e (-405)/54*((-2)/3 - 0). Let v(o) = o**4 + o**3. Let c(n) = -n**4. Let k(u) = p*v(u) + 4*c(u). Let k(r) = 0. Calculate r.
-5, 0
Let q(i) be the third derivative of -4*i**2 - 1/180*i**6 + 0*i**3 + 1 + 0*i - 11/450*i**5 - 1/60*i**4 + 1/525*i**7. Suppose q(p) = 0. What is p?
-1, -1/3, 0, 3
Let w(l) = 4*l**3 + 37*l**2 + 14*l + 17. Let j be w(-9). Let r = 57/2 + j. Factor 0*n**2 - r*n**4 + 0 + 0*n - 1/5*n**3.
-n**3*(5*n + 2)/10
Let f(o) be the first derivative of 2*o**7/3 - 2*o**6/3 - 16*o**5/5 - 4*o**4/3 + 42*o - 31. Let j(k) be the first derivative of f(k). What is s in j(s) = 0?
-1, -2/7, 0, 2
Let k(f) = -10*f**4 + 50*f**3 - 23*f**2 - 71*f + 47. Let i(y) = -5*y**4 + 25*y**3 - 11*y**2 - 37*y + 24. Let a(w) = -7*i(w) + 4*k(w). Factor a(g).
-5*(g - 4)*(g - 1)**2*(g + 1)
Let x(h) be the first derivative of -38/15*h**2 + 131 - 62/15*h**3 + 1/6*h**4 + 0*h. Factor x(a).
2*a*(a - 19)*(5*a + 2)/15
Let u = -394 - -539. Suppose 5*b**3 + 85*b**2 + 110*b**2 - u*b**2 - 115*b + 60 = 0. What is b?
-12, 1
Let c(l) be the first derivative of -7*l**2 + 0*l + 0*l**3 + 12 - 1/60*l**4 + 1/450*l**5. Let i(g) be the second derivative of c(g). Solve i(p) = 0 for p.
0, 3
Suppose -1/6*k**2 - 257/6*k - 127 = 0. Calculate k.
-254, -3
Let q(a) be the first derivative of -1/4*a**4 + 1/42*a**6 + 8/7*a - 3/35*a**5 + 1/3*a**3 - 49 + 9/7*a**2. Determine r so that q(r) = 0.
-1, 2, 4
Let q(f) = 1604*f + 54611. Let j be q(-34). Factor -5/2*g**5 - j*g**3 - 125/2*g + 15 + 25*g**4 + 100*g**2.
-5*(g - 6)*(g - 1)**4/2
Let r(s) = 6*s + 172. Let u be r(-28). Let c be u/(-54) - (-9513)/13608. Factor 1/8*k**2 - 3/4 + c*k.
(k - 1)*(k + 6)/8
Factor 38/7*q + 4 + 8/7*q**2 - 2/7*q**3.
-2*(q - 7)*(q + 1)*(q + 2)/7
Factor 98/5 - 2/5*o**3 - 26/5*o**2 - 14*o.
-2*(o - 1)*(o + 7)**2/5
Let z be (-129)/(-387)*(-1)/(-3)*32. What is v in -2/3*v**3 - 110/9*v**2 - z*v + 8 = 0?
-18, -1, 2/3
Let f(m) = 59*m + 1714. Let s be f(-29). Let z(a) be the second derivative of 0 - 37*a + 3/14*a**4 + 9/14*a**s + 6/7*a**2 + 3/140*a**5. What is u in z(u) = 0?
-4, -1
Let z(b) = 907 - 2*b**2 - 910 - 2*b - 5*b. Let k be z(-3). Factor k*t + 5*t**2 - 16*t + 36*t.
5*t*(t + 4)
Let s(w) be the second derivative of -w**4/8 - 141*w**3/4 + 8*w + 88. Solve s(m) = 0 for m.
-141, 0
Let w(m) = 121*m**2 + 329*m + 49. Let o(d) = -58*d**2 - 163*d - 24. Let r(h) = -11*o(h) - 6*w(h). Factor r(c).
-(8*c + 15)*(11*c + 2)
Suppose n = -5*n + 5*n. Let w(d) be the third derivative of -1/390*d**5 + n*d + 0*d**4 + 0*d**3 - 2*d**2 + 0 + 1/780*d**6. Let w(y) = 0. Calculate y.
0, 1
Let i(m) be the third derivative of -m**5/15 + 709*m**4 - 3016086*m**3 + 35*m**2 + 66*m. Factor i(w).
-4*(w - 2127)**2
Let n(j) be the first derivative of j**4/14 + 66*j**3/7 - 201*j**2/7 + 202*j/7 - 2498. Suppose n(v) = 0. Calculate v.
