8*n + 4*n**2 + 15*n**2 + 10*n = 0 for n.
-7
Suppose 14 = 3*d + 2*g, -d + 3*g - 4*g + 5 = 0. Let m(t) be the first derivative of -1/5*t**5 - 2*t**3 + 2*t**2 - 5/4*t**d + 2 + 8*t. Factor m(o).
-(o - 1)*(o + 2)**3
Suppose 3*q = -a - 38, 3*a + 13 = -2*q - 3. Let t be (-52)/q - 12/(-42). Factor -30*x**3 - 3*x**5 + 36*x**2 - 9*x**3 + x**4 - 12*x + 17*x**t.
-3*x*(x - 2)**2*(x - 1)**2
Solve -434/13*t**2 - 100/13 - 38/13*t**3 + 54/13*t**4 + 8/13*t**5 + 510/13*t = 0 for t.
-5, 1/4, 1, 2
Let n(i) be the first derivative of -15 + 3/5*i**2 - 2/15*i**3 - 4/5*i. Let n(c) = 0. Calculate c.
1, 2
Let h(g) = 11*g**3 - 2*g**2 + 1. Let l be h(1). Suppose u - 6*u + l = 0. Factor -4*n - 136 + 134 + 5*n**u + n.
(n - 1)*(5*n + 2)
Suppose -3*p + 2*g = 6, 5*p + 8 = 2*g + 2. Let t = -2563 + 17943/7. Factor t*v + p + 0*v**2 - 2/7*v**3.
-2*v*(v - 1)*(v + 1)/7
Let z(h) = -h**2 + 5*h + 17. Let q be z(7). Let v(u) be the second derivative of 3/28*u**4 + 0 - 3/140*u**5 + 0*u**2 - 1/7*u**q + 2*u. Factor v(r).
-3*r*(r - 2)*(r - 1)/7
Let z(c) be the second derivative of c**4/36 - 2*c**3/3 + 16*c**2/3 + 2*c + 281. Determine d so that z(d) = 0.
4, 8
Determine o so that 20/9*o**4 + 190/9*o - 2/9*o**5 - 64/9*o**2 - 44/9*o**3 - 100/9 = 0.
-2, 1, 5
Solve -36*n + 540 + 3/5*n**2 = 0.
30
Solve -53/6*o**3 + 161/6*o - 49/6 + 2/3*o**4 + 51/2*o**2 = 0.
-1, 1/4, 7
Let v = 13758 - 41974/3. Let m = 236 + v. Find w such that 0*w - 2*w**2 + 2/3*w**3 + m = 0.
-1, 2
Let v = 1/1304 + -11105/27384. Let m = -1/14 - v. Suppose 0*g + 1/3*g**2 - m = 0. Calculate g.
-1, 1
Suppose 5*h - 25 = -2*f, -5*h - 3*f + 1 = -29. Determine c so that 0 - 15*c**h - 144*c + 3*c**4 + 132*c + 24*c**2 + 0 = 0.
0, 1, 2
Let l(r) = r**3 - 3*r**2 + r + 1. Let k(x) = 7*x**3 + 99*x**2 + 5*x + 5. Let z(q) = k(q) - 5*l(q). Factor z(i).
2*i**2*(i + 57)
Let t = -82 - -414/5. Let l(h) be the first derivative of 3 - 3/5*h**2 - t*h - 2/15*h**3. Solve l(n) = 0 for n.
-2, -1
Let q = 40664/27 + -1506. Let z(c) be the second derivative of -2/27*c**4 - q*c**3 - 7*c + 1/45*c**5 + 1/3*c**2 + 0 + 1/135*c**6. Factor z(s).
2*(s - 1)**2*(s + 1)*(s + 3)/9
Suppose -2*y + 12 = -2*o, o = 5*y - 10 - 8. Factor -3/5*p**y - 3/5*p**2 + 6/5*p + 0.
-3*p*(p - 1)*(p + 2)/5
Let x = 24 + -54. Let f be (18/x)/((-1)/5). Solve 2*v**2 + f*v**3 - 2*v**3 - 4*v**2 = 0 for v.
0, 2
Let j = 27 - 24. Factor -a**2 + 8 + 2*a**j - 5*a**3 + 4 - 8*a**2.
-3*(a - 1)*(a + 2)**2
Factor 0*m + 0 - 1/4*m**3 + 1/4*m**4 + 0*m**2.
m**3*(m - 1)/4
Let p be 1274/35 + (-3)/(-5). Factor 5*g - 34*g**2 - 6 + p*g**2 - 2*g.
3*(g - 1)*(g + 2)
Let o(a) be the third derivative of a**7/560 - a**5/160 - 155*a**2. Factor o(b).
