 Let d be n(12). Let s be d/(-84) - 8/12. Factor s*f + 0 - 9/7*f**2.
-3*f*(3*f - 1)/7
Let x(i) be the first derivative of i**5/180 + 29*i**4/72 + 73*i**2/2 - 42. Let k(y) be the second derivative of x(y). Factor k(t).
t*(t + 29)/3
Let t = 123 + -116. Factor -t*w - 178 + 5*w**2 + 18*w + 166.
(w + 3)*(5*w - 4)
Let k(a) be the third derivative of -5*a**8/252 + 73*a**7/105 - 1171*a**6/180 + 154*a**5/15 - 49*a**4/9 + 3404*a**2. Solve k(v) = 0 for v.
0, 2/5, 1/2, 7, 14
Let n(m) be the first derivative of -m**6/120 + 52*m + 62. Let g(h) be the first derivative of n(h). Factor g(t).
-t**4/4
Let t(z) be the third derivative of 1/105*z**7 + 0*z - 82*z**2 - 1/20*z**6 + 0 + 1/4*z**4 - 2/3*z**3 + 1/30*z**5. Factor t(i).
2*(i - 2)*(i - 1)**2*(i + 1)
Let b(f) be the first derivative of 0*f - 5/4*f**4 + 70*f**3 - 2205/2*f**2 + 64. Factor b(l).
-5*l*(l - 21)**2
Let z(b) be the third derivative of 0*b + 14/3*b**3 + 4 - 7*b**2 + 1/15*b**5 - 4/3*b**4. Suppose z(u) = 0. Calculate u.
1, 7
Let d(l) be the first derivative of l**4/8 - 659*l**3/3 + 658*l**2 + 2619. Let d(p) = 0. What is p?
0, 2, 1316
Let t(j) be the first derivative of 1/4*j + 5 + 1/16*j**4 - 1/12*j**3 - 1/8*j**2. Let t(x) = 0. What is x?
-1, 1
Let w(y) be the second derivative of 3/5*y**5 - 14*y**2 - 1/30*y**6 + 10*y**3 - 43/12*y**4 - 4 + 28*y. Suppose w(k) = 0. What is k?
1, 2, 7
Factor 2/5*h**3 + 7714*h - 212268/5 - 544/5*h**2.
2*(h - 133)**2*(h - 6)/5
Suppose -24 = -4*h + g, -2*h = -g + 2*g - 6. Factor 3*d**5 + 3*d**5 - 6*d**3 - 2*d**h - 12*d - 44*d**2 + 12*d**2 - 18*d**3.
4*d*(d - 3)*(d + 1)**3
Let y(k) = -13*k. Let h be y(-1). Find n, given that -20*n - 18*n**3 + 12*n - 64*n - h*n**4 + 136*n**2 - 32 - n**4 = 0.
-4, -2/7, 1, 2
Let t(r) be the first derivative of -5*r**3/3 - 585*r**2 - 2320*r - 4463. Factor t(y).
-5*(y + 2)*(y + 232)
Let h(n) = -3*n**2 + 188*n + 169. Let t(q) = 16*q**2 - 942*q - 837. Let x(r) = 11*h(r) + 2*t(r). Find m such that x(m) = 0.
-1, 185
Factor -6/19*j**2 - 10/19 - 18/19*j + 2/19*j**3.
2*(j - 5)*(j + 1)**2/19
Factor -3/5*p**3 + 57/5 + 63/5*p**2 - 117/5*p.
-3*(p - 19)*(p - 1)**2/5
Let n(g) = 37*g**3 - 830*g**2 - 33597*g + 70566. Let q(h) = -88*h**3 + 1660*h**2 + 67193*h - 141134. Let v(l) = 7*n(l) + 3*q(l). Find m such that v(m) = 0.
-84, 2
Let n be (313 - 308)/((-2)/(-14)). Let q(u) be the first derivative of 0*u - n + 1/2*u**2 - 3/16*u**4 + 1/3*u**3 + 1/24*u**6 - 1/10*u**5. Factor q(b).
b*(b - 2)**2*(b + 1)**2/4
Suppose 19*p + 9*p = 0. Factor p*s**4 - 2*s**4 - 7*s**2 + 23*s**2 - 32.
-2*(s - 2)**2*(s + 2)**2
Determine c so that -26*c - 16*c**3 - 1025*c**2 - 38*c + 2*c**4 + 1073*c**2 + 32 = 0.
2
Let p(x) = 7*x**3 - 39*x**2 + 4*x + 4. Let f(z) = 6*z**3 - 35*z**2 + 3*z + 5. Let w(t) = 8*f(t) - 7*p(t). Solve w(n) = 0 for n.
