408. Let k(y) = y**3 + 4*y**2 + 2*y + 1. Let r(j) = -24*k(j) + l(j). Solve r(c) = 0.
-256, -3
Let b(t) be the second derivative of t**4/6 + 148*t**3 + 43*t - 14. Factor b(s).
2*s*(s + 444)
Let p(j) be the first derivative of -15*j**4/2 + 65*j**3/3 - 5*j**2 - 1645. Let p(v) = 0. What is v?
0, 1/6, 2
Let w be (48/(-14) - -3)*12176/(-24). Let z = w - 217. Factor 2/7*j + 0 + 1/7*j**3 - z*j**2.
j*(j - 2)*(j - 1)/7
Let z be 2/(1 + 18/39). Let h = 713869 - 713867. Let z*x**h + 40/19*x - 22/19*x**3 - 8/19 = 0. What is x?
-1, 2/11, 2
Let u(l) = 4*l + 8. Let j be u(-3). Let t be -7*j/14*3/2. Suppose -6*d**t - 2*d**4 + 16*d**3 + 2 - 2*d**5 - 16*d + 6 + 2*d**2 = 0. Calculate d.
-2, 1
Let i(r) = -r**2 - 708*r - 712. Let f(t) = 4*t**2 + 2124*t + 2136. Let k(o) = -5*f(o) - 16*i(o). Factor k(w).
-4*(w - 178)*(w + 1)
Let v = -128845/3 - -42949. Find p, given that v - 2/9*p**2 + 4/9*p = 0.
-1, 3
Let n(p) be the first derivative of 10*p - 4*p**2 + 53 - 2/3*p**3. Suppose n(q) = 0. What is q?
-5, 1
Suppose f - 4*l = -26, 10 + 15 = 5*l. Let c(s) be the third derivative of -s**5/30 + 530*s**2. Let o(t) = t**2. Let u(v) = f*o(v) - 5*c(v). Factor u(j).
4*j**2
Let x(f) = f**2 - f. Let g = 0 - -1. Let y be 9/(-1) + (-15 - -11 - -4). Let m(k) = 6*k**2 + 51*k - 300. Let q(p) = g*m(p) + y*x(p). Factor q(d).
-3*(d - 10)**2
Let l = 2 - 8. Let f(b) = b**2 + 8*b - 15. Let p(i) = -3*i. Let y(z) = l*p(z) + 3*f(z). Determine d, given that y(d) = 0.
-15, 1
Let o(q) be the second derivative of -q**6/90 - 13*q**5/20 - 59*q**4/6 + 320*q**3/9 + 400*q**2 - 3285*q. Determine b so that o(b) = 0.
-20, -2, 3
Suppose 0 = -285*d - 112 + 244 + 723. Let h(f) be the first derivative of -d*f**2 - 8 - 9*f - 1/3*f**3. Determine n so that h(n) = 0.
-3
Determine f, given that 5*f**2 - 6*f**2 - 296*f - 7345 + 16*f - 12255 = 0.
-140
Let l(y) be the second derivative of y**6/105 + y**5/5 - 26*y**4/21 - 2*y**3/3 + 51*y**2/7 - 2*y - 1. Suppose l(f) = 0. Calculate f.
-17, -1, 1, 3
Let x(f) be the third derivative of -3/14*f**3 - 1/140*f**5 + 0 - 23*f**2 - f + 1/14*f**4. Factor x(k).
-3*(k - 3)*(k - 1)/7
Let i = 62 + -69. Let v(z) = -z - 2. Let a be v(i). Solve 8*j + 3*j**2 - 18 + a - 8 - 26*j = 0.
-1, 7
Factor -22/3 - 2/3*i**3 - 26/3*i**2 - 46/3*i.
-2*(i + 1)**2*(i + 11)/3
Let x be (0/1)/(731 + -682). What is u in -5/2*u - 3/4*u**2 + 3/2*u**3 + x - 1/4*u**4 = 0?
-1, 0, 2, 5
Let c be ((-102)/(-646))/(42/532). Factor 12/5 - 2/5*l**c + 2/5*l.
-2*(l - 3)*(l + 2)/5
Let m be (-48)/(-15) - (4/15)/(64/48). Let i(n) be the second derivative of 0 - 2/27*n**m + 10*n + 0*n**2 - 1/54*n**4. Factor i(v).
-2*v*(v + 2)/9
Let k be (-768)/(-72) + -13 - 31/(-12). What is r in -2*r + k*r**2 + 7/4 = 0?
1, 7
Let n be (40/32 - 0) + (-313)/252. Let s(a) be the third derivative of -28*a**2 - n*a**7 + 0*a + 1/36*a**5 + 1/72*a**6 + 0*a**3 - 5/72*a**4 + 0. Factor s(i).
