y) = 2*y**5 + 47*y**4 - 2*y**3 - 43*y**2. Let t(w) = -w**5 + w**3 - 4*w**2. Let a(k) = -j(k) - t(k). Factor a(p).
-p**2*(p - 1)*(p + 1)*(p + 47)
Let j(l) be the first derivative of 1/3*l**3 + 5/6*l**4 - 30*l - 34 - 5*l**2 - 1/10*l**5. Let y(a) be the first derivative of j(a). Factor y(h).
-2*(h - 5)*(h - 1)*(h + 1)
Let d(o) = 10*o**4 - 398*o**3 - 1501*o**2 - 685*o - 84. Let c(y) = 9*y**4 - 399*y**3 - 1494*y**2 - 683*y - 84. Let u(t) = 6*c(t) - 7*d(t). Factor u(h).
-(h - 28)*(h + 3)*(4*h + 1)**2
Suppose 2615*w**3 + 245*w**4 - 2259*w + 12139*w - 3380 + 22012*w**2 - 31377*w**2 + w**5 + 4*w**5 = 0. Calculate w.
-26, 1
Let b(c) be the first derivative of -c**5/10 + 9*c**4/8 - 7*c**3/2 - c**2/4 + 15*c + 320. Determine v so that b(v) = 0.
-1, 2, 3, 5
Let d(n) be the second derivative of n**4/12 - 85*n**3/4 + 127*n**2/4 + 1821*n. Find r, given that d(r) = 0.
1/2, 127
Let h = -141545 + 990817/7. Factor 0 + h*q**3 - 2/7*q**2 + 0*q.
2*q**2*(q - 1)/7
Let c be 45/6*(-272)/(-1836). Let 0 - c*x**2 + 2/9*x**3 + 0*x = 0. Calculate x.
0, 5
Let l be 10/60 + 95/38 + 2/6. Let p(s) be the first derivative of -31/18*s**4 - 2/3*s**5 + 4 - 10/9*s**l + 1/3*s**2 + 4/9*s. Suppose p(q) = 0. What is q?
-1, -2/5, 1/3
Let q be (-247 - -246)*(-3)/(-1)*2/(-6). Let h(r) = -2 + 2 + r. Let i(k) = -27*k**3 + 60*k**2 + 84*k - 18. Let b(a) = q*i(a) - 15*h(a). Solve b(m) = 0 for m.
-1, 2/9, 3
Suppose 4 = -3*l - 5*t, 3*l - 5*t + t - 14 = 0. Determine w, given that 10 + 2*w**l + 6 - 4 - 3 - 3*w**2 = 0.
-3, 3
Let m(u) = 78*u + 8847. Let w be m(-113). Let s(o) be the second derivative of -1/4*o**2 - w*o + 1/12*o**4 + 0 - 1/12*o**3. Let s(z) = 0. What is z?
-1/2, 1
Factor -465/4 - 1/8*a + 1/8*a**2.
(a - 31)*(a + 30)/8
Suppose 347*s = -23*s. Factor 8/13*d**2 + 0*d + 2/13*d**3 + s.
2*d**2*(d + 4)/13
Let b(v) be the first derivative of -9*v**4 + 2392*v**3 + 2398*v**2 + 800*v - 814. Factor b(m).
-4*(m - 200)*(3*m + 1)**2
Suppose 3*i = 4*p + p - 2, -4*i - 5*p + 9 = 0. Let r(g) = g - 1. Let j(s) = 2*s**3 + 3 + 9 - 5*s**2 + 2*s + 13*s**2. Let d(z) = i*j(z) + 8*r(z). Factor d(o).
2*(o + 1)**2*(o + 2)
Let k(t) = t**2 - 5*t + 6. Let q be k(4). Suppose 3*u - 4*b = 29, -3*b - q*b = -u + 28. Factor -1 - 2 + 0 - d**u + 4 - d**2 + d.
-(d - 1)*(d + 1)**2
Let c(z) = 24*z**2 + 1667*z + 3231. Let q(d) = 13*d**2 + 834*d + 1612. Let t(g) = 4*c(g) - 7*q(g). Factor t(a).
5*(a + 2)*(a + 164)
Let g(l) be the second derivative of -243*l**5/20 + 2205*l**4/4 - 487*l**3/2 + 81*l**2/2 + 6*l + 192. Determine a so that g(a) = 0.
1/9, 27
Determine f, given that -1742/3*f**3 - 2/3*f**5 + 1400/3*f + 2768/3 - 2068/3*f**2 - 356/3*f**4 = 0.
-173, -2, 1
Let j = -7023 + 7027. Let w(r) be the first derivative of 9/2*r**6 + 33/2*r**j + 1 - 72/5*r**5 + 0*r - 8*r**3 + 3/2*r**2. Factor w(s).
