) = 4*f**3 + f**2 + f. Let n be 225/54 - 4/24. Let u(t) = 5*t**3 + 2*t**2 + t. Let y(p) = n*a(p) - 3*u(p). Determine l, given that y(l) = 0.
0, 1
Let q(l) be the first derivative of l**3/3 + 26*l**2 + 352*l - 1170. Find s such that q(s) = 0.
-44, -8
Let c(q) be the second derivative of 0 - 2*q**2 + 5/84*q**4 + 80*q + 34/21*q**3. Factor c(a).
(a + 14)*(5*a - 2)/7
Suppose 89*o + 30 = 3*m + 92*o, -3*m - 2*o = -20. Determine z, given that m + 24/7*z**4 - 15/7*z**5 + 117/7*z**3 + 24/7*z + 102/7*z**2 = 0.
-1, -2/5, 0, 4
Let y(i) be the second derivative of 18*i**4 - 7/10*i**6 - 79*i + 0 - 3/4*i**5 - 38*i**3 + 24*i**2. Suppose y(g) = 0. What is g?
-4, 2/7, 1, 2
Suppose -9*l = 2*u - 14*l - 97, -90 = -2*u - 2*l. Factor -16 + 23*x + u*x**2 - 8*x - 45*x**2.
(x - 1)*(x + 16)
Let n(r) = r**2 - 28. Let b be n(-6). Let d be (5 + (-68)/b)/((-2)/6). Factor 9*q + 11/4*q**3 - d*q**2 + 2.
(q - 2)**2*(11*q + 2)/4
Let q = 19799/2 - 9897. Let l(b) be the first derivative of -11/3*b**3 + 3/4*b**4 + 3*b + q*b**2 - 38. Factor l(u).
(u - 3)*(u - 1)*(3*u + 1)
Let z(w) = 41*w**2 + 92*w - 12. Let r be 3/(-1) + 4/(-4). Let d(f) = -81*f**2 - 185*f + 26. Let s(g) = r*d(g) - 9*z(g). Factor s(y).
-(y + 2)*(45*y - 2)
Let a = 771606243/321660526 + 5/943286. Let i = a - -2/1705. Let i - 9/5*u - 3/5*u**2 = 0. What is u?
-4, 1
What is h in -1/3*h**2 + 638/3*h + 0 = 0?
0, 638
What is s in 729*s - 1/4*s**2 - 531441 = 0?
1458
Suppose 0 = -31*m + 28*m + 21. Suppose 70 = 4*f + 2*q, -3*f - 4*q + m = -58. Let -129*i - 20*i**4 + 129*i - f*i**3 + 3*i**2 + 2*i**2 = 0. What is i?
-1, 0, 1/4
Suppose -8*j + 3*j + 160 = i, 190 = 5*j - 5*i. Let u = -31 + j. Factor u*c - 1597*c**3 - 4*c**2 + 4 + 0*c**2 + 1595*c**3.
-2*(c - 1)*(c + 1)*(c + 2)
Let z(k) = -5*k**4 - 11*k**3 + 279*k**2 - 521*k + 258. Let c(m) = -21*m**4 - 45*m**3 + 1116*m**2 - 2085*m + 1035. Let g(w) = 2*c(w) - 9*z(w). Factor g(h).
3*(h - 7)*(h - 1)**2*(h + 12)
Let y(u) be the second derivative of -3*u - 1/7*u**2 + 1/10*u**5 + 1/294*u**7 + 3/14*u**3 - 14 - 1/35*u**6 - 4/21*u**4. Determine a, given that y(a) = 0.
1, 2
Let g(k) = -134*k**2 + 685*k - 11. Let s(h) = 73*h**2 - 343*h + 6. Let a(t) = 6*g(t) + 11*s(t). Let a(d) = 0. What is d?
0, 337
Let f be ((-8)/(-110))/((-546)/(-143)). Let d(w) be the third derivative of 0*w**3 + f*w**5 + 1/210*w**6 - 2/735*w**7 + 0 + 0*w**4 + 0*w + 10*w**2. Factor d(g).
-4*g**2*(g - 2)*(g + 1)/7
Let z(u) = -56*u**2 - 6*u. Suppose -85*l + 192 = -53*l. Let y(t) = t**3 - 56*t**2 - 9*t. Let m(s) = l*z(s) - 4*y(s). Factor m(d).
-4*d**2*(d + 28)
Let h be -5 - 352/(-60) - 47/235. Let y(p) be the second derivative of 3*p**2 - 1/6*p**4 - h*p**3 - 15*p + 0. What is m in y(m) = 0?
-3, 1
Let y(a) be the first derivative of -3*a**4/20 - 1713*a**3/5 - 2934369*a**2/10 - 558508233*a/5 + 6404. Determine d, given that y(d) = 0.
