- o + 4*b + 11*b**2. Find k such that i(k) = 0.
-2/13, 1
Let n be 1/19 - (1555358/(-11210) - -138). Solve -n - 4/5*x - 1/5*x**2 = 0 for x.
-2
Let x = -454415 - -454419. Factor 0 + 0*f + 4/7*f**x - 2/7*f**5 - 2/7*f**3 + 0*f**2.
-2*f**3*(f - 1)**2/7
Let g(h) be the first derivative of -2*h**5/95 + 8*h**4/19 - 60*h**3/19 + 200*h**2/19 - 250*h/19 + 4262. Factor g(u).
-2*(u - 5)**3*(u - 1)/19
Factor -16928/3 - 16744/3*j - 1/6*j**3 + 367/6*j**2.
-(j - 184)**2*(j + 1)/6
Solve 20 + 132*s**4 - 16145*s**3 + 930*s**2 + 68*s**5 + 70*s**2 - 20*s + 15321*s**3 - 376*s = 0 for s.
-5, 1/17, 1
What is n in -828/5 - 4/5*n**2 - 128/5*n = 0?
-23, -9
Factor 264*j**3 + 3/2*j**4 + 11349*j**2 + 23763/2 - 23496*j.
3*(j - 1)**2*(j + 89)**2/2
Solve 2*t**3 + 28*t**2 + 33 + 1221*t - 33 - 1845*t = 0.
-26, 0, 12
Let f(b) be the first derivative of -2*b**3/15 - 377*b**2/5 + 756*b/5 - 2179. Factor f(x).
-2*(x - 1)*(x + 378)/5
Suppose 16*s + 92 = 124. Let -24/5*v + 0 - 20*v**s - 34/5*v**3 + 41*v**4 + 20*v**5 = 0. Calculate v.
-2, -2/5, 0, 3/4
Suppose -6*x - 103 = -115. Let 45 - 40*f**x - 3 + 28*f**2 + 57*f + 30*f**2 = 0. What is f?
-2, -7/6
Let f(u) be the second derivative of -u**4/4 + 1802*u**3 - 4870806*u**2 + 2*u - 183. Factor f(q).
-3*(q - 1802)**2
Let k be (-24)/18*3/(-2). Suppose 4*c - 18 = 18. Find y, given that k*y**2 - 6*y**2 + 3*y + 2*y + c*y**2 = 0.
-1, 0
Let j(r) = -9*r**3 + 1699*r**2 + 379*r - 189. Let t be j(189). Factor 16/3*b + 56/3*b**2 + 4/3*b**4 + t - 31/3*b**3.
b*(b - 4)**2*(4*b + 1)/3
Factor 371/3*b - 1/3*b**2 - 370/3.
-(b - 370)*(b - 1)/3
Let l(n) be the third derivative of n**6/420 - n**5/105 - 19*n**4/3 + 728*n**3/3 - n**2 - n + 2050. Factor l(a).
2*(a - 14)**2*(a + 26)/7
Let d = -28628212/15 - -1908548. Suppose 2/3 - 2/15*r**2 + d*r = 0. What is r?
-1, 5
Let i(j) be the first derivative of -2*j**5/5 - 9*j**4/2 - 2*j**3 + 89*j**2 + 168*j - 2107. Solve i(a) = 0.
-7, -4, -1, 3
Let x(q) be the first derivative of 2/33*q**3 - 8/11*q**2 + 0*q - 83. Solve x(m) = 0.
0, 8
Let s(i) be the first derivative of 2*i**3/3 + 10*i**2 + 50*i + 7254. Let s(p) = 0. What is p?
-5
Let p = -259207 - -259207. Let -3*l**3 - 16/3*l + p + 1/3*l**4 + 8*l**2 = 0. Calculate l.
0, 1, 4
Suppose 2*h + 14 - 4 = 0. Let j(n) = -43*n**2 + 12 - 5*n - 48*n**2 + 94*n**2. Let w(l) = l**2 - 3*l + 6. Let m(s) = h*w(s) + 2*j(s). Factor m(f).
(f - 1)*(f + 6)
Let u(w) be the first derivative of 0*w + 8/23*w**3 + 12/115*w**5 + 1/69*w**6 + 13/46*w**4 + 57 + 4/23*w**2. Factor u(a).
2*a*(a + 1)**2*(a + 2)**2/23
Let m(b) be the second derivative of b**4/36 + 103*b**3/18 + 112*b**2 - 4041*b. Factor m(c).
(c + 7)*(c + 96)/3
Suppose -29*j + 383*j = 48*j - 111*j - 187*j. Factor -7*p**4 - 69/2*p**3 - 1/2*p**5 - 50*p - 70*p**2 + j.