3*s*(s - 1)**2*(3*s - 1)**2
Suppose 3469703 + 4*d**2 - 10944*d + 3795854 + 1770604 + 152230 - 1702695 = 0. Calculate d.
1368
Let v(u) = 8*u**2 + 52*u - 70. Let d = -11 - -17. Let h(g) = 9*g**2 + 51*g - 72. Let y(b) = d*v(b) - 5*h(b). Factor y(q).
3*(q - 1)*(q + 20)
Let u(y) = -2*y**3 - 14*y**2 + 9*y + 14. Let n be u(-10). Let i = -522 + n. Factor 2/17*o**3 - 2/17*o - 2/17*o**i + 2/17.
2*(o - 1)**2*(o + 1)/17
Let z be -20 - (-88)/275*80. Factor 8/5*n**3 - z*n + 24/5 - 44/5*n**2.
4*(n - 6)*(n + 1)*(2*n - 1)/5
Suppose 40 = -6*o + 142. Suppose -8 = -2*d - 4*j, 13*d + 11 = o*d + 3*j. Find g, given that -4/3 - 2*g**3 + 8/3*g**d + 2/3*g = 0.
-2/3, 1
Let g(h) be the second derivative of -3*h**5/40 - h**4/8 + 15*h**3/2 - 145*h + 1. Find u such that g(u) = 0.
-6, 0, 5
Let c(j) = j**3 + 16*j**2 + 36*j - 49. Let v be c(-13). Let k be 6 - (32/12)/(v/(-15)). Factor -1/5 - 2/5*f**3 + 0*f**k + 2/5*f + 1/5*f**4.
(f - 1)**3*(f + 1)/5
Suppose f + 2*s - 1 = 0, -4*f + s = f - 5. Let c be (12/8)/(f/2). Solve -7*x**3 - 2*x - c*x + 12*x**3 = 0.
-1, 0, 1
Let f(k) be the first derivative of k**7/168 + k**6/18 - 19*k**5/24 + 35*k**4/12 - 44*k**3/3 - 37. Let r(b) be the third derivative of f(b). Factor r(c).
5*(c - 2)*(c - 1)*(c + 7)
Let n(d) = d**3 - d**2 + 10*d + 6. Suppose -11*c + 168 = -5*c. Let q = 33 - c. Let l(z) = 10*z + 5. Let u(r) = q*n(r) - 6*l(r). Factor u(v).
5*v*(v - 2)*(v + 1)
Let r = -175 + 701/4. Suppose -2*p = 5*l - 6, 0 = -4*p - p - 3*l + 15. Factor 0 + 1/8*q**2 - r*q + 1/8*q**p.
q*(q - 1)*(q + 2)/8
Let d(g) be the third derivative of -g**6/60 - 29*g**5/30 - 26*g**4/3 - 100*g**3/3 + 2101*g**2. Factor d(p).
-2*(p + 2)**2*(p + 25)
Let j(s) be the first derivative of -5*s - 1/2*s**2 - 52 + 1/12*s**4 + 0*s**3. Let g(f) be the first derivative of j(f). Determine k so that g(k) = 0.
-1, 1
Factor -169875/2*l**2 - 4218750 + 4303125*l - 5/4*l**4 + 2255/4*l**3.
-5*(l - 150)**3*(l - 1)/4
Let o(f) = 6*f**2 - 184*f + 16. Let m(h) = 17*h**2 - 550*h + 44. Let d(q) = 4*m(q) - 11*o(q). Factor d(c).
2*c*(c - 88)
Suppose -2489 = -81*y + 2457 - 4784. Factor y*i**2 + 3/2*i + 1/2*i**3 + 0.
i*(i + 1)*(i + 3)/2
Let y(d) be the first derivative of 36 + 256/7*d + 4/21*d**3 + 32/7*d**2. Factor y(s).
4*(s + 8)**2/7
Let s(r) be the first derivative of r**4/16 - 137*r**3/12 - 277*r**2/8 - 139*r/4 + 250. Factor s(j).
(j - 139)*(j + 1)**2/4
Let w(x) be the first derivative of 6*x**2 + 0*x - 10/3*x**3 + 1/2*x**4 - 331. Factor w(p).
2*p*(p - 3)*(p - 2)
Factor -53*x**3 - 172*x**3 - 400*x + 4*x**4 - 204*x**3 - 8*x**4 - 804*x**2 + 21*x**3.
-4*x*(x + 1)**2*(x + 100)
Let c(f) be the third derivative of -f**4/3 + 30*f**3 - 462*f**2. Let u be c(22). Let 2/7*t**3 - 2/7*t**2 + 2/7*t**u - 2/7*t + 0 = 0. Calculate t.
