(u + 2)/6
Factor 33*n + 124*n**2 - 366*n**2 + 21*n + 123*n**2 - 53 + 118*n**2.
-(n - 53)*(n - 1)
Let n(d) be the third derivative of -1/900*d**6 + 0*d + 1/45*d**5 - 7/45*d**4 + 11*d**2 + 8/15*d**3 - 8. Find b, given that n(b) = 0.
2, 6
Let r(f) be the third derivative of 5/126*f**5 + 69*f**2 + 2/63*f**4 + 3/140*f**6 + 0*f + 1/3528*f**8 + 0 + 11/2205*f**7 + 0*f**3. Factor r(d).
2*d*(d + 1)**3*(d + 8)/21
Factor -154*a - 21*a + 396*a + 8211 + 12914 + 429*a + 5*a**2.
5*(a + 65)**2
Let d(y) = -2*y**2 - 576*y + 9238. Let n(r) = -1671 + 2612 - r**2 - 43*r + 2139 - 149*r. Let l(b) = 4*d(b) - 11*n(b). What is v in l(v) = 0?
32
Suppose 3*v - 2131 = -2125. Factor 2*o**2 - 1 - 16 - 10 + 12*o**v + 8*o + 3 + 2*o**3.
2*(o - 1)*(o + 2)*(o + 6)
Let d(q) = 7 + 58*q - 22 + q**3 - 2*q**2 - 14*q**2. Let n be d(5). Factor -1/3*c**3 + n - c + 4/3*c**2.
-c*(c - 3)*(c - 1)/3
Let n(y) = -y**2 - 9*y - 14. Let l be n(-6). Suppose -3*x + l*c = -985, 3*c - 5*c = -10. Find z, given that -7*z**4 - 9*z**3 + x - 2*z**2 - 335 = 0.
-1, -2/7, 0
Suppose -171*n + 746 = 233. Factor 0 - 3/8*w - 1/2*w**2 - 1/8*w**n.
-w*(w + 1)*(w + 3)/8
Suppose 0 = 3*v - 2 - 19. Let y(w) = -3*w**3 + 28*w**2 + 115*w + 139. Let x(r) = 4*r**3 - 42*r**2 - 173*r - 209. Let s(k) = v*y(k) + 5*x(k). Factor s(g).
-(g + 2)*(g + 6)**2
Let u(j) be the first derivative of 9*j**5/20 - 63*j**4/8 + 29*j**3/3 + 7*j**2/4 - 13*j/4 - 2463. Find i such that u(i) = 0.
-1/3, 1/3, 1, 13
Find g, given that 12/5*g**5 + 591/5*g**3 + 972/5*g - 144/5*g**4 - 1107/5*g**2 - 324/5 = 0.
1, 3/2, 2, 6
Let p(y) be the second derivative of -y**4/102 + 1885*y**3/51 + 1886*y**2/17 - y - 4847. Solve p(h) = 0 for h.
-1, 1886
Let t(v) = -2*v**2 + v + 12. Let j be 184/(-24) + 7 - 2/(-3). Let g be t(j). Solve 12 + 3*s**2 + 15*s - 5*s + 8*s + g = 0 for s.
-4, -2
Suppose -3*v - 15 = -5*r, 3*r = v + 8 - 3. Suppose 2*h - 16 = -2*h. Solve -2/3*i**h + 0*i + 0*i**2 + r*i**3 + 0 + 2/3*i**5 = 0 for i.
0, 1
Suppose 8*f = 5*s, 121*f = 126*f + 5*s. Factor f + 2/7*a**3 + 16/7*a**2 - 18/7*a.
2*a*(a - 1)*(a + 9)/7
Let y = 66 - 63. Let z be 4/y*18/8. Let -2*q**3 + 5*q**4 - 20*q**2 - q**3 - 8*q**3 + 10*q + q**z + 15 = 0. Calculate q.
-1, 1, 3
Let r(f) be the first derivative of f**6/2 - 266*f**5/5 - 97*f**4/4 + 716*f**3/3 - 178*f**2 - 1708. What is c in r(c) = 0?
-2, 0, 2/3, 1, 89
Let w(f) be the second derivative of f**4/4 - 50*f**3 + 2457*f**2/2 + 3857*f. Suppose w(l) = 0. Calculate l.
9, 91
Factor 2/13*q**3 + 1296/13 - 648/13*q - 4/13*q**2.
2*(q - 18)*(q - 2)*(q + 18)/13
Find w such that -1/3*w**4 - 41/3*w**3 - 101*w**2 + 6076/3 + 413/3*w = 0.
-31, -7, 4
Let f(t) be the first derivative of 8/3*t - 1/18*t**3 + 17 - 1/2*t**2. Factor f(m).
