3 - n**2 + 1. Let i(x) = -10*x**5 - 40*x**4 - 55*x**3 + 445*x**2 - 480*x - 5. Let q(v) = -i(v) - 5*l(v). What is t in q(t) = 0?
-4, 0, 2, 6
Let g = 36/9683 - -19042/87147. Let a = 2/203 + 388/1827. Factor -a + 2/9*x**5 - 4/9*x**3 + 2/9*x + 4/9*x**2 - g*x**4.
2*(x - 1)**3*(x + 1)**2/9
Let h(p) = 3*p**3 - 2*p**2 + 3*p - 2. Let a be h(2). Let f be (0 - a/5)/(-2). Factor 11*k - 5*k + 5*k**2 - 3*k**3 - 2*k**f.
-3*k*(k - 2)*(k + 1)
Let v = 21 - 28. Let h be (-270)/(-42) + (-4)/v. Factor -40*j + h + 1 - 2*j**2 + 18*j + 16*j.
-2*(j - 1)*(j + 4)
Let g = -86 - -91. Factor -37*q**g + 21*q**5 + 18*q**5 - 2*q**2 - q**3 + 5*q**4 + 2*q**3.
q**2*(q + 1)*(q + 2)*(2*q - 1)
Suppose -w - 3 = -5. Suppose 0 = -22*t - 36*t - 10*t + 340. Factor 63*f - 8 + 2*f**w - 93*f - 67 - t*f**2.
-3*(f + 5)**2
Solve 268/15*h**2 - 2/15*h**4 + 0 + 46/15*h**3 + 112/5*h = 0.
-3, -2, 0, 28
Solve 14415/2*t**3 + 10/3 + 13795/2*t**2 - 920/3*t = 0.
-1, 2/93
Let w(q) = -q**3 - 909*q**2 + 2746*q - 1836. Let g(c) = -10*c**3 - 10000*c**2 + 30205*c - 20195. Let f(l) = 4*g(l) - 45*w(l). Factor f(m).
5*(m - 2)*(m - 1)*(m + 184)
Let r = -385 + 2144. Let z = 15832/9 - r. Suppose 1/9*i - 1/9*i**2 - z*i**3 + 1/9 = 0. Calculate i.
-1, 1
Suppose 2*w - 8 = 2*h - 0*h, -h + 31 = 4*w. Factor -13 + 0*b**3 + 3*b**2 + w*b**3 - 10*b**3 - 35 + 48*b.
-3*(b - 4)*(b - 1)*(b + 4)
Let s = -18333 + 18337. Factor 1/8*g**s - 1/8*g**2 + 0*g**3 + 0*g + 0.
g**2*(g - 1)*(g + 1)/8
Let m = 23226 + -23224. Let t(r) be the second derivative of 6*r**2 - 8/9*r**4 - 4/15*r**5 + 2/3*r**3 - 9 + m*r. Factor t(x).
-4*(x - 1)*(2*x + 3)**2/3
Suppose -5*w = 26 - 21 - 15. Let o(s) be the first derivative of 4/5*s - 11/3*s**3 + 5 + 5*s**4 - 2/5*s**w. Let o(z) = 0. What is z?
-1/4, 2/5
Let r(s) be the second derivative of s**4/3 + 1558*s**3/3 + 1556*s**2 + 7079*s + 1. Determine u so that r(u) = 0.
-778, -1
Let z(l) be the first derivative of l**3 + 15*l**2/2 + 48*l + 62. Let o(p) = 2*p**2 + 15*p + 47. Let u(a) = -6*o(a) + 5*z(a). Solve u(v) = 0.
-2, 7
Suppose 0*t = -9*t. Let o(g) = -2*g + 106. Let a be o(53). Find u, given that a - 2/3*u**2 + t*u = 0.
0
Let u(p) be the first derivative of -p**5/210 - p**4/28 - 2*p**3/21 + 37*p**2/2 - 2*p + 7. Let y(w) be the second derivative of u(w). What is v in y(v) = 0?
-2, -1
Let b = 309958/3 + -103319. Factor b*c**3 + 0 + 8/3*c**2 + 16/3*c.
c*(c + 4)**2/3
Let y be (-2 - -1)*(0/1)/((-34)/(-17)). Let x(b) be the first derivative of 9/5*b**5 + 0*b**2 + 30 + 1/2*b**6 + b**3 + 9/4*b**4 + y*b. Factor x(a).
3*a**2*(a + 1)**3
Let z be (2/(-4))/((-2)/80). Suppose -4*b + 16 = -52. Find c, given that -z*c**2 + 0*c - 1 - 2 - 6*c + b*c**2 = 0.
-1
Suppose 443*f - 452*f + 1521 = 0. Let -2*k**2 - 88 - k**2 - k**2 + f*k - 261*k = 0. What is k?
-22, -1
Let c be (4 - -1)*(56/(-35))/1. Let y be (-25)/(-100) - 46/c. Suppose -y*b + 2*b - b + 4*b**2 + b = 0. What is b?
0, 1
Let f(c) = -170*c - 214*c - 386*c + 58*c**2 - 563*c**2 - 110*c**3 - 330. Let w(j) = -5*j**3 - 23*j**2 - 35*j - 15. Let p(z) = 2*f(z) - 45*w(z). Factor p(x).
5*(x + 1)**2*(x + 3)
Suppose -4 = -4*n + 4. Suppose 234 = 4*o + 198. Factor -6*g - 15*g - 18 + o*g - n*g**2.
