5
Let o(g) be the first derivative of 4*g**5/15 + 2*g**4/3 - 62. Factor o(q).
4*q**3*(q + 2)/3
Let t = 6797 + -6795. What is m in 0 + 0*m**2 - 1/2*m**5 - t*m + 0*m**4 + 5/2*m**3 = 0?
-2, -1, 0, 1, 2
Let j(r) = r. Let t(g) be the third derivative of g**5/30 - g**4/6 + 2*g**2. Let m(k) = -2*j(k) - t(k). Factor m(d).
-2*d*(d - 1)
Let t = -130 + 130. Let c(a) be the second derivative of t + 1/35*a**5 + 1/105*a**6 - 2/21*a**3 + a + 0*a**2 - 1/42*a**4. Solve c(p) = 0.
-2, -1, 0, 1
Let w = 197 - 193. Suppose w*c + 0*y - 24 = -3*y, -4*c = -3*y. Solve 0*p + 3/2*p**c + 0 + 3/2*p**2 = 0.
-1, 0
Let z be (-45 + -27)/((-42)/4). Let -108/7*u**2 + z + 6/7*u**3 + 18/7*u**5 - 24/7*u + 60/7*u**4 = 0. Calculate u.
-2, -1, 2/3, 1
Let s(y) be the third derivative of 27*y**8/56 + 93*y**7/35 + 137*y**6/30 + 14*y**5/5 + 2*y**4/3 + 15*y**2. Determine t, given that s(t) = 0.
-2, -1, -2/9, 0
Let c(f) be the first derivative of -f**6/75 + 16*f + 15. Let a(m) be the first derivative of c(m). Factor a(l).
-2*l**4/5
Let l(t) be the second derivative of 0*t**2 + 4/15*t**3 + 4/15*t**4 + 1/10*t**5 + 1/75*t**6 - 6*t + 0. Find c such that l(c) = 0.
-2, -1, 0
Let n(l) be the third derivative of l**7/2520 + l**6/120 + 3*l**5/40 + 3*l**4/8 - 20*l**2. Let h(p) be the second derivative of n(p). Factor h(b).
(b + 3)**2
Let x be 0/(3*(-4)/6). Suppose 2*a - 5*s = -3*a, -2*s + 8 = x. Let 8*f**3 - f**4 + 2 - f**4 + 0*f**3 - a*f**3 - 4*f = 0. Calculate f.
-1, 1
Let t(m) be the second derivative of -m**7/336 + m**6/240 + 33*m**5/160 - 27*m**4/32 - 9*m**3/4 + 81*m**2/4 - 34*m - 7. Factor t(n).
-(n - 3)**3*(n + 2)*(n + 6)/8
Factor 2*j**4 + 60*j - j**5 + 3*j**3 + 5*j**3 - 37*j - 18*j**2 - 14*j.
-j*(j - 3)*(j - 1)**2*(j + 3)
Suppose -27/4*c**2 + 5/4*c**3 - 9/2*c + 0 = 0. What is c?
-3/5, 0, 6
Factor -2/9*f**2 + 28 + 10/9*f.
-2*(f - 14)*(f + 9)/9
Determine c so that 232 + 547 - 3040*c + 1284*c**2 + 152*c**3 + 4*c**4 + 821 = 0.
-20, 1
Suppose -3*s + j + 8 = 0, -5*s + 3 = j - 13. Let -k - 51 - 3*k**2 - k**3 + 2*k**s + 53 + k**4 = 0. Calculate k.
-2, -1, 1
Solve -4358*x**3 - 4*x**4 + 4326*x**3 + 4*x**5 - 19*x**2 + 67*x**2 = 0.
-3, 0, 2
Let p = 45 - 36. Factor 10*k - 2*k - p*k**2 + k + 6*k**2 - 6.
-3*(k - 2)*(k - 1)
Let b be (-60 - -66 - (-100)/(-18)) + 4. Let 50/9*u**3 + 5/3*u - 2/9 - 10/3*u**4 + 7/9*u**5 - b*u**2 = 0. Calculate u.
2/7, 1
Let d(g) be the first derivative of g**3/3 + 2*g**2 - 5*g - 4. Factor d(n).
(n - 1)*(n + 5)
Suppose -3*y + 18 = -n + 6*n, -y - 3*n = -10. Let h(k) = k**2 - k - 1. Let b(i) = -6*i**2 + 4*i + 4. Let o(z) = y*b(z) + 4*h(z). Factor o(j).
-2*j**2
Let f(d) = 28*d - 10. Let p be f(4). Let m = p - 508/5. Factor -m*b**3 + 0 - 2/5*b + 4/5*b**2.
-2*b*(b - 1)**2/5
Let q be (265 - 259)/(2 - 0). Suppose -100/3 - 4/3*u**q - 140/3*u - 44/3*u**2 = 0. What is u?