-1, 0, 1
Let g = 36653 - 146607/4. Factor 0 - p - 1/4*p**3 + g*p**2.
-p*(p - 4)*(p - 1)/4
Let i(n) be the first derivative of -2/7*n**3 - 70 - 1/14*n**4 + 6/7*n + 1/7*n**2. Factor i(f).
-2*(f - 1)*(f + 1)*(f + 3)/7
Let r(w) be the first derivative of w**5/30 - 4*w**4/3 + 5*w**3/3 + 336*w**2 + 1323*w/2 - 12517. What is c in r(c) = 0?
-9, -1, 21
Let i(k) = -17*k + 78. Let y be i(5). Let d be (y - -9)/(21 + 2). Determine p, given that -14/23*p + 6/23 + 10/23*p**2 - d*p**3 = 0.
1, 3
Let s(m) be the first derivative of 0*m + 1/60*m**5 - 27/2*m**2 + 1/480*m**6 - 1/96*m**4 - 1/6*m**3 - 4. Let x(u) be the second derivative of s(u). Factor x(n).
(n - 1)*(n + 1)*(n + 4)/4
Factor -10228*i + 10493*i + 3 + 5*i**2 - 5 + 2.
5*i*(i + 53)
Let v(s) = -s**2 - 34*s + 50. Let g be v(-34). Let y be (48/(-40))/((-35)/g*2). Factor 3/7*d**2 + 0 - y*d.
3*d*(d - 2)/7
Let b = -19 - -21. Find f, given that 2*f**3 + b*f + 2*f**2 - 6*f + 6*f + 6*f**2 - 12 = 0.
-3, -2, 1
Suppose -44*f = 39*f - 0 - 249. Find w, given that -3/8*w**2 - 1/2 + 1/4*w**f + 1/8*w**4 - w = 0.
-2, -1, 2
Let d(m) be the third derivative of 3*m**8/616 + 124*m**7/385 + 276*m**6/55 - 168*m**5/5 + 44*m**4 - 5*m**2 - 3*m. Solve d(z) = 0.
-22, 0, 2/3, 2
Let z = 60 + -45. Factor -142*l + 10 + 5*l**3 + 137*l + 5 - z*l**2.
5*(l - 3)*(l - 1)*(l + 1)
Let l(p) = -3*p**2 + 645*p - 924. Let m(r) = 4*r**2 - 642*r + 967. Let v(z) = -7*l(z) - 6*m(z). Find i, given that v(i) = 0.
-222, 1
Suppose 3*o - 7*o = -116. Suppose 4*h + 9 = o. Find i such that -13*i**3 + 15*i + 3*i**3 + 5*i**4 - 5*i - h = 0.
-1, 1
Let b(v) be the third derivative of -v**8/672 - v**7/70 - v**6/20 - v**5/12 - v**4/16 + 2*v**2 - 105. Find d, given that b(d) = 0.
-3, -1, 0
Let o(k) be the third derivative of -k**7/840 + k**6/240 + 3*k**5/10 + 5*k**4/12 + k**3/3 - 161*k**2. Let v(w) be the second derivative of o(w). Factor v(n).
-3*(n - 4)*(n + 3)
Let r(v) be the first derivative of 0*v**4 + 0*v**2 - 59 - 1/24*v**6 + 0*v + 3/10*v**5 + 0*v**3. Factor r(t).
-t**4*(t - 6)/4
Let q(h) be the second derivative of h**5/15 - 14*h**4/3 + 18*h**3 - 88*h**2 - 137*h. Let g(l) be the first derivative of q(l). Determine w so that g(w) = 0.
1, 27
Suppose -5*i + 15 = 5*o, 0*o - 2*i - 1 = -5*o. Suppose o = -3*v + 10. Factor v*d**2 - 2 + 9*d + 11 + 3*d.
3*(d + 1)*(d + 3)
Let v(c) be the second derivative of -c**7/98 - c**6/70 + 3*c**5/70 + 7*c + 30. What is q in v(q) = 0?
-2, 0, 1
Let p(i) be the first derivative of -375948*i**3 - 4248*i**2 - 16*i - 520. Suppose p(v) = 0. Calculate v.
-2/531
Let a(y) = -y**2 - 3*y + 3. Let p be a(0). Factor 8*n**3 - n**2 + p*n**3 - 5*n**2 - 12*n**3.
-n**2*(n + 6)
Determine i so that -27/2*i - 28 + 1/4*i**2 = 0.
-2, 56
Let o be -8 - -8 - (0 + (-28)/4). Let -o*n**2 + 6*n - 1