3*b**2*(b - 1)*(b + 1)/8
Determine y, given that 52/3*y**2 - 16 + 32/3*y + 4*y**3 = 0.
-3, -2, 2/3
Suppose -8 = -4*t - a - a, 3*a - 8 = -4*t. Suppose -5*x = 4*j + 15, -9 = -6*j + 3*j + 3*x. Determine u, given that j + 1/3*u**t + 1/3*u = 0.
-1, 0
Let m be (774/1505)/((-9)/(-42)). Let -m*a**2 - 4/5*a**4 + 0 - 12/5*a**3 - 4/5*a = 0. What is a?
-1, 0
Let z(n) be the second derivative of -2*n**6/15 - 7*n**5/15 + 13*n**4/9 + 46*n**3/9 + 4*n**2 + n - 8. Determine w, given that z(w) = 0.
-3, -1, -1/3, 2
Let x(t) be the second derivative of 3*t - 1/20*t**4 - 2/15*t**3 - 1/150*t**6 + 0 + 2/5*t**2 + 1/25*t**5. Determine q so that x(q) = 0.
-1, 1, 2
Let c(k) be the second derivative of k**6/30 - 4*k**5/15 + 2*k**4/3 - 6*k**2 + 2*k. Let w(b) be the first derivative of c(b). Determine q so that w(q) = 0.
0, 2
Suppose 1 + 9 = 2*r. Solve 5*n**5 - 4*n**r - 2*n + 7*n**2 - 3*n**4 + 3*n**2 + n**3 - 7*n**2 = 0.
-1, 0, 1, 2
Suppose -7*h + 16*h = 18. Suppose h*q**3 + 360*q + 4*q**2 - 360*q = 0. What is q?
-2, 0
Let w be -11 - 7/(-210) - -11. Let f(h) be the third derivative of 0 + 0*h**4 - 1/35*h**7 + h**2 - 1/168*h**8 + 0*h**3 - w*h**5 + 0*h - 1/20*h**6. Factor f(d).
-2*d**2*(d + 1)**3
Let u(q) be the first derivative of 3/2*q**2 + 45 + 8/3*q**3 + 3/2*q**4 - 1/6*q**6 + 0*q + 0*q**5. Factor u(j).
-j*(j - 3)*(j + 1)**3
Let v(s) = -s**3 - 51*s**2 - 45*s - 2292. Let d be v(-51). Let 16/3*q + 4/3*q**4 - 16/3 - 16/3*q**d + 4*q**2 = 0. What is q?
-1, 1, 2
Suppose -8 = -y + 2*n, n + 11 = 5*y - 4*y. What is d in -28*d - 8*d**2 + y*d**2 - 10*d**2 - 24 = 0?
-6, -1
Let c(m) be the third derivative of 1/40*m**4 - 1/200*m**6 + 1/5*m**3 + 0 - 1/50*m**5 + 0*m + 17*m**2. Factor c(z).
-3*(z - 1)*(z + 1)*(z + 2)/5
Let s(m) be the second derivative of -m**5/150 - m**4/6 + 2*m - 10. Suppose s(w) = 0. Calculate w.
-15, 0
Factor 0*k**2 + 0*k**4 + 0*k + 0 - 2/3*k**5 + 2/3*k**3.
-2*k**3*(k - 1)*(k + 1)/3
Let w = 13 + -8. Suppose 3*i = w*b - b + 2, -5*i + 8 = -2*b. Factor -u**4 - 100*u**i - 8*u**2 - u**4 + 24*u**3 + 216*u - 162.
-2*(u - 3)**4
Let q be 2 + (2 + -2)/(-2). Suppose 2*f + 195 = 237. Factor -21*s + 3*s**q + f*s + s**3.
s**2*(s + 3)
Let i(z) be the first derivative of -4*z**3/3 + 212*z**2 - 11236*z - 162. Factor i(b).
-4*(b - 53)**2
Suppose -318/5*t + 39/5*t**2 + 48/5 = 0. What is t?
2/13, 8
Let r(y) be the third derivative of 7*y**6/30 + 32*y**5/5 - 14*y**4/3 - 13*y**2 + 3. Factor r(x).
4*x*(x + 14)*(7*x - 2)
Let n(i) = -11*i + 60. Let a be n(5). Let q be a/(-4)*(-10)/25. Factor 1/4*v**2 + q*v + 1/4.
(v + 1)**2/4
Let k(z) = -2*z**4 + 4*z**3 + 2*z**2 - 2*z. Let m(w) = 10*w**4 - 19*w**3 - 9*w**2 + 9*w. Let f(i) = 9*k(i) + 2*m(i). Find t, given that f(t) = 0.
0, 1
Let d(z) = -2*z**3 + 2*z**2 - 2*z + 3. Let u be d(2). Let m(q) = -q**3 - 8*q**2 + 9*q + 6. Let i be m(u). Factor 0*r**2 - 2 + i + 4*r**2 - 8*r.
