+ 6. Let v(z) be the third derivative of 1/60*z**6 + 0*z + 0*z**3 + 0 - 16*z**2 - k*z**5 + 1/6*z**4. Factor v(p).
2*p*(p - 2)*(p - 1)
Suppose 0 = -4784*d + 4783*d + 36. Let h be 20/(-15) - (-156)/d. Find w such that 12/7*w - 12/7 + 3/7*w**5 + 15/7*w**2 - 15/7*w**h - 3/7*w**4 = 0.
-2, -1, 1, 2
Let t(h) be the first derivative of 4/7*h - 52 + 8/21*h**3 - 9/7*h**2. What is n in t(n) = 0?
1/4, 2
Suppose -52 = 4*q, -4*x = 3*q + 20 + 7. Find n, given that 3/2*n**5 - 6*n**x + 3*n**2 + 0*n**4 + 9/2*n - 3 = 0.
-2, -1, 1
Let p(i) be the second derivative of i**6/40 + 51*i**5/10 + 867*i**4/2 + 19652*i**3 - 85*i**2 - 2*i + 80. Let t(w) be the first derivative of p(w). Factor t(k).
3*(k + 34)**3
Let p(x) be the second derivative of -x**6/24 + 17*x**5/20 - 277*x**4/48 + 149*x**3/12 + 21*x**2 + 2442*x. Suppose p(k) = 0. Calculate k.
-2/5, 3, 4, 7
Let b(k) = -7*k**3 + 102*k**2 + 223*k - 306. Let i(a) = -5*a**3 + 100*a**2 + 220*a - 305. Let z(o) = 5*b(o) - 6*i(o). Factor z(m).
-5*(m - 1)*(m + 4)*(m + 15)
Factor -3095*o**2 - 1016*o + 1035*o**2 + 1036*o**2 + 1028*o**2 + 3012.
4*(o - 251)*(o - 3)
Let r = -145 - -131. Let l be (4/r)/((-3)/21). Factor 9*k**4 - l*k**4 + 0*k**4 + 4*k - 5*k**4 - 6*k**2.
2*k*(k - 1)**2*(k + 2)
Suppose -470*w + 300 = -410*w. Suppose 684/5*m**3 + 0*m + 246/5*m**4 - 216/5*m**2 + 21/5*m**w + 0 = 0. Calculate m.
-6, 0, 2/7
Let t(i) be the second derivative of 0*i**2 - 13/15*i**6 - 2*i + 1/30*i**5 - 2/7*i**7 + 25 + 16/9*i**3 + 20/9*i**4. Find u such that t(u) = 0.
-4/3, -1/2, 0, 1
Suppose -k = -4*h + 2, -5*k + 26 = 999*h - 1001*h. Let y(x) be the second derivative of 0 + 4/5*x**5 - 27*x - 8/3*x**3 + 6*x**h - x**4. Factor y(w).
4*(w - 1)*(w + 1)*(4*w - 3)
Let j be 0*-1*((-6)/(-3) - 3). Solve 27*l + 42*l**3 - 356*l**4 + j*l**5 + 3*l**5 - 11 + 5 + 338*l**4 - 48*l**2 = 0.
1, 2
Let x = 437295/278 - 1573. Let w = x + 547/2502. Factor -8/3*r + w*r**3 + 0*r**2 - 32/9.
2*(r - 4)*(r + 2)**2/9
Let l(b) be the first derivative of b**4/27 - 5*b**3/18 - 2*b**2/9 - 77*b + 145. Let f(j) be the first derivative of l(j). Determine c so that f(c) = 0.
-1/4, 4
Let b(t) = -6*t**3 + t**2 - 1. Let z be b(-1). Determine w so that -22*w**3 - 17*w**3 + 56*w**3 + z*w**2 - 16*w**3 + 8*w = 0.
-4, -2, 0
Let q(n) = n**2 + 10*n + 24. Let a be q(-7). Solve -4*f**2 - 42*f + 7*f - 42 - 6 + a*f = 0.
-6, -2
Let t = 39 - 33. Let h be (t + 2)/((-14)/7). Let g(x) = x**2 - 1. Let y(o) = 4*o**3 - 7*o**2 - 9*o + 2. Let a(f) = h*g(f) - y(f). Suppose a(u) = 0. Calculate u.
-1, -1/4, 2
Let a(b) be the second derivative of -b**7/168 - 2*b**6/15 + 14*b**5/5 - 147*b**4/8 + 459*b**3/8 - 351*b**2/4 + 5194*b. Find f such that a(f) = 0.
-26, 1, 3
Suppose 3415*t - 3409*t = 6864. Let s be t/69 + (-38)/(-437). Factor 5*f - 5/3*f**2 + s.
