1
Let w(s) be the second derivative of s**5/20 + 5*s**4/4 + 9*s**3/2 - 17*s**2/2 - 2*s + 27. Let t(v) be the first derivative of w(v). Factor t(g).
3*(g + 1)*(g + 9)
Let p(w) be the first derivative of -34 - w**4 + 20/3*w**3 + 12*w - 14*w**2. Factor p(k).
-4*(k - 3)*(k - 1)**2
Suppose 4*g - 18 = -5*r, 2*g = -r + 7 - 1. Let x(t) = -3*t**3 + 23*t**2 + 8*t. Let y be x(8). Suppose -4/11*m**g + y - 1/11*m**3 - 3/11*m = 0. What is m?
-3, -1, 0
Let w(t) be the second derivative of t**6/3780 + 3*t**5/70 + 81*t**4/28 + 89*t**3/2 + t - 23. Let r(s) be the second derivative of w(s). Factor r(x).
2*(x + 27)**2/21
Let b(z) = -7*z**2 - 12*z + 15. Let m(v) = -2*v**2 - 2*v - 1. Let o(j) = 6*j**2 + 8*j - 16. Let n(s) = -2*m(s) + o(s). Let u(g) = 4*b(g) + 3*n(g). Factor u(t).
2*(t - 3)**2
Let t(x) be the first derivative of -x**5/5 + 31*x**4/2 + 65*x**3 + 2*x**2 - 260*x + 14031. Factor t(a).
-(a - 65)*(a - 1)*(a + 2)**2
Suppose 0 = -3*p + 3*n + 870, 1153 = 4*p - 15*n + 18*n. Factor -52*x**2 + 4*x**4 + 48*x**3 - 289 + p.
4*x**2*(x - 1)*(x + 13)
Suppose -31 = -4*n - c, -5*c - 6 = -3*n - 0. Let y(u) = -u. Let l be y(-3). Let -1 + 7*w - 3*w**2 - w + n*w**2 - l = 0. What is w?
-2, 1/2
Let p(j) be the first derivative of -j**4/24 + 10*j**3/3 + 21*j**2 + 128*j/3 - 967. Factor p(r).
-(r - 64)*(r + 2)**2/6
Suppose -5*n = -5*h + 765, -n - 129 = 5*h + 42. Let m = -1388/9 - n. Find z, given that 4/9*z - 2/9*z**2 + m = 0.
-2, 4
Suppose 47*j - 43*j = v + 2938, 2*v + 3671 = 5*j. Let b = j + -732. Factor 6/7*d**b + 5/7*d**4 - 3/7 - d + 1/7*d**5 - 2/7*d**2.
(d - 1)*(d + 1)**3*(d + 3)/7
Suppose 0*i = -4*i + 4*f - 920, -5*f = 0. Let o = -230 - i. Factor o - 6/19*n**2 + 4/19*n + 2/19*n**3.
2*n*(n - 2)*(n - 1)/19
Let n be 10 + -2 + -8 + (1080/255)/18. Factor -n + 4/17*y**2 - 2/17*y**3 + 2/17*y.
-2*(y - 2)*(y - 1)*(y + 1)/17
Let t(k) be the second derivative of -k**6/20 - 1263*k**5/40 - 178081*k**4/32 - 44205*k**3/4 - 33075*k**2/4 - 5567*k. Let t(q) = 0. What is q?
-210, -1/2
Suppose 2*t - 186 = -4*s, 2*s + 0*s = 3*t + 113. Suppose -s*n - 153 = -52*n. Factor 2*c**3 - 2*c + 10*c - 21*c**2 - 22*c**2 + n*c**2.
2*c*(c + 2)**2
Suppose -47/3*h**3 + 12*h - 1/3*h**5 + 80/3 - 4*h**4 - 56/3*h**2 = 0. What is h?
-5, -4, -2, 1
Suppose -3*w + r = -8, 0 = -w - 4*r - r + 24. Let n be (-20)/14 + w + -2. Factor n*g - 3/7 - 1/7*g**2.
-(g - 3)*(g - 1)/7
Let b be (-14670)/19800 - (21/(-12) - -1). Let m(j) be the second derivative of 0*j**4 - 2/11*j**2 - b*j**5 + 1/11*j**3 - 6*j + 0. Factor m(k).
-2*(k - 1)**2*(k + 2)/11
Let y be (-1*16/(-1))/5. Let v(q) = -255*q**2 + 19379*q + 78. Let g be v(76). Factor -2/5*n**g - 32/5 + y*n.
-2*(n - 4)**2/5
Let k = -60 - -151. Let s = 93 - k. Let -1/5*u**s - 1/5 - 2/5*u = 0. What is u?