-571
Let w(l) be the first derivative of 0*l**2 + 6/7*l**5 + 3/2*l**4 + 6/7*l**3 - 23 + 1/7*l**6 + 0*l. Suppose w(f) = 0. Calculate f.
-3, -1, 0
Let d(h) be the first derivative of 188/5*h**5 - 309*h**4 + 29 - 242*h**2 + 1540/3*h**3 - 4/3*h**6 + 0*h. Solve d(r) = 0 for r.
0, 1/2, 1, 11
Solve 152 + 118 - 374 + 372 - 4*o**2 + 264*o = 0.
-1, 67
Let r(l) be the first derivative of -l**5/15 + 68*l**4/3 - 2085*l**3 + 6075*l**2 + 11214. Find a, given that r(a) = 0.
0, 2, 135
Let n(h) be the first derivative of -1/6*h**3 + 82 + 17/4*h**2 - 8*h. Factor n(a).
-(a - 16)*(a - 1)/2
Let f = 2/299 + 1471/3588. Let m = f + -1/60. Factor -m*i**4 - 2/5*i**5 - 2/5 - 2/5*i + 4/5*i**3 + 4/5*i**2.
-2*(i - 1)**2*(i + 1)**3/5
Let c(u) be the second derivative of -29*u**4/24 - 607*u**3/12 + 21*u**2/2 + 2506*u. Factor c(y).
-(y + 21)*(29*y - 2)/2
Let k(g) = -2*g**3 + 15*g**2 + 30*g - 21. Let f be k(9). Solve 34445 - 830*s - f*s**2 - s**2 - 4*s**2 + 19*s**2 - 3*s**2 = 0.
83
Suppose 5*z - 3*z = 25*v - 24*v, -z = v. Let m(n) be the third derivative of 1/6*n**3 + v + 0*n - 44*n**2 - 1/96*n**4 - 1/480*n**5. Solve m(a) = 0 for a.
-4, 2
Let b(o) be the third derivative of 0*o**3 + 4/105*o**5 + 0 + 277*o**2 + 1/420*o**6 + 4/21*o**4 + 0*o. Factor b(c).
2*c*(c + 4)**2/7
Let m be (14/(-5))/(-2) - (-7)/1015*29. Factor 4/5 + m*d**2 - 2/5*d**3 - 2*d.
-2*(d - 2)*(d - 1)**2/5
Let v(c) = c**2 - 2*c - 63. Let w be v(12). Let l be (w/(-12) - (-6)/8) + 7. Let 1/6*m**l + 25/2*m + 5/2*m**2 + 125/6 = 0. What is m?
-5
Factor 488*m**2 - 16477*m + 10252*m - 53311*m - m**3.
-m*(m - 244)**2
Suppose 0 = 15*t - 279*t - 53*t + 634. Determine v, given that -1/3*v**3 + 98/3 - 7*v - 4*v**t = 0.
-7, 2
Let m(t) be the second derivative of t**7/42 + 77*t**6/30 - 161*t**5/20 - 233*t**4/12 + 160*t**3/3 + 158*t**2 + 749*t. Factor m(k).
(k - 2)**2*(k + 1)**2*(k + 79)
Suppose 22069992/5*d - 1368668*d**2 - 223458/5*d**3 - 8/5*d**5 - 2328/5*d**4 - 16941456/5 = 0. Calculate d.
-98, 3/2
Let d(f) be the second derivative of 1/4*f**3 - f - 15/16*f**2 + 168 + 1/32*f**4. Factor d(t).
3*(t - 1)*(t + 5)/8
Let n = 267 + -71. Suppose -z**3 + n - 24*z**2 - 46 + 15*z - 4*z**3 + 8*z**3 = 0. Calculate z.
-2, 5
Suppose -7*w = -12*w + 3*h - 18, h - 6 = -3*w. Let x(r) be the second derivative of 16*r + w + 1/2*r**4 - 1/10*r**5 + r**2 - r**3. Factor x(u).
-2*(u - 1)**3
Let n(h) = -5*h**2 - 64*h - 30. Let r be n(-12). Find l, given that 51*l + 515*l**2 + 30 - 7*l + r - 519*l**2 = 0.
-1, 12
Let g = -2/2827 + 2839/16962. Let b(a) be the third derivative of -g*a**5 + 1/6*a**4 + 0*a - 7/60*a**6 + 0*a**3 + 0 - 9*a**2. Factor b(n).
-2*n*(n + 1)*(7*n - 2)
Let n be 9/((-9)/4)*25/(-20). Find j such that -3*j - 365*j**4 - 3*j**3 + 374*j**4 - 9*j**2 - 3*j**n + 9*j**5 = 0.