-6, -2, 1
Let x = -908 - -916. Suppose 0 = 34*q + x*q. Factor -1/3*f**2 + q + 1/3*f.
-f*(f - 1)/3
Let c(s) be the second derivative of s**5/10 + 181*s**4 + 131044*s**3 + 47437928*s**2 - 7*s - 258. Let c(v) = 0. What is v?
-362
Let s(d) be the third derivative of -d**5/15 - 7*d**4/2 + 874*d**2. Factor s(t).
-4*t*(t + 21)
Let t be (5 - -2) + -4 - 1357/(-3). Let b = 457 - t. Solve 7/3*q**3 - 7/3*q + 1/3*q**4 + b*q**2 - 2 = 0 for q.
-6, -1, 1
Let t be (-15)/(135/(-12)) + (-18 - 6392/(-255)). Solve -48*r**3 + 0 - 2/5*r**5 + 40*r**2 + 0*r + t*r**4 = 0.
0, 1, 10
Let u(r) be the first derivative of -r**5/15 - 5*r**4/6 + 64*r**3/9 + 173*r**2/3 + 91*r - 3888. Determine g, given that u(g) = 0.
-13, -3, -1, 7
Let x(z) be the third derivative of z**6/120 + z**5/5 - 5*z**4/8 - 13*z**3/3 + 5*z**2 + 176*z - 1. Let x(j) = 0. What is j?
-13, -1, 2
Suppose 27 = 5*j + 2*a, 4 = 2*a + 2*a. Suppose 4*c - 29 = -3*y, -17 = -6*y + 7*y - 4*c. Factor -46*n**5 - n**y + 45*n**j + 2*n**3.
-n**3*(n - 1)*(n + 1)
Factor -3*s**2 + 1565 + 153*s - 2987 + 2082.
-3*(s - 55)*(s + 4)
Let x(m) be the second derivative of m**7/126 + m**6/18 - m**5/20 - 17*m**4/36 - 5*m**3/9 - 1228*m. Find s, given that x(s) = 0.
-5, -1, 0, 2
Let i = -2/40427 - -485134/202135. Let m(k) be the first derivative of 2/5*k**4 + 1/25*k**5 + 23/15*k**3 + i*k + 14/5*k**2 + 14. Factor m(d).
(d + 1)*(d + 2)**2*(d + 3)/5
Let 132/5*o**2 + 12/5*o**5 + 72/5*o - 52/5*o**4 - 4/5*o**3 + 0 = 0. Calculate o.
-1, -2/3, 0, 3
Let w(s) be the third derivative of 3*s**7/70 + s**6/4 - 269*s**5/15 + 353*s**4/12 - 39*s**3/2 + s**2 - 147*s + 3. Let w(g) = 0. Calculate g.
-13, 1/3, 9
Let s(w) = w**2 + 87*w - 174. Let n be s(2). Let m(h) be the third derivative of 0*h - 14*h**2 - 5/24*h**n + 0 - 1/12*h**5 + 0*h**3. Factor m(k).
-5*k*(k + 1)
Let u(d) be the first derivative of -d**6/30 + d**4/6 - 9*d**2/2 - 4*d + 39. Let n(s) be the second derivative of u(s). Find h, given that n(h) = 0.
-1, 0, 1
Let h(x) = 7*x**2 + x + 2*x**2 + 20*x**2 - 30*x**2. Let k(r) = 120*r**2 - 140*r + 36. Let n(j) = 20*h(j) + k(j). Find i such that n(i) = 0.
3/5
Let a(n) = 12*n**2 - 45*n + 15. Let f(x) = -2*x + 1. Suppose 3*g + 12 = 0, 20*o = 17*o - 5*g - 47. Let z(c) = o*f(c) + a(c). Factor z(p).
3*(p - 2)*(4*p - 1)
Let p(c) be the first derivative of -5*c**3/18 + 2170*c**2/3 - 1883560*c/3 + 812. Suppose p(h) = 0. What is h?
868
Solve -8/7 - 4/7*l**2 + 2/7*l**3 - 2*l = 0.
-1, 4
Let u(w) be the third derivative of -w**6/360 - 11*w**5/180 - 13*w**4/24 - 5*w**3/2 + 297*w**2. Factor u(f).
-(f + 3)**2*(f + 5)/3
Let m(c) = 29*c**5 - 119*c**4 - 248*c**3 - 76*c**2 - 4*c. Let q(b) = -4*b**5 - b**4 - 2*b**3 + b**2 - b. Let j(r) = -m(r) + 4*q(r). Find x, given that j(x) = 0.
-1, -4/9, 0, 4
Factor -259200/19 - 468/19*s**3 - 2/19*s**4 + 168480/19*s - 25938/19*s**2.