-5*i*(i - 1)**2*(i + 1)/3
Let v(x) be the third derivative of x**7/105 - 7*x**6/60 - 19*x**5/10 + 455*x**4/12 - 392*x**3/3 - 319*x**2. Solve v(k) = 0 for k.
-8, 1, 7
Suppose 0 = -7*r - 7 + 28. Let c(u) = -u**3 + 6*u**2 - 6*u + 45. Let p be c(5). Let 12*k - p*k**3 + 2*k**4 - 5*k**4 - 43*k**3 + 74*k**r = 0. Calculate k.
-2, 0, 1
Let q be -6 - (-369)/(-1398)*(-884)/39. Let g = 273/2330 + q. Let 0*d**4 - 1/5*d**3 + 0*d**2 + 0 + 1/10*d**5 + g*d = 0. What is d?
-1, 0, 1
Suppose -356/3*t**3 - 20*t - 76/3*t**4 + 24 - 412/3*t**2 = 0. What is t?
-3, -1, 6/19
Determine l, given that 1/8*l**5 + 109/8*l + 35/4 - 19/4*l**3 - 1/4*l**4 + 1/2*l**2 = 0.
-5, -1, 2, 7
Let q(z) be the second derivative of -2*z + 1/84*z**4 + 6 + 1/7*z**2 + 1/14*z**3. Factor q(h).
(h + 1)*(h + 2)/7
Factor 400/13*m**3 + 2/13*m**5 + 0*m + 0 + 0*m**2 + 204/13*m**4.
2*m**3*(m + 2)*(m + 100)/13
Determine a so that -1/3 - 2/3*a**3 + 1/3*a**2 + 1/2*a + 1/6*a**5 + 0*a**4 = 0.
-2, -1, 1
Let w(n) be the second derivative of n**5/240 + 7*n**4/48 + n**3 - 22*n**2 - 17*n. Let i(r) be the first derivative of w(r). Let i(p) = 0. Calculate p.
-12, -2
Let i = 4610 + -4598. Let d(w) be the third derivative of i*w**2 - 2*w**3 + 1/20*w**5 + 0*w**4 + 0*w + 0. Suppose d(q) = 0. Calculate q.
-2, 2
Solve 1008/11 - 2/11*q**2 + 500/11*q = 0 for q.
-2, 252
Solve 1923/2*m - 3/4*m**2 - 1232643/4 = 0 for m.
641
Let y(v) be the first derivative of 1/2*v**6 - 6*v**4 + 0*v + 6/5*v**5 - 27/2*v**2 - 160 - 18*v**3. Solve y(q) = 0 for q.
-3, -1, 0, 3
Let v(u) be the first derivative of -u**4/2 + 476*u**3/3 + 1455*u**2 + 4392*u - 7163. What is t in v(t) = 0?
-3, 244
Let m be 26 - (-506)/(-53 - -31). Let b = 2 + -2. Factor -m*w**2 + 0 + 3/4*w**3 + b*w.
3*w**2*(w - 4)/4
Factor 1/5*k**3 + 16/5*k**2 + 3*k + 0.
k*(k + 1)*(k + 15)/5
Let p(m) be the first derivative of m**5/630 - m**4/28 - 10*m**3/63 - 24*m**2 - 31. Let f(i) be the second derivative of p(i). Factor f(g).
2*(g - 10)*(g + 1)/21
Factor 1/8*o**4 - 1/4 + 5/8*o - 1/8*o**3 - 3/8*o**2.
(o - 1)**3*(o + 2)/8
Let r = -35 + 43. Factor 20*n**2 - 20 + 4*n + 4*n**3 - r*n + 0 + 0*n**3.
4*(n - 1)*(n + 1)*(n + 5)
Suppose 380/3*k**3 + 12*k**2 - 17/3*k + 1/3 - 400/3*k**4 = 0. Calculate k.
-1/4, 1/10, 1
Find c, given that -20*c**3 - 198*c**2 - 50*c + 106 + 300*c - 42*c**3 - 118 + 22*c**3 = 0.
-6, 1/20, 1
Let f = 9871 - 108557/11. Solve 0 - 2/11*w**4 + 18/11*w**3 - 40/11*w**2 + f*w = 0 for w.
0, 1, 2, 6
Let b be ((-5472)/126)/38*(-8)/64. Factor -6/7*h**2 + 0 - b*h**3 - 8/7*h.
-h*(h + 2)*(h + 4)/7
Let p(h) = -h**3 - 3*h**2 - h + 2. Let v(a) = 30*a**2 - 155*a - 430. Let y(m) = 5*p(m) - v(m). Solve y(g) = 0.