4*(r - 1)**2
Let a(k) = 3*k**5 + k**4 + 3*k**3 - 5*k**2 + 4. Let j(m) = -2*m**5 + m**4 - m**3 - m**2. Let x(d) = 5*a(d) + 10*j(d). Solve x(z) = 0.
-1, 1, 2
Let f(x) = 3*x**2 - x + 2. Let n(v) = -4*v**2 + 3*v - 2. Let s(b) = 3*f(b) + 2*n(b). Suppose s(a) = 0. Calculate a.
-2, -1
Suppose -2*w + 11*w - 18 = 0. Find b, given that 6 + 0 - 6 - b + b**w = 0.
0, 1
Find g such that 170/7*g - 1/7*g**2 - 7225/7 = 0.
85
Let m(y) be the second derivative of y**4/12 + 17*y**3/6 - 30*y**2 + 2*y - 37. Determine n so that m(n) = 0.
-20, 3
Let 1849/7 - 1/7*k**3 - 1935/7*k + 87/7*k**2 = 0. What is k?
1, 43
Let h(c) be the third derivative of -3/8*c**3 + 0*c - 1/80*c**5 + 1/8*c**4 - 10*c**2 + 0. Let h(q) = 0. What is q?
1, 3
Let z(j) be the second derivative of -j**5/20 + j**4/6 - j**3/6 + 3*j**2/2 - 4*j. Let n be z(0). Factor 4*t + 2*t**n + 0*t**3 - 4*t**2 - 2*t**2.
2*t*(t - 2)*(t - 1)
Suppose -27*k + 49*k = 30*k - 16. Factor -2/17*i**3 - 6/17 - 10/17*i**k - 14/17*i.
-2*(i + 1)**2*(i + 3)/17
Suppose -3*t - 4 = -7*t. Let m = 50/37 - -233/74. Solve t + m*z + 7/2*z**2 = 0 for z.
-1, -2/7
Let b be ((-1)/(-7))/(132/77). Let j(x) be the first derivative of 3 + 4/3*x + 4/3*x**2 + 5/9*x**3 + b*x**4. Suppose j(l) = 0. What is l?
-2, -1
Let j = -3/518 - -1081/7770. Let n be (-14)/84*16/(-10). Factor j*d**3 + n*d**2 - 4/15 - 2/15*d.
2*(d - 1)*(d + 1)*(d + 2)/15
Let h(v) be the second derivative of 2*v**6/15 + 26*v**5/5 + 72*v**4 + 324*v**3 - 1458*v**2 - 36*v. Factor h(c).
4*(c - 1)*(c + 9)**3
Let q(r) = -3*r**5 - 21*r**3 + 24*r**2 - 6*r - 3. Let h(p) = -5*p**5 - 22*p**3 + 24*p**2 - 5*p - 4. Let g(l) = -3*h(l) + 4*q(l). Factor g(k).
3*k*(k - 1)**3*(k + 3)
Let d(t) be the first derivative of -1/4*t**4 - 16 - 3*t**3 + 0*t + 0*t**2. Determine i so that d(i) = 0.
-9, 0
Find o such that -72*o - 27/2*o**2 - 3/4*o**3 - 120 = 0.
-10, -4
Let y(w) be the third derivative of w**8/12320 - w**7/13860 - 13*w**5/60 - 4*w**2. Let s(d) be the third derivative of y(d). Factor s(l).
2*l*(9*l - 2)/11
Let a(r) be the second derivative of r**9/756 + r**8/210 + r**7/210 - 5*r**3 + r**2 + 6*r. Let s(y) be the second derivative of a(y). Let s(o) = 0. Calculate o.
-1, 0
Let j(g) be the first derivative of g**6/3240 + g**5/1080 - g**4/108 + 5*g**3/3 - 2. Let f(k) be the third derivative of j(k). Find n, given that f(n) = 0.
-2, 1
Let y(j) be the second derivative of -j**6/180 + 3*j**5/10 - 27*j**4/4 + 81*j**3 - 2187*j**2/4 - 28*j - 2. Factor y(w).
-(w - 9)**4/6
Let c be (-2)/11 + 11/((-968)/(-82)). Let o = 21/44 - -3/11. Factor -3/4*s**3 - c + o*s**2 + 3/4*s.
-3*(s - 1)**2*(s + 1)/4
Let d be 20 + -18 - 130/(-7). Let z = 1598/77 - d. Factor 0*n**2 - z*n**3 + 0*n + 0.
-2*n**3/11
Suppose -s - 6 = -3*s. Factor -b**2 + 10*b**s - 4*b**3 - 7*b**3.
-b**2*(b + 1)
Let c(q) = q**3