*2. Factor t(v).
-3*v**2*(v - 1)*(v + 1)
Let t(y) be the second derivative of -1/110*y**5 - 2*y - 7/66*y**4 - 5/11*y**3 + 0 - 9/11*y**2. Solve t(d) = 0.
-3, -1
Let v(p) be the first derivative of 0*p - 1/21*p**6 + 1/7*p**4 + 0*p**5 + 0*p**3 - 1/7*p**2 - 8. Factor v(a).
-2*a*(a - 1)**2*(a + 1)**2/7
Let r(n) be the first derivative of -n**4/30 + 14*n**3/15 - 49*n**2/5 - n + 14. Let f(v) be the first derivative of r(v). Suppose f(j) = 0. Calculate j.
7
Let g = -1949/4 + 1719/4. Let v = -53 - g. Solve 3*y**3 - v*y**2 + 3/2*y**4 + 6 - 6*y = 0 for y.
-2, 1
Let z be 3/27 + (-615)/(-1755). Factor -2/13*n**2 - 4/13 - z*n.
-2*(n + 1)*(n + 2)/13
Let z(a) = -a**2 + a. Let h(f) = -5*f**2 + 3*f - 9. Let v(w) = -3*w**2 + 2*w - 5. Let b(q) = 6*h(q) - 11*v(q). Let j(o) = -b(o) - z(o). What is g in j(g) = 0?
1/2, 1
Suppose -4*s - w - 33 - 62 = 0, -5*w - 130 = 5*s. Let z = s + 25. Find g, given that -4*g**2 - 7*g**3 + 3*g**3 - 4*g**5 + 4*g**z + 8*g**4 = 0.
0, 1
Let i be (6 - 180/27) + 1. Suppose -2/3 + i*b + 1/3*b**2 = 0. What is b?
-2, 1
Let m(j) be the second derivative of -j**5/5 + j**4/3 + 2*j**3/3 - 2*j**2 + j. Determine d so that m(d) = 0.
-1, 1
Let h(s) be the first derivative of -1/5*s**3 + 1/25*s**5 + 1/20*s**4 + 4 - 1/10*s**2 + 2/5*s. Factor h(x).
(x - 1)**2*(x + 1)*(x + 2)/5
Let t = -76510 - -843174/11. Let d = t + -142. Determine p, given that 2/11*p**5 + 0 - 2/11*p**3 + 2/11*p**4 + 0*p - d*p**2 = 0.
-1, 0, 1
Let k be (-5)/(-10) - (-4)/((-240)/(-758)). Let b = k + -39/5. Factor -14/3*y**2 + 4/3*y + 0 + b*y**3 - 2*y**4.
-2*y*(y - 1)**2*(3*y - 2)/3
Let d be 473/165 - (-4)/30. Let t be 5 + -2 + d/(-1). Factor 0 + t*w - 1/2*w**3 - 1/2*w**5 - w**4 + 0*w**2.
-w**3*(w + 1)**2/2
Let b(f) = 2*f**2 - 39*f - 55. Let t be b(21). Suppose -3*r + 6 = -5*z + r, t = -4*z + 4*r. Determine k, given that -4/7*k + 0 - 4/7*k**z = 0.
-1, 0
Let z(t) be the second derivative of t**7/420 - t**6/240 - t**5/120 + t**4/48 - 11*t**2/2 + 14*t. Let i(q) be the first derivative of z(q). Solve i(w) = 0.
-1, 0, 1
Let j(u) be the third derivative of -u**8/1512 + 4*u**6/135 + 8*u**5/135 - 4*u**4/9 - 64*u**3/27 + 20*u**2 - 2. Determine n, given that j(n) = 0.
-2, 2, 4
Suppose 0 = -2*x - 3*x + 275. Let p be (-22)/x + 154/10. Factor p*g**3 - 14*g**3 + 0*g**2 + 0*g**2 - g.
g*(g - 1)*(g + 1)
Factor 5*t - 1/2 + 1/2*t**2 - 5*t**3.
-(t - 1)*(t + 1)*(10*t - 1)/2
Let r(s) be the second derivative of 3*s**5/100 - 9*s**4/20 + 12*s**3/5 - 24*s**2/5 + 11*s. Find n, given that r(n) = 0.
1, 4
Let i be (1/(-2))/(17/68). Let z be 8/5 + 9/((-45)/i). Factor -66/13*t**z - 32/13*t**4 - 20/13*t - 2/13 - 80/13*t**3.
-2*(t + 1)**2*(4*t + 1)**2/13
Suppose -k = -3*k + 4. Factor 0*s - 9*s - 11*s**2 + 10*s**2 - 2*s**k + 12.
