4*p**5 + 2/3*p**6 + 0*p**2. Factor o(q).
5*q**2*(q + 1)*(4*q + 1)
Suppose -64 + 328/3*u - 2/3*u**4 - 52/3*u**3 - 82/3*u**2 = 0. What is u?
-24, -4, 1
Let f(a) be the second derivative of a**5/5 - 9*a**4 + 94*a**3/3 + 150*a**2 + 131*a - 1. Let f(p) = 0. Calculate p.
-1, 3, 25
Let f(k) be the second derivative of -11*k**6/90 - 533*k**5/48 + 595*k**4/72 + 1885*k**3/72 - 61*k**2/4 - 10455*k. Let f(u) = 0. What is u?
-61, -3/4, 2/11, 1
Let f = 117320 - 117318. Factor 2/7*j**f + 12/7 - 2*j.
2*(j - 6)*(j - 1)/7
Let x(j) be the second derivative of -j**6/10 - 63*j**5/10 + 241*j**4/4 + 141*j**3 - 4804*j. What is b in x(b) = 0?
-47, -1, 0, 6
Let v(f) be the first derivative of -2*f**5/45 - 49*f**4 + 1768*f**3/9 - 2654*f**2/9 + 590*f/3 - 11129. Find b, given that v(b) = 0.
-885, 1
Factor -24*w**2 + 4*w**4 + 113*w**2 - 2208*w + 99*w**2 + 68*w**3 + 1948*w.
4*w*(w - 1)*(w + 5)*(w + 13)
Let f be ((-12)/2 - -27) + -8. Let o be 57/f - (-33)/(-12 - -1). Factor -14/13*p**2 - 30/13*p - 2/13*p**3 - o.
-2*(p + 1)*(p + 3)**2/13
Factor 1/2*m**2 - 49 + 7/2*m.
(m - 7)*(m + 14)/2
Let b(c) = c**2 + 2*c - 1. Let s(d) = 94*d - 29*d - 33*d - 29*d + 5. Let y(a) = -b(a) + s(a). What is p in y(p) = 0?
-2, 3
Let z = -205825/3 + 411689/6. Factor -41/4*b + 13/4*b**3 + z - 1/4*b**4 + 3/4*b**2.
-(b - 13)*(b - 1)**2*(b + 2)/4
Let v(n) be the third derivative of n**6/120 - 152*n**5/5 + 1215*n**4/8 - 911*n**3/3 - 79*n**2 + 2*n - 1. Factor v(p).
(p - 1822)*(p - 1)**2
Factor 23/6 + 15*x**2 - 1/3*x**3 + 61/4*x.
-(x - 46)*(2*x + 1)**2/12
Let d(a) be the third derivative of 2*a**5/75 - 313*a**4/12 + 391*a**3/15 + 263*a**2. Factor d(p).
2*(p - 391)*(4*p - 1)/5
Suppose 1149 - 4761 = -6*r. Factor -138*i + 52*i**2 - 629*i**3 - 24 - 193*i**2 + r*i**3.
-3*(i + 1)*(i + 4)*(9*i + 2)
Let n(j) = -50*j**2 - 527*j + 3. Let i(d) = 51*d**2 + 529*d + 8. Let b(q) = -6*i(q) - 4*n(q). Suppose b(g) = 0. What is g?
-10, -3/53
Let h = 104736/7 + -14958. Factor -h*a + 3 + 9/7*a**2.
3*(a - 1)*(3*a - 7)/7
Let x = -2779 + 2782. Let q(p) be the first derivative of -2*p**2 + 4/5*p**5 - 6 + 0*p + p**4 - 4/3*p**x. Factor q(j).
4*j*(j - 1)*(j + 1)**2
Let x be 3/(-13)*(17280/162)/(-32). Find b such that -x*b**2 + 32/13*b - 6/13 = 0.
1/5, 3
Let c = 21651 + -21649. Let b(s) be the second derivative of -13*s + 0 + 1/2*s**c - 2/3*s**3 + 1/4*s**4. Solve b(i) = 0 for i.
1/3, 1
Let s(d) = d**5 - 3*d**4 + d**3 + 2*d**2 + d - 3. Let u(o) = -3*o**5 + 15*o**4 - 21*o**3 - 47*o**2 - 24*o + 12. Let m(b) = 4*s(b) + u(b). Factor m(x).
x*(x - 4)*(x + 1)**2*(x + 5)
Suppose -34*a - 15480 = 9*a. Let t be 10*((-12)/21)/(a/28). Factor 0 + t*m**3 + 0*m + 2/9*m**4 + 0*m**2.