-101, 1
Let p(o) = 3*o**4 + 71*o**3 - 191*o**2 + 93*o + 16. Let d(t) = 4*t**4 + 94*t**3 - 255*t**2 + 124*t + 22. Let b(j) = 8*d(j) - 11*p(j). Factor b(i).
-i*(i - 1)**2*(i + 31)
Let d(f) be the second derivative of -f**4/7 - 33*f**3/14 + 81*f**2/14 - 4576*f. Let d(z) = 0. What is z?
-9, 3/4
Factor -222*s + 63718*s**4 - 63715*s**4 + 66*s**3 + 288*s**2 - 642*s.
3*s*(s - 2)*(s + 12)**2
Let d(x) be the third derivative of x**6/20 - 37*x**5/90 + 10*x**4/9 - 4*x**3/9 + 158*x**2. Factor d(j).
2*(j - 2)**2*(9*j - 1)/3
Let r(j) be the second derivative of 169*j + 0 + 12/17*j**2 - 3/34*j**4 - 3/85*j**5 - 1/255*j**6 + 4/51*j**3. Solve r(s) = 0 for s.
-3, -2, 1
Let b(g) = -g**3 - 5*g**2 + 7*g + 15. Let q be b(-6). Factor -152*n**3 + 4*n + 165*n**3 - q*n - 5*n**4 + n - 4*n**2.
-n*(n - 2)*(n - 1)*(5*n + 2)
Factor -382/3*o**2 + 104*o + 68/3*o**3 + 0 + 2/3*o**4.
2*o*(o - 4)*(o - 1)*(o + 39)/3
Let z(n) = 3*n**4 + 7*n**3 + 17*n**2 - 7*n - 8. Let q(p) = 4*p**4 + 6*p**3 + 18*p**2 - 6*p - 7. Let w(o) = -4*q(o) + 5*z(o). What is b in w(b) = 0?
-1, 1, 12
Let t(f) be the second derivative of -f**6/270 - f**5/6 - f**4/4 + 29*f**3/27 + 26*f + 112. What is u in t(u) = 0?
-29, -2, 0, 1
Let q(l) be the second derivative of l**6/10 - 18*l**5/5 + 29*l**4 - 72*l**3 - 2569*l. Solve q(g) = 0 for g.
0, 2, 4, 18
Suppose 2*v + m + 142 = -3*m, 0 = v + 4*m + 65. Let j be ((-4)/22)/(7/v). Factor -13/3*y**j - 4/3*y**3 - 11/3*y - 2/3.
-(y + 1)*(y + 2)*(4*y + 1)/3
Let i(d) = -4*d**2 + 88*d - 12. Let t(s) = 8*s**2 - 176*s + 26. Let z(r) = 13*i(r) + 6*t(r). Factor z(a).
-4*a*(a - 22)
Let v = -71 + 280. Let t = 2802 - 2755. Determine c so that -384*c**2 + t*c**4 + 108*c + 816*c**2 + v*c**4 + 576*c**3 = 0.
-3/4, 0
Let b(s) = s**3 - 3*s**2 - 9*s + 19. Let w be b(5). Suppose 5*z - 4*o - 8 = w, 27 = 3*z - 5*o. Factor 0 - 1/6*f - 1/2*f**3 - 1/6*f**z - 1/2*f**2.
-f*(f + 1)**3/6
Let -120 + 376*a - 173*a - 13*a + 35*a**3 + 195*a**2 = 0. Calculate a.
-4, -2, 3/7
Let y(w) = 27054*w**2 - 1054*w + 24. Let o(q) = -5115*q**2 - 5 - 803*q + 1014*q - 296*q**2. Let h(c) = -14*o(c) - 3*y(c). Factor h(m).
-2*(52*m - 1)**2
Let u(w) = -66*w**2 + 83*w - 32. Let p(n) be the first derivative of 428*n**3/3 - 270*n**2 + 208*n + 104. Let r(g) = -5*p(g) - 32*u(g). Factor r(y).
-4*(y - 1)*(7*y - 4)
Let m(x) = 9*x**3 + 885*x**2 + 136806*x + 6885923. Let h(c) = 5*c**3 + 441*c**2 + 68403*c + 3442963. Let z(t) = -7*h(t) + 4*m(t). Factor z(g).
(g + 151)**3
Let y(u) be the third derivative of -1/45*u**5 - 1/504*u**8 - 7/270*u**6 + 0 + 12*u**2 + 1/108*u**4 - 11/945*u**7 + 0*u + 1/27*u**3. Find k such that y(k) = 0.
-1, 1/3
Let n be (-5 - 1)*(2 - 35/14). Let j = -1 + 1. Factor 9*h**4 - 2*h**n + 3*h**2 - 13*h**3 + 3*h + j*h.
