*(g + 1)
Let a = 12855 + -12850. Factor -2/5*w**3 + 2/5*w**a + 0*w + 0 + 0*w**2 + 0*w**4.
2*w**3*(w - 1)*(w + 1)/5
Suppose -1 - 33 = -l. Let d(m) = -m**2 + 3*m + 3. Let z(j) = -6*j**2 + 18*j + 17. Let f(v) = l*d(v) - 6*z(v). Factor f(g).
2*g*(g - 3)
Let l be 46/(-4)*(-5 - -3). Suppose 5*g - g = 3*z + l, 3*z = g - 17. Factor -27*n**g + 4 - 4 - 6 + 21*n + 15*n**3 - 3*n**4.
-3*(n - 2)*(n - 1)**3
Let g(c) be the first derivative of -4*c**3/21 + 30*c**2/7 - 98. Solve g(u) = 0.
0, 15
Let w(l) be the third derivative of -l**8/112 + 3*l**7/70 + 3*l**6/8 + 17*l**5/20 + 3*l**4/4 + 96*l**2. Find c, given that w(c) = 0.
-1, 0, 6
Let u be 6/14*60/270. Let 0 - u*c**2 + 0*c = 0. Calculate c.
0
Factor -10/21*c**2 + 4/7*c - 2/21*c**3 + 0.
-2*c*(c - 1)*(c + 6)/21
Let h = -63 - -63. Let v(r) be the first derivative of -2/33*r**3 - 1 + h*r**2 + 8/11*r. Factor v(f).
-2*(f - 2)*(f + 2)/11
Let j = 508087/17 + -29887. Find u, given that 2/17*u + 0 - j*u**2 + 6/17*u**3 = 0.
0, 1/3, 1
Let s(n) be the third derivative of 0 + 4/15*n**5 + 2/105*n**7 + 0*n - 2/15*n**6 + 0*n**4 + 0*n**3 - n**2. Suppose s(d) = 0. What is d?
0, 2
Let n = -6514 + 149824/23. Solve -n*w**5 - 30/23*w**4 - 486/23 - 540/23*w**2 - 180/23*w**3 - 810/23*w = 0.
-3
Let v = 141 + -137. Suppose 3*x = 0, s - x = v - 1. What is u in 0 + 4/3*u**2 - 2/3*u**s + 0*u = 0?
0, 2
Solve -38/11*n + 40/11*n**2 - 2/11*n**3 + 0 = 0 for n.
0, 1, 19
Let m(n) be the second derivative of n**4/30 - 317*n. Let m(f) = 0. Calculate f.
0
Let s be (-1 + 2/8)/((-2745)/2928). Factor s + 8/5*v + 4/5*v**2.
4*(v + 1)**2/5
Let z(q) be the first derivative of q**4/12 - 40*q**3/3 + 1159*q**2/2 + 7442*q/3 + 83. Let z(s) = 0. Calculate s.
-2, 61
Let j(q) be the third derivative of q**5/15 - 7*q**4/6 + 49*q**3/6 + 4*q**2. Factor j(a).
(2*a - 7)**2
Let m(q) = -10*q + 50. Let j be m(5). Let a(t) be the second derivative of 0 + 0*t**2 + 1/80*t**5 + 3*t + j*t**3 + 0*t**4. Factor a(r).
r**3/4
Find c, given that 23*c**3 - 100*c**2 - 1741*c - 47*c**3 + 491*c + 22*c**3 = 0.
-25, 0
Let -24/7 - 2/7*m**2 + 16/7*m = 0. What is m?
2, 6
Factor 8*x**2 + 0 - 1/2*x**5 + 4*x**4 - 5/2*x - 9*x**3.
-x*(x - 5)*(x - 1)**3/2
Let f(n) be the second derivative of 1/6*n**3 - 1/24*n**4 + 0 + 1/30*n**5 + 1/72*n**6 + 4*n + 0*n**2. Let j(o) be the second derivative of f(o). Factor j(t).
(t + 1)*(5*t - 1)
Let a(c) be the first derivative of -c**3/3 - 3*c**2/2 + 7*c - 12. Let t be a(-4). Let 0*q + 1/5*q**2 + 0 - 1/5*q**4 + 0*q**t = 0. Calculate q.
-1, 0, 1
Factor 7/2*q + 6 + 1/2*q**2.
(q + 3)*(q + 4)/2
Factor 34/3*n - 1/3*n**4 - 34/3*n**3 - 32/3*n**2 + 11.
-(n - 1)*(n + 1)**2*(n + 33)/3
Suppose -q + 5 = 2*x, -2 = x + 2*q + 3*q. Let j be (-27)/6*8/(-12). Factor -9*t**4 - 12*t**j - 3*t**2 + 3*t**3 - x*t**5 - 4*t + 4*t.