-3*(s - 1)*(s + 4)
Let c(t) be the second derivative of -t**6/180 - 167*t**5/60 - 518*t**4 - 78033*t**3/2 - 455877*t**2/4 + 227*t + 1. Suppose c(v) = 0. What is v?
-111, -1
Let n(z) = -z**4 - z**3 - z**2. Let u(b) = 4*b**5 + 31*b**4 + 24*b**3 - 12*b**2 - 21*b - 5. Let f(d) = -28*n(d) - 4*u(d). Suppose f(m) = 0. Calculate m.
-5, -1, -1/2, 1
Let l(o) be the third derivative of o**7/10080 - o**6/1440 - o**5/160 - 5*o**4/8 - 20*o**2. Let m(j) be the second derivative of l(j). What is a in m(a) = 0?
-1, 3
Let h(k) be the first derivative of 0*k**5 + 1 + 0*k**3 + 0*k - 1/6*k**6 - 1/2*k**2 + 1/2*k**4. Factor h(t).
-t*(t - 1)**2*(t + 1)**2
Let u be 5/(-2*(5/30)/1). Let q be ((-10)/4)/(-5 - 50/u). Factor 1 - 3*o + 1/4*o**4 - q*o**3 + 13/4*o**2.
(o - 2)**2*(o - 1)**2/4
Let n(w) be the second derivative of w**5/35 - w**4/21 - 10*w**3/21 - 6*w**2/7 - 3*w - 2. Factor n(z).
4*(z - 3)*(z + 1)**2/7
Let n(k) be the third derivative of k**5/140 + 45*k**4/28 + 2025*k**3/14 - 19*k**2 + 4. Factor n(r).
3*(r + 45)**2/7
Let -44/7*o**2 - 36/7*o**3 + 4/7*o**4 + 36/7*o + 40/7 = 0. What is o?
-1, 1, 10
Let f be 0/(-29)*2/4. Let t(a) be the second derivative of f + 0*a**2 + 1/24*a**3 - 1/16*a**4 + 6*a. Factor t(m).
-m*(3*m - 1)/4
Let k(r) be the third derivative of r**8/168 - 13*r**7/420 - 17*r**6/48 + 59*r**5/60 - r**4/2 - 384*r**2. Suppose k(h) = 0. What is h?
-4, 0, 1/4, 1, 6
Suppose -4*n + o = -7, 3*n + o - 7 = -0. Suppose -9 = -4*z - 3*x, -3*z + 4*z - 1 = -n*x. Solve 0*h**2 - 1/4 + 1/4*h**4 - 1/2*h + 1/2*h**z = 0.
-1, 1
Let m(q) = q**2 - q - 1. Let w(p) = -3*p**2 + 9*p - 1. Let k = -11 - -6. Let t(y) = k*m(y) - w(y). Find z such that t(z) = 0.
-3, 1
Let y = 101605/6 + -16934. What is d in 1/2*d**2 - y*d**3 + 0 + 2/3*d = 0?
-1, 0, 4
Let i(n) be the second derivative of -7*n**4/6 + 2*n**3/3 + 204*n. Solve i(h) = 0.
0, 2/7
Let t(q) = 70*q**3 + 520*q**2 + 560*q + 280. Let h(o) = 5*o**3 + 37*o**2 + 40*o + 20. Let z(v) = -85*h(v) + 6*t(v). Find d, given that z(d) = 0.
-2, -1
Let j = -361 - -361. Let q(o) be the third derivative of 1/3*o**3 + j - 1/60*o**5 + 5*o**2 + 0*o - 1/24*o**4. What is k in q(k) = 0?
-2, 1
Suppose -d - 47*d + 144 = 0. Let b be (-26)/(-10) + 2/2. Solve -4/5 - b*l - 32/5*l**2 - 12/5*l**4 - 2/5*l**5 - 28/5*l**d = 0 for l.
-2, -1
Let l = -4 - -4. Suppose -2*y = 2*w, l*y + 24 = 5*w - 3*y. Find p such that -2/3*p**4 + 4/3 + 10/3*p + 2*p**2 - 2/3*p**w = 0.
-1, 2
Let y(f) be the second derivative of f**4/18 - 34*f**3/9 + 2*f + 82. Factor y(o).
2*o*(o - 34)/3
Let j(s) = -s**3 - s**2. Let c(p) = 2*p**4 - 20*p**2 - 36*p - 18. Suppose -5*l = -10*l - 20. Let m(r) = l*j(r) + c(r). Factor m(d).
2*(d - 3)*(d + 1)**2*(d + 3)
Let i(u) be the third derivative of u**5/120 + 11*u**4/4 + 363*u**3 + 78*u**2. Determine x so that i(x) = 0.
-66
Find d such that -13*d + 0*d - 15*d + 4*d + 48*d**2 + 28*d**2 = 0.