-11, -2, 4
Suppose -2*g - 2*r + 71 + 29 = 0, 2*g + r = 98. Factor -g*m - 95 - m**2 + 126*m - 62*m + 31.
-(m - 8)**2
Let h(f) be the first derivative of f**4/12 - 52*f**3/9 - f**2/6 + 52*f/3 - 1027. Factor h(o).
(o - 52)*(o - 1)*(o + 1)/3
Let a(c) be the first derivative of -2*c**5/5 - 29*c**4/2 + 188*c**3/3 - 64*c**2 - 12437. Suppose a(r) = 0. Calculate r.
-32, 0, 1, 2
Let a(g) be the first derivative of -4*g**5/5 - 19*g**4 - 24*g**3 + 2938. Suppose a(j) = 0. What is j?
-18, -1, 0
Let q(i) = 2*i - 19 - 12*i**2 + 5*i**2 + 2*i**2 + 6*i**2. Let c be q(-7). Factor -23 + 37 - 10 - c + 3*p**2.
3*(p - 2)*(p + 2)
Let t(r) be the second derivative of 17*r**5/100 - r**4/20 - 49*r**2 + 27*r. Let a(i) be the first derivative of t(i). Factor a(b).
3*b*(17*b - 2)/5
Let g(y) be the third derivative of -y**7/42 - 19*y**6/24 + 5*y**5/3 + 1405*y**2. Factor g(v).
-5*v**2*(v - 1)*(v + 20)
Let v(w) = w**3 + 22*w**2 - w + 32. Suppose -66 = -5*h + 8*h. Let o be v(h). Factor 2*c**5 - 4*c**5 + o*c**3 + 2*c**4 - 52*c**3 - 2*c**2.
-2*c**2*(c - 1)**2*(c + 1)
Factor 68*q**3 + 7*q**2 - 19*q**3 + 9*q - 26*q**3 - 24*q**3 - q.
-q*(q - 8)*(q + 1)
Factor 8*o**2 + 2*o**2 + 749*o - 257 - 183 - 170 + 466*o.
5*(o + 122)*(2*o - 1)
Let s = -3/362 - -1819/1086. Let b(p) be the first derivative of 16 - 125*p - 25*p**2 - s*p**3. Factor b(h).
-5*(h + 5)**2
Factor -13091 + 140*l**2 - 272*l - 2*l**3 + 13091.
-2*l*(l - 68)*(l - 2)
Suppose 33*w + 155 = 254. Let g(n) be the third derivative of 0 + 0*n**5 + 23*n**2 - 1/210*n**6 + 0*n + 0*n**w + 2/21*n**4. Factor g(l).
-4*l*(l - 2)*(l + 2)/7
Let a(n) = 5*n + 133. Let q be a(-26). Let k be 153/(-68)*(-14)/q. Factor 0*l - 3*l**2 + 0 - 27/2*l**3 - k*l**4.
-3*l**2*(l + 1)*(7*l + 2)/2
Factor -5/6*j**3 - 82810*j + 455*j**2 + 15071420/3.
-5*(j - 182)**3/6
Let j = 154 - 150. Suppose -1285*w - 4*w**j + 10985 - 2890*w - w**4 - 2340*w**2 - 190*w**3 - 4275*w = 0. What is w?
-13, 1
Let l(b) be the third derivative of 1/525*b**7 - 2/75*b**5 + 0*b - 2 + 0*b**4 + 1/100*b**6 + 0*b**3 - 34*b**2. Suppose l(k) = 0. What is k?
-4, 0, 1
Let j(q) = -2*q**3 + 38*q**2 - 150*q + 143. Let u be j(14). Factor 0 - 1/4*y**4 + 1/4*y + 3/4*y**u - 3/4*y**2.
-y*(y - 1)**3/4
Let t(r) = -4*r**3 + 840*r**2 - 1696*r + 850. Let d(u) = 4*u**3 + 2*u - 1. Let h(x) = 2*d(x) + t(x). Factor h(m).
4*(m - 1)**2*(m + 212)
Let o(q) be the third derivative of -q**7/1365 - 67*q**6/390 - 35*q**5/26 - 163*q**4/39 - 20*q**3/3 - 75*q**2 - 17*q. Solve o(v) = 0.
-130, -2, -1
Let o(x) = -x**2 + 11*x - 21. Let n be o(9). Let h be (n - -1)*(2 - 3). Find l, given that 19*l + 2*l**2 + l - h*l**2 - 5*l**3 = 0.
-2, 0, 2
Let o(l) be the first derivative of 0*l**2 - 4/5*l**4 - 55 + 0*l + 16/15*l**3 + 4/25*l**5. Factor o(a).
4*a**2*(a - 2)**2/5
Let l(j) be the second d