-1, -1/2, 0, 1
Let f(d) = -5606*d + 56062. Let m be f(10). Let g = -2021/9 - -225. Factor -g*p**3 + 16 - 32/3*p - 44/9*p**m.
-4*(p - 1)*(p + 6)**2/9
Let a(t) be the first derivative of t**4/4 - 9*t**2/2 - 1007. Suppose a(c) = 0. Calculate c.
-3, 0, 3
Let x(t) = -3*t**2 + 607*t + 408. Let d be x(203). Let a be 40/18 - (-2)/(-9). Factor -5/3*m**a - 11/3*m - d.
-(m + 1)*(5*m + 6)/3
Suppose 0 = 5*d + 2*a - 2501 - 4818, 2*d + a - 2927 = 0. Let y be 1/2*3 - d/1172. Factor 1/2*w**2 - w**3 - 9/4 - y*w**4 + 3*w.
-(w - 1)**2*(w + 3)**2/4
Find v such that -45/7*v + 79/7*v**3 + 0 + 25/7*v**4 - 2/7*v**5 - 57/7*v**2 = 0.
-3, -1/2, 0, 1, 15
Let d = 11495 + -34483/3. Let q be (-1 - 141/(-27)) + -2. Find c, given that q*c + 2/3 + d*c**2 = 0.
-3, -1/3
Let r = -9 - -30. Factor 4*j - 337*j**2 + 673*j**2 + r*j - 341*j**2.
-5*j*(j - 5)
Let d(w) be the third derivative of -8/3*w**3 + 2*w**2 + 0 - 1922/105*w**7 + 82*w - 1213/15*w**5 + 22*w**4 + 341/5*w**6. Determine c so that d(c) = 0.
2/31, 1
Let n be 2/(-4)*-12 - 2181/3. Let l = n - -5053/7. Find y such that -l*y + 3/7 + 6/7*y**3 - 3/7*y**2 = 0.
-1, 1/2, 1
Let h(t) = -5*t**2 - 23*t - 8. Let d be h(-5). Let w be (d/15)/(26/(-78)). Determine v so that 6/5*v**2 - 24/5*v + w = 0.
1, 3
Let l(b) = -b**2 + 18*b - 17. Let f be l(17). Suppose k - 2 = -f*k. Factor -s**k + 16*s**2 + 5*s**2 + 5*s**4 + 0*s**2 - 25*s**3.
5*s**2*(s - 4)*(s - 1)
Factor 103*s**2 - 44*s**2 - 2577*s + 117*s**2 + 2505*s + 10*s**3.
2*s*(s + 18)*(5*s - 2)
Let s = 212 - 206. Let g(y) = -5*y**4 - 10*y**3 - y**2 + 4*y + 6. Let r(u) = u**2 + u - 1. Let c(v) = s*r(v) + g(v). Find t, given that c(t) = 0.
-2, -1, 0, 1
Let j(o) be the second derivative of 7*o**4/36 + 776*o**3/27 - 74*o**2/9 - 3830*o. Factor j(d).
(d + 74)*(21*d - 2)/9
Let i(m) be the first derivative of -10/33*m**3 - 4/55*m**5 + 1/4*m**4 - 40 + 3/22*m**2 + 0*m. Factor i(g).
-g*(g - 1)**2*(4*g - 3)/11
Let t(f) be the second derivative of 2/5*f**5 + 0 - 20/3*f**3 + 1/84*f**7 + 12*f**2 + f**4 + 197*f - 3/20*f**6. Suppose t(p) = 0. Calculate p.
-2, 1, 2, 6
Let b(s) be the second derivative of 0 + 1/8*s**4 + 95*s - 9*s**3 + 0*s**2. Factor b(h).
3*h*(h - 36)/2
Let j(n) be the third derivative of -n**7/1575 + n**6/180 - n**5/150 - n**4/36 + 4*n**3/45 + 3*n**2 - 129. Determine v, given that j(v) = 0.
-1, 1, 4
Suppose 0 = 9*k - 15*k - 5*k + 33. Let p(q) be the first derivative of 7*q**k - 14 + 6*q + 3/2*q**4 + 21/2*q**2. Factor p(l).
3*(l + 1)*(l + 2)*(2*l + 1)
Suppose -4/5*v**5 + 0 + 788/5*v**2 + 156*v**4 + 1572/5*v**3 + 0*v = 0. Calculate v.
-1, 0, 197
Let l be 145/(-58) + (-1511)/6. Let y = l - -255. Factor 4/9*v**2 - y + 10/9*v.
2*(v + 3)*(2*v - 1)/9
Let w be (-6 - 981/(-30)) + 2/2