-3*t**2*(t + 1)**3
Let m(j) = 2*j**3 - j**2 - j + 1. Let p(b) be the first derivative of -b**4/4 + 2*b**3/3 - b**2/2 - b + 42. Let h(r) = 4*m(r) + 4*p(r). Factor h(a).
4*a*(a - 1)*(a + 2)
Suppose -2*r - 3*r + 36 = 4*c, -3*c = -r - 8. Suppose -3 = -c*b + 5. Find u such that u - 2 + 7 + 2*u**3 - 3*u**3 - 2*u**b - 3 = 0.
-2, -1, 1
Suppose h - 53 = -9. Suppose 0 = 11*z - h - 11. Solve -1/3*b**2 - b**4 + 1/3*b**z + 0*b + 0 + b**3 = 0.
0, 1
Let n(l) be the third derivative of -l**7/140 - l**6/80 + l**5/10 + l**4/4 + 109*l**2. Factor n(s).
-3*s*(s - 2)*(s + 1)*(s + 2)/2
Let i(n) = 6*n**2 + n - 1. Let d(c) = c - 1. Let r(v) = -3*d(v) - i(v). Let p(a) = -a**2 - a + 1. Let f(q) = 4*p(q) - r(q). Factor f(u).
2*u**2
Determine y so that 21 - 31*y**3 - 24*y**2 - 81 - 32*y**3 - 31*y**3 + 82*y + 96*y**3 = 0.
1, 5, 6
Suppose 42*c - 37*c - 10 = 0. Find n such that -40 + 14*n - 52*n + 25*n**3 + 5*n**4 + 30*n**c + 18*n = 0.
-2, 1
Let b(x) = 2*x**2 + 61*x - 24. Let f be b(-31). Let g(v) = v**2 - v - 39. Let k be g(f). Factor 1/3*c**2 + 0*c - 1/3*c**k + 0.
-c**2*(c - 1)/3
What is j in -26*j - 77*j**2 + 79*j**2 - 105*j - 33*j + 3362 = 0?
41
Let s(a) be the second derivative of -2*a**7/735 + a**5/105 + 4*a**2 + 33*a. Let z(r) be the first derivative of s(r). Find y, given that z(y) = 0.
-1, 0, 1
Let x(z) be the second derivative of z**5/12 + 5*z**4/4 - 10*z**3/3 - 50*z**2/3 + 49*z. Factor x(l).
5*(l - 2)*(l + 1)*(l + 10)/3
Let l(g) be the third derivative of 5/12*g**4 + 1/60*g**6 + 2/15*g**5 + 0*g + 0 + 2*g**2 + 2/3*g**3. Determine a so that l(a) = 0.
-2, -1
Let d(y) be the first derivative of -y**6/240 + y**5/60 - y**4/48 + y**2/2 - 10. Let v(o) be the second derivative of d(o). Suppose v(j) = 0. Calculate j.
0, 1
Let d(z) = 103*z + 9. Let a be d(13). Factor 24*u**3 - 32*u**2 - 5*u**4 - 24*u - a + 1384 + u**4.
-4*(u - 3)**2*(u - 1)*(u + 1)
Let i = 51 + -34. Suppose 4*u - 4*c = 24, -3*u - c + i = -5. What is h in 9*h**3 - 3*h**4 + 5*h**2 + 3*h - 7*h**2 - u*h**2 = 0?
0, 1
Let x(p) be the first derivative of 3/8*p**2 + 1/8*p**3 + 0*p - 8. Factor x(n).
3*n*(n + 2)/8
Suppose 0 = -2*k - 4*j + 14, -3*k + 19 = 3*j + 2*j. Suppose -h = -0*h + 5*r - 21, 3*h = k*r + 9. Suppose -3*d**2 - h*d - 27 - 21 - 18*d = 0. What is d?
-4
Find s, given that 0*s - 2/11*s**4 + 8/11*s**3 - 8/11*s**2 + 0 = 0.
0, 2
Factor 5 - 56*x**3 + 3 + 26*x + 3 - 7 + 26*x**2.
-2*(x - 1)*(4*x + 1)*(7*x + 2)
Let r be 10/(-15) + (-1)/(6/(-4)). Suppose r = i - 3 + 1. Factor -2/9*g**3 + 4/9*g + 2/9*g**i + 0.
-2*g*(g - 2)*(g + 1)/9
Determine u so that -4/5*u**5 + 0*u + 0 - 8/5*u**3 + 0*u**2 + 12/5*u**4 = 0.
0, 1, 2
Let z(u) be the second derivative of u**6/80 - u**5/20 - 5*u**2 - 2*u. Let c(m) be the first derivative of z(m). Factor c(f).