-(m - 2)*(m + 8)/6
Let j(n) = 4*n + 48. Let d be j(-11). Find a such that d - 87*a**2 + 86*a**2 - 3*a + 3*a = 0.
-2, 2
Suppose 4*z - 3*v + 8*v = -10, 0 = 4*z - 4*v - 44. Let h(c) be the first derivative of 21/2*c**2 - 9*c - z*c**3 + 3/4*c**4 + 6. Solve h(b) = 0.
1, 3
Let t(r) = r**2 + 25*r + 17. Let f(o) = -2*o - 3. Let j(n) = -n - 3. Let a(v) = -6*f(v) + 4*j(v). Let q(l) = -7*a(l) + 2*t(l). Factor q(c).
2*(c - 4)*(c + 1)
Let v(z) = -356*z + 2136. Let x be v(6). Let f(l) be the second derivative of 0 + 24*l + 1/36*l**4 + x*l**2 + 2/9*l**3. Suppose f(m) = 0. Calculate m.
-4, 0
Let t(n) be the first derivative of -3/2*n**2 + 11/12*n**3 - 11 - 7/20*n**5 + 3/4*n**4 - n. Determine f so that t(f) = 0.
-1, -2/7, 1, 2
Let l(a) be the second derivative of a**6/15 + 17*a**5/10 + 5*a**4/2 - 17*a**3/3 - 16*a**2 - 1766*a - 2. Factor l(m).
2*(m - 1)*(m + 1)**2*(m + 16)
Solve -117/7*b + 222/7 + 3/7*b**2 = 0 for b.
2, 37
Let o(f) = -2*f**2 - 5*f - 3. Suppose 2*k - 6 = -7*b + 3*b, -b + 15 = 5*k. Let x(v) = 3*v**2 + 9*v + 6. Let j(r) = k*x(r) + 5*o(r). Factor j(h).
-(h - 3)*(h + 1)
Factor 372*n + 6*n**2 - 3 - 109*n**3 + 151 - 37*n**3 - 2*n**4 + 144 + 70*n.
-2*(n - 2)*(n + 1)**2*(n + 73)
Let r(y) be the first derivative of -y**6/1620 + y**5/27 - 19*y**4/108 + 77*y**3/3 - 211. Let o(v) be the third derivative of r(v). Let o(p) = 0. What is p?
1, 19
Find q, given that 80 + 46/7*q**2 - 2/7*q**3 - 292/7*q = 0.
4, 5, 14
Let u be (-20)/(77/(7238/(-705))). Find g such that -16/15*g**2 - 22/15*g**3 + 4/15*g**4 + 32/15 + 2/15*g**5 + u*g = 0.
-4, -1, 2
Let j(z) be the second derivative of z**6/135 + 2*z**5/15 - z**4/18 - 34*z**3/27 + 8*z**2/3 - 401*z. Suppose j(d) = 0. Calculate d.
-12, -2, 1
Let a(x) be the first derivative of -3*x**4/4 - 64*x**3 - 153*x**2/2 + 2268*x - 7398. Suppose a(j) = 0. Calculate j.
-63, -4, 3
Suppose -2*i - 79 = -181. Suppose -720*h - 48*h**3 - 87*h**2 - 3*h**4 - 32*h**3 - 334*h**2 - h**4 - 324 - i*h**2 = 0. What is h?
-9, -1
Let d(p) = 75*p**2 + 9*p + 6. Let l be d(-1). Factor l*m**2 + 180*m - 12 + 5*m**4 - 252*m**2 + 95*m**2 - 88.
5*(m - 2)**2*(m - 1)*(m + 5)
Let o(a) be the second derivative of 0*a**2 + 3/28*a**4 + 3/35*a**5 - 97*a - 9/7*a**3 + 0 - 1/70*a**6. Factor o(w).
-3*w*(w - 3)**2*(w + 2)/7
Let g(b) = -b**4 + b**3 - b**2 - b - 9. Let w(x) = -6*x**4 - 19*x**3 - 16*x**2 + 19*x + 11. Let q(f) = -g(f) + w(f). Factor q(c).
-5*(c - 1)*(c + 1)*(c + 2)**2
Let k = 175 - 115. Suppose 24 + 26 - 5*v + 13*v + 2*v**2 - k = 0. Calculate v.
-5, 1
Let t(x) be the second derivative of -x**5/80 + 103*x**4/16 - 10609*x**3/8 + 1092727*x**2/8 + 1204*x. Suppose t(u) = 0. Calculate u.
103
Let w be 1*(-15)/(-18) - (-14225)/30. Suppose 432*f - w*f + 129 = 0. Determine g, given that -4*g**5 + 17/4*g + 3/4 - 3/4*g**2 - 73/4*g**f + 18*g**4 = 0.