0, 6/19
Let m = 10945 - 10943. Factor 14/9*y - 4/9 + 8/9*y**m.
2*(y + 2)*(4*y - 1)/9
Let o(n) be the second derivative of 3/40*n**5 + 1/2*n**2 - 1/60*n**6 - 1/24*n**4 - 1/4*n**3 + 0 + n. Find m such that o(m) = 0.
-1, 1, 2
Let k(t) be the second derivative of -9*t**5/5 + 31*t**4/4 + 17*t**3/2 - 9*t**2 + 2*t + 4. Factor k(a).
-3*(a - 3)*(3*a + 2)*(4*a - 1)
Let u(s) = -2*s**2 + 510*s - 4428. Let j be u(9). Determine o so that 21/5*o**3 + j + 1/5*o + 6/5*o**5 + 19/5*o**4 + 9/5*o**2 = 0.
-1, -1/6, 0
Let r = 728 + -728. Let f(k) be the second derivative of 1/168*k**7 - 1/24*k**4 - 9*k + r*k**2 - 1/24*k**3 + 0 + 1/60*k**6 + 0*k**5. Factor f(u).
u*(u - 1)*(u + 1)**3/4
Suppose 0 = 31*r - 59 - 34. Factor 2/3*u + 0 + 0*u**2 + 0*u**4 - 4/3*u**r + 2/3*u**5.
2*u*(u - 1)**2*(u + 1)**2/3
Factor 0 + 0*h + 13/5*h**2 + 1/5*h**3.
h**2*(h + 13)/5
Suppose 4*c - 71 + 131 = 68. Factor -1/2*j**3 + 2 + c*j - 1/2*j**2.
-(j - 2)*(j + 1)*(j + 2)/2
Let y(i) be the second derivative of 0*i**3 - 1/4*i**4 + 12*i + 3/2*i**2 + 0. Factor y(p).
-3*(p - 1)*(p + 1)
Suppose z + 2*z - 4*k = 6, k - 6 = -3*z. Suppose -22*w + 16 - 14*w + 4*w**z + 16*w = 0. Calculate w.
1, 4
Let z(r) be the second derivative of r**7/3780 + r**6/810 + r**5/540 - 19*r**3/6 - 16*r. Let g(h) be the second derivative of z(h). Factor g(x).
2*x*(x + 1)**2/9
Let y(b) be the third derivative of -1/6*b**3 + 0*b - b**2 + 0 + 1/54*b**4 - 1/180*b**5 + 1/1620*b**6. Let s(k) be the first derivative of y(k). Factor s(m).
2*(m - 2)*(m - 1)/9
Suppose 0*c = y - 3*c + 54, -189 = 4*y - 3*c. Let b be 2/((-20)/y)*2/3. Factor 1/3*j**b + 2/3*j**2 - 1/3*j - 2/3.
(j - 1)*(j + 1)*(j + 2)/3
Let i(u) be the first derivative of -51*u**4/38 - 208*u**3/57 - 55*u**2/19 - 4*u/19 + 197. Solve i(z) = 0.
-1, -2/51
Factor 2/5*x**3 - 56/5*x - 8 - 14/5*x**2.
2*(x - 10)*(x + 1)*(x + 2)/5
Suppose -2*a - 414 = -8*a. Let g = 74 - a. Solve 0*j - 3/5*j**g - 3/5*j**4 + 3/5*j**2 + 0 + 3/5*j**3 = 0.
-1, 0, 1
Let z(v) be the first derivative of -8*v**2 + 20*v - 4/3*v**3 + 24. Solve z(y) = 0 for y.
-5, 1
Solve -8/15*x - 2/15*x**2 - 8/15 = 0.
-2
Suppose 26*t = 5 + 1 - 6. Let s be 1/3 + 2/(-30). Factor t - s*b + 2/15*b**2.
2*b*(b - 2)/15
Let l = 23637 - 23637. Solve 2/9*j**2 + 0*j + 0*j**3 - 2/9*j**4 + l = 0.
-1, 0, 1
Let z = -63 + 67. Let f(w) be the first derivative of -1/2*w**3 - 1/4*w**6 - 4 + 0*w**2 + 0*w - 9/10*w**5 - 9/8*w**z. Factor f(q).
-3*q**2*(q + 1)**3/2
Factor 94653*h**5 + 1 - 11*h**2 + 8*h + 28*h**3 + 17*h**4 + 33*h**2 - 94649*h**5.
(h + 1)**4*(4*h + 1)
Let b be 32/12 - (-1)/3. Factor 37*r**4 - 12 + 60*r - 60*r**b - 60*r**2 - 3*r**2 + 38*r**4.
3*(r - 1)*(r + 1)*(5*r - 2)**2
Suppose -3*y - 32 + 7*y + 8*y + 7*y - 7*y