-5*(f - 5)*(f + 2)/3
Factor -1/9*l**2 - 7/3*l - 80/9.
-(l + 5)*(l + 16)/9
Let x(d) be the first derivative of d**6/1260 + d**5/70 - 11*d**3/3 - d**2 - 4. Let l(v) be the third derivative of x(v). Suppose l(t) = 0. Calculate t.
-6, 0
Suppose 0 = -5*q + 133 - 53. Determine u so that 17*u - 46*u**2 - 2*u**4 + 23*u + q*u + 16*u**3 - 24 = 0.
1, 2, 3
Let l(d) = -165*d**3 + 865*d**2 - 3995*d + 4765. Let y(s) = -14*s**3 + 72*s**2 - 333*s + 397. Let t(o) = 3*l(o) - 35*y(o). Suppose t(z) = 0. Calculate z.
2, 5, 8
Let d(a) = -1. Let q(o) = 4*o + 16. Let w(t) = -2*d(t) - q(t). Let m be w(-4). Factor s + 4 - 5 + 17*s**4 + m*s**3 - 16*s**4 - 3*s.
(s - 1)*(s + 1)**3
Let c(p) = 50*p**3 + 11035*p**2 + 63565*p + 93955. Let j(r) = -3*r**3 - 649*r**2 - 3739*r - 5527. Let w(o) = -2*c(o) - 35*j(o). Let w(y) = 0. Calculate y.
-123, -3
Suppose 5*z + 6*f - 69 = 0, -3*z + 5*f = -6012 + 5876. Let -z*q + 3/2*q**4 - 12*q**3 + 0 + 63/2*q**2 = 0. Calculate q.
0, 2, 3
Suppose 22 = -710*b + 36 - 14. Factor b + 3/2*p**4 + 3/2*p - 3/2*p**2 - 3/2*p**3.
3*p*(p - 1)**2*(p + 1)/2
Let d(j) be the first derivative of j**6/18 - 4*j**5/3 - j**4/12 + 20*j**3/9 + 95. Suppose d(v) = 0. Calculate v.
-1, 0, 1, 20
Let b(m) = 255*m**2 - 480*m + 205. Let f(w) = w**3 + 512*w**2 - 961*w + 404. Let x(o) = 11*b(o) - 5*f(o). Factor x(z).
-5*(z - 47)*(z - 1)**2
Let c = 3122 - 3122. Let z(o) be the second derivative of -2/5*o**5 + 2*o**2 + 2/3*o**3 + 16*o + 2/15*o**6 + c + 2/21*o**7 - 2/3*o**4. Solve z(x) = 0 for x.
-1, 1
Let t(d) be the first derivative of d**6/24 - d**5/4 + 5*d**4/12 + d**2 - 6*d + 64. Let g(r) be the second derivative of t(r). Determine k, given that g(k) = 0.
0, 1, 2
Let k(u) = -1. Let d be (-2 + 3)/(0 + 1). Let h(q) = 2*q**3 + 6*q**2 + 4*q - 5. Let x(b) = d*h(b) - 5*k(b). Let x(z) = 0. Calculate z.
-2, -1, 0
Let i(f) be the second derivative of f**7/210 + f**6/3 - 21*f**5/10 + 16*f**4/3 - 43*f**3/6 + 27*f**2/5 + 30*f + 76. Solve i(t) = 0 for t.
-54, 1
Factor 7/3*f**3 - 85/6 + 1/6*f**4 - 79/3*f - 10*f**2.
(f - 5)*(f + 1)**2*(f + 17)/6
Suppose 3*p - q - 7 = 0, 2*q - 17 = -3*p - 13. Let m = 2 + 0. Find s, given that 5/2*s + 1/2*s**3 - m*s**p - 1 = 0.
1, 2
Factor 14*z**4 + 54*z + 18*z**3 - 41*z**4 - 75*z**2 + 30*z**4.
3*z*(z - 2)*(z - 1)*(z + 9)
Let q(x) be the first derivative of 27 + 29*x - 8*x**2 + 2/3*x**3 + 1/6*x**4. Let o(i) be the first derivative of q(i). Factor o(j).
2*(j - 2)*(j + 4)
Suppose -161 = 10*k - 51. Let o = k + 71. Determine d so that -o*d**2 + 4*d**3 + 61*d**2 - d**3 - 4*d**3 = 0.
0, 1
What is g in 163/2*g**4 + 21*g**2 + 0*g + 2*g**5 - 209/2*g**3 + 0 = 0?
-42, 0, 1/4, 1
Let g = 2/37573 - -225412/488449. Solve -30/13*b**2 - 16/13*b - 8/13*b**3 + g = 0.