-2*(s - 3)**2*(s + 120)**2/19
Factor -1/3*k**3 + 360*k**2 - 129600*k + 15552000.
-(k - 360)**3/3
Suppose n - 3*s + 4 = -4, 4*n = -4*s + 32. Suppose -v + 2 = -h, -5 - 6 = -n*v + h. Determine j, given that 12 - 6*j - 4*j + j - v*j**2 = 0.
-4, 1
Let k(j) = 57 - 12 - 43*j + 12*j**2 + 10*j**2 - 24*j**2. Let i(d) = d**2 + 29*d - 30. Let y(h) = 7*i(h) + 5*k(h). Factor y(b).
-3*(b - 1)*(b + 5)
Find y, given that 0 + 2886/7*y**3 + 22*y**4 - 3042/7*y**2 + 0*y + 2/7*y**5 = 0.
-39, 0, 1
Suppose 55*z - 74*z = -2660. Suppose 135*g + 20 = z*g. Determine d so that 1/6*d + 1/3*d**2 + 0*d**3 + 0 - 1/3*d**g - 1/6*d**5 = 0.
-1, 0, 1
Let c(y) be the third derivative of -2*y**7/735 + 11*y**6/21 - 31*y**5/15 + 18*y**4/7 + 23*y**2 + 58. Factor c(n).
-4*n*(n - 108)*(n - 1)**2/7
Let g(i) = 6*i - 29. Let r be g(5). Suppose 4*x = -r + 21. Factor -u**3 - 2*u**2 + 7*u**3 - 2*u**4 - 6*u - 5*u**2 + 4 + x*u**2.
-2*(u - 2)*(u - 1)**2*(u + 1)
Suppose -376*h + 405 = -240 - 483. Solve -5*s**h + 9/4*s**4 - 113/4*s**2 - 16*s + 5 = 0.
-2, -1, 2/9, 5
Suppose 30 = -555*t + 558*t + 3*z, 4*z + 68 = 5*t. Suppose -t*i + 1/2*i**2 + 72 = 0. What is i?
12
Let g = -195 - -199. Factor 53 - 143 - 7*f + 4*f**4 + f**g + 65*f**2 + 22*f - 35*f**3.
5*(f - 3)**2*(f - 2)*(f + 1)
Factor -21/4*f**2 + 1/4*f**4 - 11/4*f - 9/4*f**3 + 0.
f*(f - 11)*(f + 1)**2/4
Let v(r) = -r**2 - 3218*r + 22577. Let c be v(7). Factor -2/9*n**3 - 28/9*n - 16/9 - 14/9*n**c.
-2*(n + 1)*(n + 2)*(n + 4)/9
Let g(y) be the first derivative of 1/24*y**3 + 11 - 3/2*y**2 - 1/48*y**4 + 1/240*y**5 + 0*y. Let v(x) be the second derivative of g(x). Solve v(w) = 0 for w.
1
Let b(h) be the second derivative of h**4/6 - 53*h**3/3 + 240*h**2 - 64*h - 22. Factor b(s).
2*(s - 48)*(s - 5)
Let w be (-24)/144*16/(-12). Let q(c) be the third derivative of 0 - 5/9*c**3 - 5/24*c**4 - 1/24*c**6 + w*c**5 + 0*c + 14*c**2. Determine n so that q(n) = 0.
-1/3, 1, 2
Suppose 0 = -4*f - 17*c - 60, 471*c - 466*c = 5*f - 30. Factor -21/2 - 23*z - z**3 - 14*z**f + 1/2*z**4.
(z - 7)*(z + 1)**2*(z + 3)/2
Let q(c) = -3*c**4 - 2*c**3 - 5*c**2 + 12*c - 2. Let v(i) = 7*i**4 + 2*i**3 + 10*i**2 - 24*i + 5. Let z(l) = 15*q(l) + 6*v(l). Factor z(g).
-3*g*(g - 1)*(g + 3)*(g + 4)
Let l(r) = 1. Let q be (-11)/(-55) + 48/10. Let f(p) = -q*p**2 - 24*p - 10*p - 25*p + 9*p - 150. Let z(t) = -f(t) - 25*l(t). Factor z(c).
5*(c + 5)**2
Let g be 1 + (-2)/2*-4 + 0/(-10). Let b(x) be the third derivative of -2/3*x**3 + 0*x - 1/12*x**4 + 0 + 14/15*x**g + 9*x**2. Suppose b(n) = 0. Calculate n.
-1/4, 2/7
Let t(i) be the second derivative of 10/3*i**4 + 0 + 1/4*i**5 + 95/6*i**3 + 30*i**2 + 138*i. Factor t(g).
5*(g + 1)*(g + 3)*(g + 4)
Let 972 + 756*y + 11*y**3 