-1
Let t(h) be the first derivative of 6/5*h**3 + 21/20*h**4 + 0*h**5 + 0*h - 78 - 1/10*h**6 + 0*h**2. Solve t(l) = 0 for l.
-2, -1, 0, 3
Let q(m) = 25*m**3 - 100*m**2 + 60*m + 20. Suppose 24*d - 30*d = 24. Let g(f) = -24*f**3 + 99*f**2 - 59*f - 20. Let x(o) = d*q(o) - 5*g(o). Factor x(l).
5*(l - 4)*(l - 1)*(4*l + 1)
Let h be 2/(0 + 4 + -2) + 2. Let w(d) be the first derivative of -d**h + 2*d**3 + 54*d - 18*d**2 + 1 + 54*d. Factor w(y).
3*(y - 6)**2
Let s(l) = -4*l**2 - 6519*l - 2663421. Let q(o) = 44*o**2 + 71712*o + 29297632. Let p(a) = 3*q(a) + 32*s(a). Factor p(m).
4*(m + 816)**2
Suppose 36000 = 14*l + 61*l. Let t be (l/(-2800))/(23/(-14) - -1). Factor 2/15*n + 0 + 2/15*n**3 - t*n**2.
2*n*(n - 1)**2/15
Let y(s) = 5*s**2 - 18*s - 33. Let j(c) = 3*c**2 - 16*c - 31. Let v(x) = 3*j(x) - 2*y(x). Suppose v(m) = 0. What is m?
-9, -3
Let i(f) be the first derivative of -2/35*f**5 - 44/21*f**3 - 18/7*f - 24/7*f**2 - 24 - 4/7*f**4. Solve i(g) = 0.
-3, -1
Let n = 462 + -501. Let s be (n/(-18) + -3)*27/(-15). Suppose 0 + s*i**3 + 3*i - 11/2*i**2 = 0. Calculate i.
0, 2/3, 3
Let -17*q**2 - 31 - 332 - 8*q**2 - 187*q + 12668*q**3 - 12669*q**3 = 0. What is q?
-11, -3
Let j(z) be the first derivative of 5/14*z**2 - 2/7*z - 24 + 1/7*z**3. Determine l, given that j(l) = 0.
-2, 1/3
Let w(c) = 49391*c**2 - 5 + c**5 - 49391*c**2 - 52*c**4 + 46*c**3. Let u(t) = -52*t**4 + 48*t**3 - 4. Let v(h) = -5*u(h) + 4*w(h). Factor v(g).
4*g**3*(g - 1)*(g + 14)
Let z(g) be the third derivative of g**5/120 - 11*g**4/4 + 2420*g**2. Factor z(t).
t*(t - 132)/2
Let y = -2555/1738 + 261/158. Factor -4/11*o**3 - y*o**4 + 0 + 6/11*o**2 + 0*o.
-2*o**2*(o - 1)*(o + 3)/11
Let s = -5285089/68 - -77724. Let g = 5/34 + s. Factor -3/4 + 3/4*f**3 + g*f - 9/4*f**2.
3*(f - 1)**3/4
Let j(b) be the first derivative of -4/3*b**3 - 14*b**2 + 94 + 32*b. Suppose j(o) = 0. Calculate o.
-8, 1
Let p(a) = 14*a**2 + 18*a + 8. Let y(n) = 11*n**2 + 16*n + 8. Let s(d) = -3*p(d) + 4*y(d). Factor s(m).
2*(m + 1)*(m + 4)
Let w(t) = -4*t**2 + 2*t + 7. Let s be w(-3). Let j = s + 39. Solve 13*z + 9*z**2 - 26*z + 9*z**3 + 21*z**j + 19*z - 45*z**3 = 0.
-2/7, 0, 1
Let m be (-15)/(-65) - (12 + 23015/(-1950)). Let t(r) be the third derivative of 0*r**3 + 0*r + 0 + m*r**5 - 9*r**2 - 1/6*r**4 + 1/60*r**6. Factor t(d).
2*d*(d - 1)*(d + 2)
Let f(m) be the second derivative of -5/3*m**3 + 0 + 5/12*m**4 + 0*m**2 + 59*m. Solve f(l) = 0 for l.
0, 2
Let r = 1081670 - 5408349/5. Let 107/5*z + 106/5*z**2 + r = 0. What is z?
-1, -1/106
Let y = 2/30047 + 991511/600940. Let u(m) be the second derivative of 0 - 3*m**4 + 0*m**2 - 1/5*m**6 + y*m**5 - 9/2*m**3 + 35*m. Factor u(a).
-3*a*(a - 3)**2*(2*a + 1)
Let s(m) be the first derivative of 320*m - 170*m**2 - 5/4*m**4 - 266 + 100/3*m**3. Factor s(r).