3*f**2*(f - 2)/2
Let s(k) = k**2 + 8*k + 6. Let h be s(-6). Let w = h - -8. Determine m, given that 2 + 0*m**2 + 2*m**2 - w*m**3 + 2*m - 4*m**2 = 0.
-1, 1
Factor -2/9*c**2 + 2/9*c**4 - 16/9*c + 0 + 16/9*c**3.
2*c*(c - 1)*(c + 1)*(c + 8)/9
Let m = -6 - -41. Let j be (-1)/m*-3 - (-1)/5. Factor 0 + 4/7*w + j*w**2.
2*w*(w + 2)/7
Let h(l) be the third derivative of -l**5/105 + l**4/21 + 109*l**2. Suppose h(b) = 0. What is b?
0, 2
Let y(d) = d**4 + 13*d**3 + 144*d**2 + 394*d + 442. Let s(x) = 3*x**4 + 40*x**3 + 430*x**2 + 1183*x + 1327. Let o(a) = 6*s(a) - 17*y(a). Factor o(w).
(w + 4)**3*(w + 7)
Let d be -3*(5 - 6) + 106900/(-76). Let v = 1404 + d. Find a such that -2/19*a**4 - 8/19*a**3 + 8/19*a + v - 6/19*a**2 = 0.
-2, -1, 1
Let u be ((-21)/42)/(1/(-20)). Let i = -10 + u. Determine s, given that 0*s + 3/5*s**2 + i = 0.
0
Suppose 111 = -8*b + 61 + 66. Factor 0 + 0*z**b - 2/17*z**4 - 12/17*z**3 + 0*z.
-2*z**3*(z + 6)/17
Let u be (49 - 48)/((-2)/(-14)). Let s be (8/(-20))/(u/(-35)). Suppose -4/5*v + 8/5*v**3 + 0 - 4/5*v**s = 0. Calculate v.
-1/2, 0, 1
Let n = 82 - 73. Factor -n*i**2 - 39 + 51 + 2*i**3 + i**3.
3*(i - 2)**2*(i + 1)
Let h(s) = 12*s**4 - 6*s**3 + 6*s**2 - 3*s. Let m(z) = -z - 338*z**4 + z**2 + 0*z**2 + 339*z**4. Let i(n) = -h(n) + 9*m(n). Suppose i(d) = 0. Calculate d.
-1, 0, 1, 2
Let l(q) = 4*q**3 - 2*q**2 - 4*q + 2. Let r(c) = c**3 - c. Suppose 2*h - 4 = -8. Let t(n) = h*r(n) + l(n). Suppose t(k) = 0. What is k?
-1, 1
Let r(x) be the third derivative of 0*x + 0*x**4 - 4/15*x**3 - 1/300*x**6 - 8*x**2 + 1/840*x**8 - 1/175*x**7 + 0 + 7/150*x**5. Let r(h) = 0. What is h?
-1, 1, 2
Let v = 35 - 30. Determine k, given that -10 - 5*k**v + 20*k**3 + 259*k**2 - 249*k**2 - 2*k**4 - 15*k + 2*k**4 = 0.
-1, 1, 2
Let u(q) = 245*q + 10049. Let r be u(-41). Factor -3*n**3 + 3/2*n**2 + 3*n - 9/4 + 3/4*n**r.
3*(n - 3)*(n - 1)**2*(n + 1)/4
Let g be (4234/(-44))/((60/64)/15). Let p = -1538 - g. Let 24/11*v - 2/11*v**4 + 4/11*v**2 - 8/11*v**3 - p = 0. Calculate v.
-3, 1
Let m(p) = -6*p**2 + 21*p - 6. Let s = 10 + -8. Suppose 4 = s*k - k. Let t(h) = -3*h**2 + 10*h - 3. Let q(f) = k*m(f) - 9*t(f). Factor q(l).
3*(l - 1)**2
Let a(j) be the first derivative of 1/5*j**3 - 3/25*j**5 + 0*j + 14 - 3/20*j**4 + 3/10*j**2. Factor a(p).
-3*p*(p - 1)*(p + 1)**2/5
Let y(b) = b**2 - 4*b - 10. Let z be y(-2). Let 1/6*j**5 + 0 + 1/3*j**4 + 0*j**3 - 1/3*j**z - 1/6*j = 0. Calculate j.
-1, 0, 1
Let c(f) be the first derivative of 1/5*f**3 + 1/20*f**4 - 9/10*f**2 + f + 29. What is s in c(s) = 0?
-5, 1
Let m = 8 - 4. Let z(p) = -8*p**2 - 12*p + 2. Let u(f) = f**2 + f. Let h(r) = m*z(r) + 36*u(r). Suppose h(v) = 0. Calculate v.
1, 2
Let q(w) be the second derivative of -w**7/315 + w**5/75 - w**3/45 - 53*w. Let q(n) = 0. What i