2*m**3*(m + 2)/9
Let z(n) be the second derivative of -n**4/12 - 245*n**3/6 - 243*n**2 + 4*n - 178. Determine u so that z(u) = 0.
-243, -2
Let m = 1454 + -1448. Let n be (-53)/m - (-78 - -69). Let -50/3 - n*g**2 - 10/3*g = 0. Calculate g.
-10
Let c be 31/(-10)*1 - -6*(4389/(-252) + 18). Solve -64/5*o + c*o**4 - 16/5*o**3 + 48/5*o**2 + 32/5 = 0 for o.
2
Let d(q) be the second derivative of -q**6/10 - 201*q**5/20 - 33*q**4/2 - 2*q - 395. Determine v, given that d(v) = 0.
-66, -1, 0
Let w(p) = 1140*p + 1185. Let t(r) = -r**2 - 1716*r - 1778. Let n(y) = 5*t(y) + 7*w(y). Factor n(s).
-5*(s + 1)*(s + 119)
Factor -3480 - 3747*j**2 + 1063*j**2 + 3460*j - 5*j**3 + 826*j**2 + 483*j**2 + 525*j**2.
-5*(j - 2)**2*(j + 174)
Suppose -392 = 9*x - 23*x. Let m be (92/x - 3)*14/6. Factor -m*p**3 - 2/9*p**5 - 8/9*p**4 + 0 + 0*p + 0*p**2.
-2*p**3*(p + 1)*(p + 3)/9
Find p, given that -270*p**3 + 175*p - 80*p**2 - 90 - 235*p**3 + 500*p**3 = 0.
-18, 1
Find b such that 2/13*b**2 + 142578/13 + 1068/13*b = 0.
-267
Let w be (-9 - (-280)/30)*18 - (-64)/(-11). Factor 6/11*k + 0*k**2 - 4/11 - w*k**3.
-2*(k - 1)**2*(k + 2)/11
Suppose 5*o = -1 + 26. Factor o*q**4 - 7*q**3 - 2*q**3 - 5 + q**3 - 2*q**3 + 10*q.
5*(q - 1)**3*(q + 1)
Let s(z) be the first derivative of -6*z**2 - 3*z**3 + 12*z - 3/5*z**5 - 66 + 3*z**4. Suppose s(n) = 0. What is n?
-1, 1, 2
Let t(g) be the first derivative of -g**6/48 + 13*g**5/20 - 37*g**4/8 + 149*g**3/12 - 251*g**2/16 + 19*g/2 - 632. What is s in t(s) = 0?
1, 4, 19
Factor -231378*m - 928918*m**3 - 840462*m + 4625*m**2 + 928913*m**3 + 1067220.
-5*(m - 462)**2*(m - 1)
Let f(w) = 27*w - w**3 - 8 - 13*w**2 - 11 - 16 + 12. Let p(s) = -5*s**3 - 53*s**2 + 106*s - 93. Let m(t) = -18*f(t) + 4*p(t). Factor m(a).
-2*(a - 7)*(a - 3)*(a - 1)
Suppose 3*t = 15 + 15. Let p be t + (-3)/(-1) + (2 - -1). Factor -p*z - 8*z + 12 + 15*z**2 - 3*z**3 + 0*z.
-3*(z - 2)**2*(z - 1)
Let g(c) be the third derivative of -5*c**2 + 1/120*c**6 + 0*c - 1/10*c**5 + 3 + 3/8*c**4 + 0*c**3. Factor g(r).
r*(r - 3)**2
Suppose 6*x = 28 - 118. Let v(w) = w**3 + 17*w**2 + 30*w + 2. Let o be v(x). What is d in 1/2 + 1/2*d**5 - 5/4*d**o - 5/4*d**3 + 3/4*d**4 + 3/4*d = 0?
-2, -1, -1/2, 1
Let r be ((-11 - 7) + 18)/(-2). Let g(k) be the third derivative of 1/150*k**5 + r - 1/15*k**4 - 28*k**2 + 0*k**3 + 0*k. Factor g(j).
2*j*(j - 4)/5
Let j(y) be the second derivative of y**7/504 - 2*y**6/9 + 32*y**5/3 + 3*y**4/4 + 5*y**2/2 + 14*y. Let o(n) be the third derivative of j(n). Factor o(s).
5*(s - 16)**2
What is w in -3038359 + 543127 + 22*w + 5450*w - 3*w**2 = 0?
912
Determine c, given that 4598 + 44*c + 2/19*c**2 = 0.
-209
Let t(x) = -20*x**3 - 20*x**2 + 290*x - 410. Let f(y) = -9*y**3 - 10*y**2 + 145*y - 206. Let k(b) = 5*f(b) - 2*t(b). Determine u, given that k(u) = 0.
