given that k(v) = 0.
-12, 1, 7
Let z be (-10 + -5)/(-5) + (-2 - -7). What is o in o**2 + 4*o - 2*o - 3*o + z*o = 0?
-7, 0
What is t in 0*t + 1586/5*t**2 + 1584/5*t**3 - 2/5*t**4 + 0 = 0?
-1, 0, 793
Let x be 1/(-124)*-12*-6. Let j = 219/217 + x. Factor 0*b + 0 - j*b**3 - 6/7*b**2.
-3*b**2*(b + 2)/7
Factor -837*n - 8425 - 4364*n - 4674*n + 3*n**2 + 2*n**2 + 1455*n.
5*(n - 1685)*(n + 1)
Suppose -21*g = -9*g - 396. Let d be g/(18 + -7) - 23/8. Factor d*y**2 + 2 + y.
(y + 4)**2/8
Suppose -5*h + 3*p = 8*p - 65, 2*p = 3*h - 34. Solve h*o**2 + 9*o - 217*o**5 - 18 + 34*o**3 + 434*o**5 + 3 - 41*o - 219*o**5 + 3*o**4 = 0.
-3, -1, -1/2, 1, 5
Suppose 1834*x - 1831*x - 32 = -q, 0 = -2*q - 3*x + 34. Determine k, given that 2048 + 1/2*k**q + 64*k = 0.
-64
Let q be 2 - (6/(-2) + 3). Suppose 14 = -q*v + 4, -2 = 4*c + 2*v. Factor -2*k**3 + 864 + 404*k + 72*k**c + 39*k + 6*k**3 - 11*k.
4*(k + 6)**3
Let a(i) be the third derivative of i**8/192 + i**7/56 + i**6/96 - i**5/48 + 41*i**3/3 - 51*i**2. Let v(o) be the first derivative of a(o). Solve v(p) = 0.
-1, 0, 2/7
Suppose -7*r = 6*r - 1300. Let a = 103 - r. Factor 2 + d**3 - 12*d + 42*d**5 + 6*d**a + 6 - 2*d**2 - 43*d**5.
-(d - 2)*(d - 1)**2*(d + 2)**2
Let x(t) be the second derivative of t**5/90 + 8*t**4/27 - 35*t**3/9 + 224*t + 2. Determine m, given that x(m) = 0.
-21, 0, 5
Let c(y) be the second derivative of -y**5/90 - 23*y**4/54 + 136*y**3/27 - 112*y**2/9 + 1027*y. What is f in c(f) = 0?
-28, 1, 4
Let i(v) be the third derivative of v**6/120 - 19*v**5/60 + v**4 + 120*v**3 - 158*v**2 - 2*v. Let i(x) = 0. What is x?
-5, 12
Let c be 1 - (-2)/2 - (1742 + -19). Let a = c + 1723. Factor 1 - 3/4*q - 1/4*q**a.
-(q - 1)*(q + 4)/4
Let b(x) = -45*x**2 + 359*x - 484. Let s be b(6). Let 2/9*j**2 + 20/3*j + s = 0. What is j?
-15
Let a(u) be the first derivative of 1/5*u**5 + 79/3*u**3 + 100*u + 15/4*u**4 + 165/2*u**2 - 279. Factor a(x).
(x + 1)*(x + 4)*(x + 5)**2
Suppose -3*b = 5*o + 30, 2727 - 2733 = -2*b + o. Let i(n) be the first derivative of 3 + 9/14*n**2 - 1/7*n**3 + b*n. Solve i(x) = 0 for x.
0, 3
Let p be 4/(-14)*7/(-4). Suppose 0 = 703*t + 793*t - 1645*t. Factor -p*k**3 + t - k - 3/2*k**2.
-k*(k + 1)*(k + 2)/2
Let j(s) = -s**2 - 6*s + 18. Let l be j(-7). Let f be 17/(-34)*22*(-2)/l. Find o, given that 2/15*o**5 + 0*o + 2/5*o**4 + 0 + 2/15*o**f + 2/5*o**3 = 0.
-1, 0
Let j be (1858/(-1858))/(((-7)/2 + 3)/((-9)/(-6))). What is s in -2/13*s**5 - 94/13*s**j + 0 + 60/13*s**2 + 36/13*s**4 + 0*s = 0?
0, 1, 2, 15
Let s(z) = -2*z**3 - 3*z**2 - 6*z - 3. Let i be s(5). Let f = -356 - i. Factor 0 + 3/5*j**f - 3/5*j.
3*j*(j - 1)/5
Let b(w) be the second derivative of w**6/10 - 9*w**5/10 + 11*w**4/4 - 3*w**3 - w + 633. Suppose b(p) = 0. Calculate p.