-5*(r - 16)*(r - 2)**2
Let s(k) = k - 2*k + 13*k. Let j(o) be the second derivative of o**4/12 - 2*o. Let a(b) = 3*j(b) - s(b). Factor a(c).
3*c*(c - 4)
Factor 0*p + 1/6*p**4 - 133/6*p**3 - 67/3*p**2 + 0.
p**2*(p - 134)*(p + 1)/6
Let h(v) = -2*v**3 - v**2 - 11*v - 15. Let t(l) = 5*l**3 + 5*l**2 + 22*l + 29. Suppose 164*u - 6 = 162*u. Let z(i) = u*t(i) + 7*h(i). Factor z(c).
(c - 2)*(c + 1)*(c + 9)
Suppose -15*v + 7*v = 3320. Let p = v - -1661/4. Determine q, given that p*q**4 - 1/2*q**3 - 1/4 + 0*q**2 + 1/2*q = 0.
-1, 1
Let w be (-2)/(-4)*(-100 + 1344). Factor -94*z**3 + 4331*z - w*z + 3060*z**2 - 104*z**3 + 3*z**4 + 3227*z.
3*z*(z - 34)**2*(z + 2)
Let n = 10 + 1. Suppose -5*l = 2*a - 60, 5*a - 3*l + 7*l - 184 = 0. Determine q so that a*q**3 + q**5 - 4*q**2 - 3 - 32*q + 67 - 20*q**2 - n*q**4 - 20*q**2 = 0.
-1, 2, 4
Let r(y) be the first derivative of -y**6/180 + y**5/45 + 7*y**4/36 + 4*y**3/9 + y**2 + 6*y - 13. Let m(b) be the second derivative of r(b). Factor m(u).
-2*(u - 4)*(u + 1)**2/3
Suppose 460 = r + g, 25*g = -5*r + 23*g + 2300. Let m = 3681/8 - r. Factor m + 1/8*q**3 - 1/8*q**2 - 1/8*q.
(q - 1)**2*(q + 1)/8
Let p(g) = g**2 + 45*g + 1. Let a(t) = -7*t**2 - 420*t - 4. Let q(y) = a(y) + 4*p(y). Find r such that q(r) = 0.
-80, 0
Let v(r) be the third derivative of 0*r + 1/24*r**6 - 302*r**2 + 1/336*r**8 - 1/30*r**5 + 0*r**3 - 2/105*r**7 + 0*r**4 + 0. Factor v(s).
s**2*(s - 2)*(s - 1)**2
Let l(j) be the third derivative of -j**5/360 - 11*j**4/72 + 15*j**3/4 - 26*j**2. Factor l(b).
-(b - 5)*(b + 27)/6
Suppose -2*n + 14 = 2*h, 10*n = -h + 11*n - 1. Let s(j) be the second derivative of 0*j**h + 0 - 1/48*j**4 + 0*j**2 - 9*j. Factor s(a).
-a**2/4
Let b(z) be the first derivative of z**7/1365 - z**6/780 - z**5/65 + 3*z**2/2 - 20*z - 6. Let w(r) be the second derivative of b(r). Let w(o) = 0. Calculate o.
-2, 0, 3
Let j = 9 - 1. Let i(y) = 3*y - 24. Let f be i(j). Factor f*h + h - 5*h**3 + 2*h + 5 - 5*h**2 + 2*h.
-5*(h - 1)*(h + 1)**2
Let b(w) be the third derivative of w**5/15 - 139*w**4/3 + 554*w**3/3 - 2858*w**2. Factor b(r).
4*(r - 277)*(r - 1)
Let v be (-1363)/(-50431) - (-104)/259. Find l, given that 0*l + 0 - 6/7*l**4 - 12/7*l**2 + 3*l**3 - v*l**5 = 0.
-4, 0, 1
Let m be 71/3 - (16/(-48) + 0). Factor -m*r**4 - 64*r**2 - 2*r**5 - 19*r**3 - 8 - 36*r - 2*r**5 - 21*r**3 - 16*r**3.
-4*(r + 1)**4*(r + 2)
Let d be 0/((2 - (8 - 12))/2). Let s(w) be the second derivative of 1/160*w**5 - 1/48*w**3 + 0*w**2 - 2*w + d + 0*w**4. Suppose s(r) = 0. Calculate r.
-1, 0, 1
Let m(i) be the third derivative of i**7/1155 + 53*i**6/660 - i**5/2 + 167*i**4/132 - 56*i**3/33 - 4*i**2 + i + 47. Factor m(u).
2*(u - 1)**3*(u + 56)/11
Let q(f) = f**3 + 19*f**2 - 58*f + 178. Let o be q(-22). Let p(b)