3*h*(h - 1)**2*(3*h + 1)
Let 6/5*u**4 + 0*u**3 + 0 + 0*u**2 + 0*u - 3/5*u**5 = 0. What is u?
0, 2
Let v(f) be the first derivative of -f**3 + 3/16*f**4 + 0*f + 16 - 1/32*f**5 + 0*f**2 - 1/480*f**6. Let b(w) be the third derivative of v(w). Factor b(h).
-3*(h - 1)*(h + 6)/4
Suppose 17*i - 148 = -112*i + 110. Let t(l) be the second derivative of 0*l**i + 0*l**4 + 1/30*l**6 + 0 - 18*l + 0*l**3 - 1/10*l**5 + 1/42*l**7. Factor t(j).
j**3*(j - 1)*(j + 2)
Let o(v) be the third derivative of -7*v**7/30 + 7*v**6/6 - 47*v**5/60 - 13*v**4/3 + 10*v**3 - 4909*v**2. Determine y, given that o(y) = 0.
-6/7, 5/7, 1, 2
Suppose 3*l = -34 + 40. Let v(o) = 3*o - 4*o**2 + 3*o**3 - 2*o**4 + 5 - 2 - l. Let i(g) = g**4 + g**3 - g**2 - g - 1. Let n(k) = i(k) + v(k). Factor n(f).
-f*(f - 2)*(f - 1)**2
Factor -10/3*z**4 + 4/3*z**2 - 14/3*z + 2/3*z**5 + 4*z**3 + 2.
2*(z - 3)*(z - 1)**3*(z + 1)/3
Let j(i) be the third derivative of i**9/3024 - i**7/120 + i**6/60 - i**3 - 20*i**2. Let s(n) be the first derivative of j(n). Factor s(r).
r**2*(r - 2)*(r - 1)*(r + 3)
Factor 85 + 118*k**3 - 14*k**2 + 25 + 3*k - 116*k**3 - 101*k.
2*(k - 11)*(k - 1)*(k + 5)
Let m(p) be the third derivative of 1606081923*p**6/100 - 2852721*p**5/25 + 1689*p**4/5 - 8*p**3/15 - 3528*p**2. Factor m(y).
2*(1689*y - 2)**3/5
Solve -38*h + 24 - h**4 - 1/2*h**5 + 2*h**2 + 27/2*h**3 = 0 for h.
-6, -2, 1, 4
Factor 408/7*w**3 - 807/7*w**2 + 0 - 3/7*w**4 + 402/7*w.
-3*w*(w - 134)*(w - 1)**2/7
Suppose 4*k + 32 = -4*k. Let m be 793/104 + k - 6/(-16). Suppose 0 - 32/7*v**3 - 4/7*v - 2*v**m - 22/7*v**2 = 0. What is v?
-1, -2/7, 0
Let t(z) be the second derivative of -z**7/8820 + z**6/63 - 13*z**5/140 + 43*z**4/3 + 52*z - 1. Let d(p) be the third derivative of t(p). Factor d(n).
-2*(n - 39)*(n - 1)/7
Suppose -10*z - 37 = -297. Let b be z/10 + (-8)/(-20). Suppose 36*w**2 + 5*w**b - 45*w**2 + w**3 = 0. What is w?
0, 3/2
Suppose 191*k - 303 = -13*k + 105. Find q such that -8/9*q - 2/3*q**k + 2/9*q**3 + 8/3 = 0.
-2, 2, 3
Factor 36 - 39/2*k**2 - 15*k - 3/2*k**3.
-3*(k - 1)*(k + 2)*(k + 12)/2
Let p = -16285217/32652 + 8/8163. Let t = p + 504. Factor 21/4*k + 3/2*k**3 + t*k**2 + 3/2.
3*(k + 1)*(k + 2)*(2*k + 1)/4
Let u(p) = -70*p**3 - 88*p**2 + 304*p - 286. Let v(s) = -107*s**3 - 88*s**2 + 304*s - 285. Let a(r) = -3*u(r) + 2*v(r). Factor a(f).
-4*(f - 18)*(f - 2)**2
Let k = 65429 - 327139/5. Find u such that -k*u**3 + 12/5*u**2 + 0*u + 0 = 0.
0, 2
Let h be (3/25)/((-55)/(-416515)). Let b = 909 - h. Let 4/25 - b*i + 2/25*i**2 = 0. What is i?
1, 2
Let m(n) be the first derivative of -n**4/54 + 2*n**3/9 + 24*n + 6. Let c(w) be the first derivative of m(w). Factor c(t).
-2*t*(t - 6)/9
Solve 0*k**3 + 76/5*k**2 - 4/5*k**4 - 288/5 + 24/5*k = 0.
-3, 2, 4
Suppose -1033 = 5*t + c, -14*c +