-5, -1
Let x = -279 - -283. Let a(l) be the third derivative of -2/21*l**3 + 5*l**2 + 1/84*l**x + 1/210*l**5 + 0*l + 0. Determine p, given that a(p) = 0.
-2, 1
Let l(r) be the first derivative of r**5/35 + r**4/4 + 10*r**3/21 - 70. What is k in l(k) = 0?
-5, -2, 0
Let q(i) be the third derivative of -36*i**2 + 0*i**3 + 1/90*i**5 + 1/180*i**6 + 0 + 0*i**4 + 0*i. Factor q(l).
2*l**2*(l + 1)/3
Suppose 4*z - 18 = -5*c + 13, 4*c - 3*z = 0. Solve -c - 3*t + 3*t**2 + 3 + 2 - 8 = 0.
-1, 2
Let n(o) be the second derivative of 20*o + 0 + 3/4*o**2 - 1/40*o**5 + 1/12*o**3 - 1/8*o**4. Suppose n(c) = 0. Calculate c.
-3, -1, 1
Let g be -2*1/3*555/(-74). Suppose -3*b - 5*r + g = -5*b, b = 5*r - 5. Factor 2/9*k + 0*k**2 - 2/9*k**3 + b.
-2*k*(k - 1)*(k + 1)/9
Let g(p) = p**3 + 3*p**2 + 2*p + 2. Let r be g(-4). Let z = 22 + r. Determine n so that 2/5*n**4 - 2/5*n**5 + 4/5*n**3 + 0*n**2 + 0*n + z = 0.
-1, 0, 2
Factor 29/8*q**2 - 3/4*q - 9/8*q**3 + 0.
-q*(q - 3)*(9*q - 2)/8
Factor -42*x + 2*x**2 + x**2 + 225 - 2*x**2 + 12*x.
(x - 15)**2
Suppose 2*r = -2, 0 = 6*j - j + 3*r + 248. Let p = 51 + j. Factor -1/2*n**p + 4*n - 8.
-(n - 4)**2/2
Let d(b) be the third derivative of -b**7/210 + 29*b**6/10 - 7569*b**5/10 + 219501*b**4/2 - 19096587*b**3/2 + 316*b**2 - 2*b. Find y such that d(y) = 0.
87
Suppose -104*w + 16 = 16. Let z(v) be the third derivative of -3*v**2 + 0 + 3/20*v**5 + 1/4*v**4 + 1/40*v**6 + 0*v**3 + w*v. Factor z(a).
3*a*(a + 1)*(a + 2)
Let h be ((-1)/(1/4))/(24/(-36)). Determine v, given that 127*v - 112*v - h*v**2 + v**2 = 0.
0, 3
Let f = 100 + -407. Let x = f + 949/3. Determine a, given that -7*a**5 + 14/3*a**3 - 43/3*a**4 + x*a**2 + 0 - 8/3*a = 0.
-2, -1, 0, 2/7, 2/3
Let z(c) be the third derivative of -c**7/70 + 49*c**6/40 + c**5/20 - 49*c**4/8 - 2*c**2 + 8*c. Suppose z(u) = 0. Calculate u.
-1, 0, 1, 49
Factor 0 + 0*m**2 + 1/3*m**4 - 5/3*m**3 + 0*m.
m**3*(m - 5)/3
Let a be 33/(-4) + (-8)/(-32). Let u be (3 - (-170)/(-56)) + a/(-28). Solve 1/4*f**4 - u*f**2 + 1/2*f + 1/4*f**5 - 3/4*f**3 + 0 = 0.
-2, -1, 0, 1
Factor 7*d + 24*d**2 + 62*d - d**2 + 15*d - 3*d**2 + d**3.
d*(d + 6)*(d + 14)
Let m(p) be the third derivative of -5/3*p**4 + 0*p + 0 - 3*p**2 + 1/12*p**5 + 40/3*p**3. Let m(l) = 0. Calculate l.
4
Let f(b) be the third derivative of 1/40*b**5 + 0*b**4 + 0*b + 9/140*b**7 + 0 + 0*b**3 - 1/56*b**8 - 3/40*b**6 + 13*b**2. Factor f(d).
-3*d**2*(d - 1)**2*(4*d - 1)/2
Find c such that -131 + 5*c**2 + 161 - c**2 + c**2 + 35*c = 0.
-6, -1
Let s(q) be the first derivative of 2*q**3/3 + 84*q**2 + 3528*q + 109. Factor s(u).
2*(u + 42)**2
Let v be 2/(-9) - (-5230)/45. Suppose -4*q + 0*q + t = -97, -5*q = 4*t - v. Suppose 4*i - 32*i**4 + 27*i**2 - 12*i**5 - q*i**3 - 27*i**2 = 0. What is i?