-p*(p + 2)**2*(p + 5)**2/2
Let a be 1/(55/(-10)) + (-2976)/(-396). Let b(s) be the first derivative of -13*s**2 - 8*s - s**4 - a*s**3 - 22. Suppose b(z) = 0. What is z?
-4, -1, -1/2
Find k such that -330 - 538 + 50 + 114 - 5*k**2 - 820*k - 111 = 0.
-163, -1
Suppose 4*c - 92 = 4*z, 160 = -18*z - 87 - 113. Suppose -50 + 6/7*p**2 - 90/7*p + 2/7*p**c = 0. Calculate p.
-5, 7
Suppose 0 = -4*q - 228 + 56. Let n = 51 + q. Solve -8 + 3*i + n + i**2 + 2 = 0.
-2, -1
Let i(g) = -g**2 - 1. Let n(d) = 19*d**2 - 2*d - 5*d**2 - 2*d - 9*d**2 - 3. Let z(o) = 6*i(o) + 2*n(o). Let z(l) = 0. What is l?
-1, 3
Let s(m) be the first derivative of 48*m**2 + 40 - 92/3*m**3 + 576*m - 2*m**4 + 4/5*m**5. Determine n so that s(n) = 0.
-3, 4
Let d = -14 - -14. Suppose -113*y = -119*y + 12. Factor -2/3*z**y + 0 + d*z.
-2*z**2/3
Suppose -81 = -2*t - g, -6*t + 9*t = 4*g + 116. Solve 110*p + 75*p**2 + 40*p**3 + 26*p**4 - 48*p**4 + 27*p**4 + t + 30*p**2 = 0 for p.
-4, -2, -1
Let x(k) be the second derivative of 78*k - 1/90*k**5 - 2 + 19/27*k**3 + 4/27*k**4 + 10/9*k**2. Factor x(v).
-2*(v - 10)*(v + 1)**2/9
Let p = -1/2511 + 907/175770. Let u(q) be the second derivative of 8*q + 0*q**3 + 2/15*q**4 - 3/25*q**5 + 0*q**2 + 0 + 1/25*q**6 - p*q**7. Factor u(z).
-z**2*(z - 2)**3/5
Factor 70*v - 110*v**3 + 446*v**3 - 109*v**3 - 113*v**3 + 34 + 38*v**2 - 112*v**3.
2*(v + 1)**2*(v + 17)
Factor 308*m - 409 - 83 + 45 + 4*m**2 - 185.
4*(m - 2)*(m + 79)
Let d = -9159 + 9166. Let i(s) be the third derivative of 0*s - 35*s**2 + 1/525*s**d + 4/25*s**5 + 0 - 4/15*s**4 - 3/100*s**6 + 0*s**3. Factor i(h).
2*h*(h - 4)**2*(h - 1)/5
Let y = -296991 + 296996. Determine o, given that 1/3*o**3 - 1/3*o**y + 0 - 5/3*o**4 + 5/3*o**2 + 0*o = 0.
-5, -1, 0, 1
Let k(h) be the first derivative of -7/15*h**5 + 5/2*h**4 + 0*h + 1/30*h**6 - 19/2*h**2 + 1 - 6*h**3. Let g(c) be the second derivative of k(c). Factor g(x).
4*(x - 3)**2*(x - 1)
Let a = 327681 + -327679. Determine m so that -2500/7 - 1/7*m**a + 100/7*m = 0.
50
Let j(w) be the third derivative of -w**5/150 + 839*w**4/30 - 703921*w**3/15 - 365*w**2 + 2. Solve j(z) = 0 for z.
839
Suppose 17*m - 19 + 76 - 52 = 39. Factor 1/2*n**3 + 1/4 + 1/12*n**m - 5/6*n.
(n - 1)*(2*n + 3)*(3*n - 1)/12
Let g = -11/6856 + 13921/130264. Suppose 16/19 + g*f**5 - 22/19*f**3 - 14/19*f**2 - 2/19*f**4 + 20/19*f = 0. What is f?
-2, -1, 1, 4
Let a be (-2)/15 + 1938/12240. Let c(u) be the third derivative of 0*u**3 - 8*u**2 + 0*u - 3/20*u**5 - 1/4*u**4 + 0 - a*u**6. Factor c(s).
-3*s*(s + 1)*(s + 2)
Let v = -5502599/15 + 367695. Solve -1034/5*c**2 - 2662/5 + v*c + 18*c**3 - 8/15*c**4 = 0.
3/4, 11
Let j = -158 + 178. Let f be j/45*-125*-3. Solve -5/3*y**2 + 100/3*y - f = 0.
10
Let q(k) be the second derivative of -2 - 8*k + 19/6*k**4 + 1/10*k**5 - 100*k**2 + 80/3*k**3. Find l, given that q(l) = 0.