-1/4, 1, 3
Let n = 704 - 578. Factor 75*d + 10*d**2 + n*d**3 + 123*d**3 - 380*d**3 + 126*d**3.
-5*d*(d - 5)*(d + 3)
Let i(b) = -b**2 - 9*b - 15. Let o be i(-6). Factor 105*m - 5*m + 5*m**2 - 1991 + 99*m**2 + 1991 + 4*m**o.
4*m*(m + 1)*(m + 25)
Let s(y) be the first derivative of 3/2*y**3 - 6*y + 3*y**2 + 0*y**4 - 3/20*y**5 - 1. Let i(r) be the first derivative of s(r). Factor i(f).
-3*(f - 2)*(f + 1)**2
Let p(w) be the first derivative of 7/6*w**3 + 290 + 9/2*w + 15/4*w**2 + 1/8*w**4. Factor p(r).
(r + 1)*(r + 3)**2/2
Let v(m) = 252*m + 2522. Let u be v(-10). Let y(a) be the first derivative of -12/11*a - 4/33*a**3 + 4 - 19/11*a**u + 3/22*a**4. Factor y(z).
2*(z - 3)*(z + 2)*(3*z + 1)/11
Find i, given that 329*i + 5*i**4 - 150*i**3 + 1135*i**2 - 516*i - 170*i - 977*i - 376*i = 0.
0, 2, 9, 19
Let k = 110593/32 - 3456. Let n(g) be the third derivative of k*g**4 - 1/80*g**5 - 15*g**2 + 1/4*g**3 + 0*g + 0. Factor n(r).
-3*(r - 2)*(r + 1)/4
Let g be (-38)/6*(-14 + (-3 - -14)). Factor g - m**2 + 28 - 37 + 9*m.
-(m - 10)*(m + 1)
Let w = -228 - -140. Let f = w - -92. Solve 197 + 2*q**5 - 197 - f*q**4 = 0.
0, 2
Let h(a) = -325*a - 1948. Let u be h(-6). Let s(j) be the first derivative of 24*j + 4/3*j**3 + 6 - 10*j**u. Factor s(l).
4*(l - 3)*(l - 2)
Determine t, given that 8188/7*t + 4182025/7*t**4 + 4/7 + 8372230/7*t**3 + 4198389/7*t**2 = 0.
-1, -2/2045
Let f be (-5)/2 - (-18 + (-270)/(-20)). Suppose -10*u + f = -28. Factor -2/5*j**u + 0 - 2/5*j**4 + 2/5*j**2 + 2/5*j.
-2*j*(j - 1)*(j + 1)**2/5
Suppose 3*g + 2*d = -2*g - 78, d = -4. Let j be 28/g - 5*(2 - 3). Suppose 5*r**4 - 59*r**j - r**5 + 55*r**3 + r**4 - r**5 = 0. What is r?
0, 1, 2
Let c(r) be the first derivative of 583*r - 2*r**3 + 3*r**3 - 220*r - 3 + 33*r**2. Find w, given that c(w) = 0.
-11
Let w = 2/1485 + 491/2970. Let v = 517/6 + -86. Find m, given that 1/2*m - v + w*m**3 - 1/2*m**2 = 0.
1
Let k be (1/1)/(3/63). Let u be k/14*3/((-3)/(-2)). Find q, given that -6 - u*q**2 - 5*q - q + 15 = 0.
-3, 1
Factor 3288*l**2 - 17717*l + 606*l - 171*l**3 + 19200 - 5209*l + 3*l**4.
3*(l - 20)**2*(l - 16)*(l - 1)
Let a = -135157/10 + 67586/5. Suppose 1/2*c**5 + 0 + 3/2*c**4 - a*c**2 - 1/2*c**3 + 0*c = 0. What is c?
-3, -1, 0, 1
Find a, given that 198 - 9*a + 89 + 134*a + 49 - 4*a**3 + 51*a - 4*a**2 = 0.
-6, -2, 7
Let p(q) be the third derivative of 25*q**8/504 - 24*q**7/35 + 182*q**6/45 - 592*q**5/45 + 76*q**4/3 - 256*q**3/9 - q**2 + 1496*q. Solve p(o) = 0 for o.
16/25, 2
Determine a, given that 90*a**2 - 24 - 60*a - a**3 - 22*a**4 + 7*a**3 + 9*a**3 + a**4 = 0.
-2, -2/7, 1, 2
Find t such that 7717 - 25*t + 4999 - 15*t - 4*t**3 + 380*t + 456*t**2 - 548*t**2 = 0.
-17, 11
Let j = 527 + -521. Suppose 10 = 2*p, 4*p = 3*b + 5 + j. What is n in 14/13*n**4 + 4/13*n**2 + 1