(l - 2)*(l - 1)**2/5
Determine w, given that -3*w**4 - 504*w - 17*w**3 - 219*w**2 - 19*w**3 - 14*w**3 - 432 + 8*w**3 = 0.
-4, -3
Let m(d) be the second derivative of d**4/42 - 116*d**3/21 + 3364*d**2/7 + 115*d + 1. Factor m(w).
2*(w - 58)**2/7
Let i be ((-3)/3)/((-84)/24) - (-156)/483. Find a, given that -10/23 - i*a**2 - 22/23*a - 2/23*a**3 = 0.
-5, -1
Let n = 6156/5 + -1231. Find a, given that -n*a**2 + 0*a + 1/5 = 0.
-1, 1
Let f(s) be the second derivative of -s**4/4 + 5*s**3/2 - 6*s**2 - 3*s + 5. Factor f(x).
-3*(x - 4)*(x - 1)
Let y(d) be the first derivative of d**6/120 - 2*d**3/3 + 5. Let o(p) be the third derivative of y(p). Factor o(j).
3*j**2
Let c(r) be the third derivative of r**7/525 - r**5/50 - r**4/30 - 84*r**2. Determine d, given that c(d) = 0.
-1, 0, 2
Let n(j) be the first derivative of 7*j**3/3 - 8*j**2 + 4*j - 156. De