0, 1, 2, 3
Let q = 6557911/2660 - 12323/5. Let s = -4/133 + q. Determine p so that -s*p**3 - 3*p**2 - 9/4*p + 0 = 0.
-3, -1, 0
Find t, given that -27/5*t**2 - 618/5*t + 69/5 = 0.
-23, 1/9
Suppose 0 = 4*n - 5*a - 60, -10*n + 70 = -5*n - 5*a. Let i(m) = -3*m**2 - 11*m - 13. Let f(t) = -2*t**2 - 5*t - 6. Let b(p) = n*f(p) - 6*i(p). Factor b(j).
-2*(j - 9)*(j + 1)
Let a(k) = -3*k**3 + 41*k**2 + 15*k - 10. Let w be a(14). Factor -12*y**5 - 40*y**4 - 48*y**3 - 19*y**2 - 14*y**2 - 14*y**2 + 23*y**2 - w*y.
-4*y*(y + 1)**3*(3*y + 1)
Let a(n) be the second derivative of 0*n**3 - 1/70*n**5 + 0*n**2 + 22*n - 1/6*n**4 + 0. Factor a(w).
-2*w**2*(w + 7)/7
Let q be (-6021)/10704*-4*(-4)/(-12). Factor -q*r**3 + 0 + 45/4*r**2 + 12*r.
-3*r*(r - 16)*(r + 1)/4
Let i be ((-206)/(-1648))/((-70)/(-800)). Solve -26/7*k**3 + 0 + i*k**4 + 8/7*k + 8/7*k**2 = 0.
-2/5, 0, 1, 2
Let n(m) be the second derivative of -m**5/100 - 43*m**4/20 + 3070*m. Find w, given that n(w) = 0.
-129, 0
Let g(w) be the second derivative of 0*w**4 + 1/36*w**6 + 0 - 17*w - 1/30*w**5 + 0*w**2 - 1/2*w**3. Let r(i) be the second derivative of g(i). Factor r(o).
2*o*(5*o - 2)
Let d(p) = -3 + 6*p - 7 - 2*p - 3*p. Let i be d(12). Solve 5 - 9*a + 9 - 20 - 3*a**i = 0.
-2, -1
Let i(l) = 2*l - 7. Let y be i(7). Let v = y + -2. Find f, given that f + 2*f**3 + 2*f**2 - 1 - f**4 + 4*f**5 - 2*f - v*f**5 = 0.
-1, 1
Let c(v) = -1362*v**2 + 21488*v - 2160*v**2 + 21 - 9*v**3 - 122429*v. Let l(k) = -k**3 - 352*k**2 - 10094*k + 2. Let x(s) = -2*c(s) + 21*l(s). Factor x(a).
-3*a*(a + 58)**2
Let r = -100850 + 100854. Factor 8/5*k + 12/5*k**r + 0 + 2/5*k**5 + 26/5*k**3 + 24/5*k**2.
2*k*(k + 1)**2*(k + 2)**2/5
Let m = 65671/131378 - -9/65689. Let -f**2 - m + 3/2*f = 0. What is f?
1/2, 1
Let a = 1724 - 1724. Let w(y) be the second derivative of -2/15*y**6 - 4/3*y**3 + 0 + a*y**5 + 9*y + 0*y**2 + y**4. Determine f, given that w(f) = 0.
-2, 0, 1
Let t = 108103/399504 - -2/8323. Let m(w) be the second derivative of -1/20*w**5 + 0 + 17*w - 1/4*w**2 - t*w**4 - 11/24*w**3. Suppose m(r) = 0. Calculate r.
-2, -1, -1/4
Let a(t) be the first derivative of 41 - 3/5*t**5 - 5*t**3 + 0*t**2 + 9/2*t**4 + 0*t. Suppose a(k) = 0. Calculate k.
0, 1, 5
Let j(k) be the first derivative of -2/25*k**5 - 211 + 4/9*k**3 + 6/5*k - 1/45*k**6 - 7/5*k**2 + 1/5*k**4. Factor j(l).
-2*(l - 1)**3*(l + 3)**2/15
Factor 7/3*f**5 - 80/3*f**2 - 52/3*f**3 + 0 + 8/3*f**4 + 0*f.
f**2*(f + 2)**2*(7*f - 20)/3
Let i(u) be the third derivative of -u**7/6300 - u**6/675 + u**5/300 + u**4/10 - 85*u**3/6 - 75*u**2. Let a(w) be the first derivative of i(w). Solve a(l) = 0.
-3, 2
Let x be (1 + 0)*(6 + 712/(-120)). Let n(c) be the first derivative of -x*c**3 - 16/5*c - 4/5*c**2 + 17. Factor n(z).