-3, -1, 1/4
Factor 128*z**3 - 7196 - 10944 - 374*z**3 + 131*z**3 - 4555*z**2 + 18160*z + 120*z**3.
5*(z - 907)*(z - 2)**2
Let j = 10131 + -10128. Let c(k) be the second derivative of -1/18*k**4 + 0 + 19*k + 0*k**j + 1/3*k**2. Suppose c(m) = 0. Calculate m.
-1, 1
Factor -3/5*r**3 + 2/5*r**5 + 0 - 7/5*r**2 + 3/5*r**4 - 3/5*r.
r*(r + 1)**3*(2*r - 3)/5
Suppose -3*u = -o - 6, 3*u = -3*o - 5 - 13. Let s be ((-2)/o)/((-4)/(-36)). Find y, given that s*y - 66*y**2 - 67*y**2 + 136*y**2 = 0.
-1, 0
Factor 1/5*j**5 - 3127*j**4 + 19556258*j**3 - 61152418766*j**2 + 95611806740641*j - 298978119677984407/5.
(j - 3127)**5/5
Let t = -391609 + 5090919/13. Solve -22/13*o**2 + 0 - t*o**3 + 0*o = 0.
-11, 0
Let h(y) be the second derivative of y**6/30 - y**5/15 - 28*y**2 + 8*y + 9. Let g(b) be the first derivative of h(b). Let g(t) = 0. Calculate t.
0, 1
Let d(l) be the first derivative of 2*l**6/15 + 2*l**5/5 + l**4/3 - 89*l + 79. Let n(p) be the first derivative of d(p). Factor n(h).
4*h**2*(h + 1)**2
Factor 2815/4*n + 1/2*n**2 + 1407/4.
(n + 1407)*(2*n + 1)/4
Let l = -259083 + 1295424/5. Suppose -3*s + 2 = -5*s + 4*w, -4*s + 5*w = -2. What is o in 6/5*o**2 + s*o - l = 0?
-3, 1/2
Let l(k) be the third derivative of k**8/420 - k**7/36 - k**6/60 + 7*k**5/30 - k**4/4 + 41*k**2 - 3*k. Let u(j) be the third derivative of l(j). Factor u(f).
4*(f - 3)*(12*f + 1)
Let t(m) = 2*m**3 + 19*m**2 + 11*m + 5. Let a be t(-9). Let c be a/(-12) - 13/(-52). Factor 2/3*g**3 - 7/3*g**2 + 4/3*g + c.
(g - 2)**2*(2*g + 1)/3
Let c(u) = 3*u + 93*u**4 - 3 - 95*u**4 + 4 - 4*u + u**2 + u**3. Let j(t) = 9*t**4 - 2*t**3 - 7*t**2 + 4*t - 4. Let z(b) = -20*c(b) - 5*j(b). Factor z(f).
-5*f**2*(f - 1)*(f + 3)
Let t(y) be the third derivative of y**5/100 + 279*y**4/40 + 139*y**3/5 - 638*y**2. Let t(s) = 0. What is s?
-278, -1
Let x(d) = 13*d**2 - 7346*d - 16. Let k(w) = -11*w**2 + 7347*w + 12. Let s(b) = -4*k(b) - 3*x(b). Determine o, given that s(o) = 0.
0, 1470
Let y be 2 + 1 + (-84)/32. Let o be (20 - 3140/160) + (2 - 2). Factor y*v**2 + o*v - 3/8 - 3/8*v**3.
-3*(v - 1)**2*(v + 1)/8
Factor 50/3*d**4 + 6520*d**3 + 307328/3 + 1905128/3*d**2 - 511168*d.
2*(d + 196)**2*(5*d - 2)**2/3
Determine a, given that 118/3*a**3 - 38*a**2 + 116/3 - 2/3*a**4 - 118/3*a = 0.
-1, 1, 58
Let k = 3356 - 3350. Let h(s) be the second derivative of -3/20*s**5 + 0 + 2*s**3 - 1/4*s**4 + k*s**2 + 19*s. Determine q so that h(q) = 0.
-2, -1, 2
Suppose 18 = 41954*s - 41945*s. Let q(z) be the first derivative of 3/2*z + 1/6*z**3 - z**s - 41. Find i such that q(i) = 0.
1, 3
Let z = 329238 + -329238. Factor 6/11*c**2 + z - 12*c.
6*c*(c - 22)/11
Let z be 24/(-138)*414/(-36). Let x(j) be the third derivative of -1/42*j**4 + 0 + 1/420*j**5 + 1/210*j**6 + 0*j - 37*j**z - 1/42*j**3. Factor x(b).
(b - 1)*(b + 1)*(4*b + 1)/7