-7, 2, 3
Let y(o) be the first derivative of -4/5*o**5 - 20*o**3 + 0*o - 7*o**4 + 174 - 18*o**2. Find s such that y(s) = 0.
-3, -1, 0
Let t = 140428 - 140425. Find d such that 9/4*d**3 + 15/4*d**4 + 0 + 3/4*d**5 - t*d - 15/4*d**2 = 0.
-4, -1, 0, 1
Let u(b) = -b**2 + 11*b - 22. Let m(j) = j**3 - 4*j**2 + 5*j + 2. Let x be m(3). Let w be u(x). Factor 33*a + 0*a**2 - 24*a + 3*a**w.
3*a*(a + 3)
Let b be (-470)/(-90) + -2 - (-4)/(-18). Let q(r) = 61*r - 180. Let d be q(b). Suppose 2/3*p**2 + 2/9 + 2/9*p**d + 2/3*p = 0. Calculate p.
-1
Let j(l) be the first derivative of 0*l**2 + 1/51*l**6 + 0*l + 5/34*l**4 - 12/85*l**5 - 138 + 0*l**3. Find u, given that j(u) = 0.
0, 1, 5
Let f(u) be the first derivative of -4*u**5/5 - 44*u**4 + 4*u**3 + 260*u**2 - 352*u - 1068. Suppose f(y) = 0. What is y?
-44, -2, 1
Let r = 7215/58 - 21529/174. Factor r*o + o**2 + 0*o**3 - 1/3*o**4 + 0.
-o*(o - 2)*(o + 1)**2/3
Let f(a) be the first derivative of 119 + 8*a + 20*a**2 - 74/3*a**3 + 13/2*a**4. Factor f(m).
2*(m - 2)*(m - 1)*(13*m + 2)
Let d(t) be the first derivative of 0*t - 2/9*t**3 + 29/3*t**2 - 71. Factor d(n).
-2*n*(n - 29)/3
Let f(u) = -4044*u - 186024. Let q be f(-46). Factor -252/5*k**3 - 162/5*k**2 + 0*k + q - 98/5*k**4.
-2*k**2*(7*k + 9)**2/5
Suppose -4*d + 300 = -m, 7*d - 244 = 4*d - 4*m. Factor 4*r**2 + 8*r + d - 72 + 0*r.
4*(r + 1)**2
Let b(l) be the first derivative of 4*l**5/5 + 9*l**4/2 - 90*l**3 + 136*l**2 + 1056*l + 4299. Suppose b(q) = 0. What is q?
-11, -3/2, 4
Let i = -10285 + 10313. Let j(v) be the first derivative of -v**4 + i + 20/3*v**3 - 33/2*v**2 + 18*v. Factor j(y).
-(y - 2)*(2*y - 3)**2
Let x = -71597 + 71600. Let 5/7*u**4 + 1/7*u**5 + 5/7 + 1/7*u - 10/7*u**2 - 2/7*u**x = 0. Calculate u.
-5, -1, 1
Let i(l) = l**3 + 43*l**2 - 195*l - 8383. Let s be i(-43). Find q such that 3/4*q**s - 1/8*q**3 + 0 + 0*q = 0.
0, 6
Determine b, given that -145751 + 18443 - 603*b - 3*b**2 - 688*b - 572*b + 627*b = 0.
-206
Let k = 2/39349 + 39319/590235. Let w(i) be the third derivative of -21*i**2 - 1/12*i**4 - k*i**5 + 0*i - 1/60*i**6 + 0*i**3 + 0. Determine v so that w(v) = 0.
-1, 0
Let v(a) be the first derivative of -a**3/12 + 71*a**2/8 + 18*a - 122. Factor v(p).
-(p - 72)*(p + 1)/4
Let s(k) be the third derivative of k**6/600 - 2*k**5/3 + 185*k**4/6 - 600*k**3 - 360*k**2 + 3*k. Solve s(g) = 0.
10, 180
Solve -2/3*r**2 - 1591328/3 - 3568/3*r = 0 for r.
-892
Let y(k) be the third derivative of -5/2*k**4 + 0 - 7/30*k**5 + 0*k - 12*k**3 - 1/120*k**6 - 72*k**2. Solve y(p) = 0 for p.
-6, -2
Let j(h) be the first derivative of -4*h**5/5 - 50*h**4 - 828*h**3 + 400*h**2 + 10000*h - 4129. Solve j(n) = 0 for n.
-25, -2, 2
Let l(t) be the first derivative of 1/12*t**4 + 0*t + 76 - t**3 + 0*t**2. Suppose l(j) = 0. Calculate j.
0, 9
Let b(m) = -m - 6. Let w be b(-6). Let l(a) = 32*a*