-(z + 4)**2/5
Let f(l) be the third derivative of -l**7/1680 - l**6/240 + l**5/240 + l**4/16 - 3*l**3/16 - 375*l**2. Factor f(x).
-(x - 1)**2*(x + 3)**2/8
Let o(l) = 6*l**2 + 5*l + 7. Suppose 2*t = 5*w - 37, -4*w + 5 = -2*t - 33. Let z(r) = r**2 + 4*r + 1. Let g(v) = t*z(v) + 3*o(v). Factor g(u).
-3*u*(u + 23)
Suppose -j = -11 + 9. Let v**4 + 2*v**3 + 178*v**2 + 4 - 4 - 177*v**j = 0. What is v?
-1, 0
Suppose 9*r - 60 = -5*m, 5*r = -0*r. Let g be (13/(-4))/(m + 50/(-4)). Factor -1/3 - 7/6*t + g*t**2.
(3*t - 1)*(13*t + 2)/6
Let q be (-132)/(-88) + 1/2. Let -201*x**4 - 237*x**q - 763*x**2 - 3465*x + 3462*x**3 + 3267 - 2066*x**2 + 3*x**5 = 0. What is x?
-1, 1, 33
Let t(u) be the second derivative of -2/15*u**3 + 0 - 1/6*u**4 + 1/15*u**6 + 0*u**2 - 1/35*u**7 - 86*u + 1/10*u**5. Let t(o) = 0. Calculate o.
-1, -1/3, 0, 1, 2
Let w(h) = -1. Let v(u) = 3. Let m(q) = 4*v(q) + 14*w(q). Let g(o) = -2*o**2 + 2*o - 40. Let y(p) = -2*g(p) + 44*m(p). Find i, given that y(i) = 0.
-1, 2
Let f = 497 + -500. Let t be (92/28 + f)/(9/63). Determine l, given that 2/5*l**t + 0 + 2*l = 0.
-5, 0
Let o(y) be the first derivative of y**5/100 + 7*y**4/60 - 4*y**3/15 + 95*y + 48. Let h(r) be the first derivative of o(r). Find v, given that h(v) = 0.
-8, 0, 1
Suppose -12*t - 164 = 272*t - 1016. Find l such that 6/11*l**t + 6/11*l**2 + 0 + 2/11*l**4 + 2/11*l = 0.
-1, 0
Factor 0 + 378/5*r + 76*r**2 + 2/5*r**3.
2*r*(r + 1)*(r + 189)/5
Let h(g) = -21 - g**2 + 2*g**2 + 29 - 13*g. Let b be h(13). Determine j, given that 4*j**4 + 4 + 8*j - 3*j**4 - b*j**3 - 5*j**4 = 0.
-1, 1
Let p(j) be the first derivative of -2*j**3/21 - 67*j**2/7 - 486. Solve p(x) = 0 for x.
-67, 0
Let v(d) be the first derivative of 5*d**3/3 + 6840*d**2 + 9357120*d + 9663. Solve v(c) = 0 for c.
-1368
Suppose 318*s - 225 = 315*s. Let j = -70 + s. Suppose -45*u**2 - 35*u**4 + 114*u**5 - 58*u**j - 75*u**3 - 61*u**5 = 0. Calculate u.
-3, -1, 0
Suppose 6*f - 50 = -14. Let v be (3/(-9)*1)/((-1)/f). Factor -16*a**5 - 2*a - 2*a**4 + 4*a**v - 10*a**5 - 1 - 1 + 4*a**3 + 24*a**5.
-2*(a - 1)**2*(a + 1)**3
Let p = 0 - 40. Let m be 42 + p + 26/5. Factor -2/5*x**5 + 16/5*x**4 + 32/5*x**2 - m*x**3 - 2*x + 0.
-2*x*(x - 5)*(x - 1)**3/5
Let b(z) be the third derivative of z**8/2856 - 2*z**7/595 + 1215*z**2 + z. Factor b(h).
2*h**4*(h - 6)/17
Let u(g) be the first derivative of -g**4/26 + 8*g**3/13 - 27*g**2/13 - 80*g/13 - 8825. Factor u(f).
-2*(f - 8)*(f - 5)*(f + 1)/13
Let m(s) = s**2 + 8*s. Let l be m(-10). Suppose -5*x + 20 = -x. Factor -l + 12*g**3 + 20*g - 10*g**3 + 15*g**2 - 12*g**3 - x*g**4.
-5*(g - 1)**2*(g + 2)**2
Let s = -3/227 + -13/33369. Let d = s + 17/49. Factor -w**2 + 0*w - d*w**3 + 0.
-w**2*(w + 3)/3
Let j(p) be the second derivative of -1/126*p**7 - 1/20*p**5 + 2/9*p**3 + 1/9*p**4 + 0