-10, 1
Let a be ((-50)/(-150))/((-1)/15). Let x be (-273)/(-585) - (-1)/a. Factor x*c**2 + 0*c**3 - 2/15 - 2/15*c**4 + 0*c.
-2*(c - 1)**2*(c + 1)**2/15
Let l be 22*8/16 + -1 + 0. Let -10*v**3 - l + 8*v**3 + 0*v**3 - 6*v**4 + 14*v**2 + 2 + 2*v**5 = 0. Calculate v.
-1, 1, 2
Let m be 39/9 - (-1659)/(-711). Determine a, given that 2*a**3 - 2*a + 3*a**m - 5/2 - 1/2*a**4 = 0.
-1, 1, 5
Let m(j) = j**2 + 3*j + 3. Let a be m(0). Let c be -4*9*a/(-4). Factor -33*i**2 - 31*i - 11*i + 105*i**2 + 3*i**4 - c*i**3 - 6*i.
3*i*(i - 4)**2*(i - 1)
Let a(i) be the first derivative of i**6/18 + 62*i**5/15 + 1429*i**4/12 + 1612*i**3 + 9126*i**2 + 2676. Factor a(t).
t*(t + 13)**2*(t + 18)**2/3
Suppose 11*y + 60 = 23*y. Let u(w) = 6*w**2 + 48*w + 30. Let d(p) = 12*p**2 + 91*p + 59. Let r(k) = y*u(k) - 3*d(k). Factor r(i).
-3*(i + 1)*(2*i + 9)
Let d be (-13 - -8) + (-7053)/156*-4. Let q = 176 - d. Factor -q*h**3 + 2/13*h - 4/13*h**2 + 4/13.
-2*(h - 1)*(h + 1)*(h + 2)/13
Suppose 4*t - f = 14, 5*t = -3*f + 6*f + 21. Solve -75*o**2 - 85 - 29*o**3 - 165*o + 5*o**3 + 29*o**t = 0 for o.
-1, 17
Let z(c) = -5*c**5 - 20*c**4 - 80*c**3 - 60*c**2 - 20. Let p(h) = -h**4 - h**3 - h**2 + 1. Suppose -32*n = -9 + 41. Let o(q) = n*z(q) - 20*p(q). Solve o(w) = 0.
-4, -2, 0
Let h(d) = -2*d**3 - 205*d**2 + 4*d - 10195. Let u be h(-103). Factor 0*w**u + 1/5*w**3 + 0*w + 0.
w**3/5
Let x(z) be the third derivative of z**8/84 - 8*z**7/525 - 13*z**6/75 - 4*z**5/15 - z**4/10 + 26*z**2 + 14*z. Find l, given that x(l) = 0.
-1, -1/5, 0, 3
Let x(p) be the third derivative of 5*p + 0*p**3 + 0 - 1/40*p**6 + 2*p**2 + 0*p**5 + 1/6*p**4 - 1/210*p**7. Suppose x(m) = 0. What is m?
-2, 0, 1
Suppose -2*d + 20*d = 594. Factor 86*c**4 - 43*c**4 - 5*c**5 - 2*c + 2*c + 15*c**3 - d*c**4.
-5*c**3*(c - 3)*(c + 1)
Let r(i) be the third derivative of -i**6/90 - i**5/6 - i**4 - 110*i**3/3 - 59*i**2 + 3. Let b(x) be the first derivative of r(x). Factor b(c).
-4*(c + 2)*(c + 3)
Let a(x) be the second derivative of 2/3*x**3 + 1/10*x**5 + 43*x + 1/2*x**4 + 0*x**2 + 0. Find b such that a(b) = 0.
-2, -1, 0
Suppose 4/5*r**3 + 84/5*r**4 + 0*r - 8/5*r**2 + 0 = 0. Calculate r.
-1/3, 0, 2/7
Let h be (51/48 - 1)/((-3492)/(-96) + -36). Factor 1/2*j - h*j**2 + 2/3.
-(j - 4)*(j + 1)/6
Suppose -11 + 27 = h. Solve t**2 - 3*t + 6 - h + 12 + 0 = 0.
1, 2
Let h = 2859573/5 - 571907. Factor 11/5*u**3 + 24/5 + h*u**2 + 1/5*u**4 + 52/5*u.
(u + 1)*(u + 2)**2*(u + 6)/5
Let k(o) be the third derivative of o**5/60 - o**4/24 - o**3/6 + 4*o**2. Let y(c) = -10*c**3 + 10*c**2 - 2*c + 14. Let b(j) = -12*k(j) - y(j). Factor b(f).
2*(f - 1)**2*(5*f - 1)
Suppose 6 = 11*w - 49. Factor 63*t**5 - 5*t**4 - 22*t**5 - 23*t**w + 5*t**3 - 