-1, 0, 1/3
Let r(q) be the second derivative of -q**7/7560 - q**6/360 - q**5/72 - 11*q**4/12 - q. Let t(n) be the third derivative of r(n). Factor t(i).
-(i + 1)*(i + 5)/3
Let f(h) be the third derivative of -1/252*h**8 - 11*h**2 + 0 + 0*h + 2/105*h**7 + 0*h**3 + 0*h**5 + 0*h**4 - 1/45*h**6. Let f(n) = 0. Calculate n.
0, 1, 2
Suppose -6*l = -9 - 15. Let m be 6/l*4/10. Solve 9/5 + 6/5*o - m*o**2 = 0 for o.
-1, 3
Let n(f) be the third derivative of f**6/84 - f**5/15 - 8*f**4/21 + 32*f**3/21 + f**2 + 63*f. What is s in n(s) = 0?
-2, 4/5, 4
Let j(v) = 3*v**2 + v - 2. Let h be j(2). Suppose -h*w - 13*w**4 + 0 + 2*w**2 - 22*w**3 + 45*w**4 + 70*w**3 + 2 = 0. Calculate w.
-1, 1/4
Let i(x) = -3*x**3 + 12*x**2 - x - 6. Let u be 1 - 2 - (-2 + 6). Let v(l) = l**3 + l**2 - 1. Let h(t) = u*i(t) + 30*v(t). Factor h(r).
5*r*(3*r - 1)**2
Factor -16/7*y + 2/7*y**2 + 2.
2*(y - 7)*(y - 1)/7
Let f be ((0/(-2))/(-4))/(-2). Let k be 12/(-5)*(5/(-20) - f). Determine p, given that 0 + p**2 - k*p**3 - 2/5*p = 0.
0, 2/3, 1
What is a in -2/3*a - 2/3*a**2 + 8 = 0?
-4, 3
Let g(d) = 4*d**4 - 52*d**3 + 37*d**2 + 45*d - 13. Let a(n) = 5*n**4 - 51*n**3 + 37*n**2 + 51*n - 14. Let m(x) = 5*a(x) - 4*g(x). Solve m(h) = 0 for h.
-1, 2/9, 3
Let o(t) be the first derivative of -t**5/20 - t**4/16 + t**3/3 + t**2/2 - 76. Factor o(l).
-l*(l - 2)*(l + 1)*(l + 2)/4
Factor 125*x**2 - 530*x**2 + 20*x**3 + 507*x - 23 - 320*x**2 - 152 + 373*x.
5*(x - 35)*(x - 1)*(4*x - 1)
Let z(v) = -3*v**2 - 101*v - 965. Let c(w) = -3*w**2 - 102*w - 966. Let k(b) = -7*c(b) + 6*z(b). Determine q so that k(q) = 0.
-18
Let k(g) be the second derivative of 5*g**7/63 - 2*g**6/45 - 14*g**5/15 - 5*g**4/3 - g**3 + 386*g. What is f in k(f) = 0?
-1, -3/5, 0, 3
Let k = -3749 - -3752. Find c, given that 0 + 2/3*c**4 + 2/3*c + 2*c**2 + 2*c**k = 0.
-1, 0
Suppose -4*m + 18 = -5*t, -5*m = -4*t - 11 - 7. Suppose -m*n - 1 + 5 = 0. Let -1 + n + 2*p + 2*p**2 + 3*p**2 - 4*p**2 = 0. Calculate p.
-1
Suppose 268 = -11*x + 78*x. Let k(f) be the first derivative of -1/2*f**x + 9 + 0*f - f**2 + 4/3*f**3. Solve k(d) = 0.
0, 1
Let m = -8 + 13. Factor f + m*f + 17*f**2 + 4 - 15*f**2.
2*(f + 1)*(f + 2)
Let b(s) = -55*s**2 + 33*s. Let n(y) = -110*y**2 + 67*y. Let t(u) = 7*b(u) - 3*n(u). Determine j so that t(j) = 0.
0, 6/11
Let u = 159 + -155. Let i(s) be the third derivative of 0*s + 0 + 1/240*s**5 + 1/48*s**u + 1/24*s**3 + 4*s**2. Let i(t) = 0. Calculate t.
-1
Let r(l) = 35*l**4 - 47*l**3 - 89*l**2 - 24*l - 5. Let o(a) = 2*a**4 + a**3 + a**2 + 1. Let c(j) = -5*o(j) - r(j). Determine i so that c(i) = 0.
-2/3, -2/5, 0, 2
Let k = 65 + -61. Suppose 3*m + 1 = 4*x + x, -7 = -5*m + k*x. What is f in -f**2 - 3/2*f**m + f**4 + 0 + 3/2*f**5 + 0*f = 0?
-1, -2/