-2*(g + 3)**2
Suppose -2*m - 1 = -k - 3, 0 = -k - 4*m + 10. Let q be (-15)/(-2) - 2 - (-13)/(-26). Factor -q*l + 3*l - 3*l**3 + 2*l**4 + l - 2*l**k + 4*l**3.
l*(l - 1)*(l + 1)*(2*l + 1)
Let j(f) be the first derivative of f**4/28 + f**3 + 39*f**2/14 + 183*f + 1. Let c(o) be the first derivative of j(o). Determine a so that c(a) = 0.
-13, -1
Let s(g) be the second derivative of -g**5/5 - 26*g**4/3 - 322*g**3/3 - 272*g**2 - g - 1612. Factor s(v).
-4*(v + 1)*(v + 8)*(v + 17)
Let g(h) be the second derivative of 78*h - 1/72*h**4 - 13/120*h**5 + 0 + 1/180*h**6 + 13/36*h**3 + 0*h**2. Factor g(s).
s*(s - 13)*(s - 1)*(s + 1)/6
Let z(x) = -x**3 + 3*x**2 - x + 6. Suppose 2*f + 6 = 4*f. Let m be z(f). Factor 2*a**2 + 4*a**m + 7*a**4 - 2*a**5 - 9*a**4 - 2*a**3.
-2*a**2*(a - 1)*(a + 1)**2
Factor -35609764*r + 35609764*r + r**3 + 904*r**2.
r**2*(r + 904)
Let i(f) be the third derivative of -f**7/315 + 47*f**6/180 - 23*f**5/45 + 911*f**2. Determine j so that i(j) = 0.
0, 1, 46
Let f(x) be the second derivative of -5/48*x**4 - x + 22 - 1/80*x**5 + 0*x**2 - 1/6*x**3. Determine i, given that f(i) = 0.
-4, -1, 0
Suppose 3*i + 4*b + 4 = 2*b, 5*i = 2*b + 20. Let c be ((-220)/50 - (-6)/(-10)) + 20. Determine g so that -11*g**2 + c*g**i - 7*g**2 - 6*g + 9 = 0.
-3, 1
Let a be 7/(28/39) + (-3)/4. Factor 5*d + a*d + 3*d**2 + 7*d + 6*d.
3*d*(d + 9)
Let a(r) be the second derivative of r**6/135 - r**5/15 - 5*r**4/18 + 44*r**3/27 + 28*r**2/3 + 160*r - 2. Factor a(f).
2*(f - 7)*(f - 3)*(f + 2)**2/9
Solve 20*y**2 - 3733987*y + 3733972*y + 5 - 5*y**3 - 5 = 0 for y.
0, 1, 3
Let c(q) be the first derivative of q**8/168 - q**6/12 + q**4/3 - 67*q**2/2 - 256. Let o(r) be the second derivative of c(r). Suppose o(l) = 0. Calculate l.
-2, -1, 0, 1, 2
Let a(m) be the first derivative of -9/4*m**2 - 6 + 1/180*m**6 + 1/15*m**5 + 1/4*m**4 + 16*m + 0*m**3. Let v(u) be the first derivative of a(u). Factor v(j).
(j - 1)*(j + 3)**3/6
What is f in 3/5*f**5 + 129/5*f**4 - 1323/5 - 858/5*f**3 + 1194/5*f**2 + 171*f = 0?
-49, -1, 1, 3
Suppose 94/13*s + 264/13 + 2/13*s**2 = 0. What is s?
-44, -3
Let d be ((-18904)/48)/(-17) + -23. Factor -7/6*v**5 + 1/3 + d*v - 8/3*v**2 - 13/3*v**4 - 17/3*v**3.
-(v + 1)**4*(7*v - 2)/6
Let m(l) be the third derivative of -l**7/980 + l**6/126 + 3*l**5/140 - l**4/21 + 25*l**3 - 140*l**2. Let y(n) be the first derivative of m(n). Factor y(b).
-2*(b - 4)*(b + 1)*(3*b - 1)/7
Suppose 5*l = 5*v - 45, -3*l + 2508*v - 2506*v = 16. Find d, given that 10/3*d - 2/3*d**l + 16 = 0.
-3, 8
Let a = 95916 - 95914. Factor 21/5*j**3 + 51/5*j + 3 + 57/5*j**a.
3*(j + 1)**2*(7*j + 5)/5
Let g(j) be the third derivative of -1/780*j**6 + 0*j - 74 - 37/130*j**5 + 3136/39*j**3 + j**2 - 252/13*j**4. Factor g(k).
-2*(k - 1)*(k + 56)**2/13
Let c be 56/224 - (1 - 3/4). Solve 14*u + 26*u**4 + 6*u**5 + c + 2 + 97*u**3 + 36*u**2 - 53*u**3 = 0.
-1, -1/3
Let m = -2686 - -2406. Let n be m/(-160) - (-10)/(-8). Factor 2197/2 - 507/2*v + 39/2*v**2 - n*v**3.
-(v - 13)**3/2
Let p = -888 + 948. Suppose -3*q - p = -66. Factor -16/7 + 4/7*l**3 - 16/7*l + 4/7*l**q.
4*(l - 2)*(l + 1)*(l + 2)/7
Suppose 876*c = -759*c + 1972*c - 1011. Solve 0 + 1/3*o**c + 1/6*o**4 + 0*o + 1/6*o**2 = 0 for o.
-1, 0
Let t(r) be the first derivative of r**4/14 + 4*r**3/3 + 8*r**2 + 128*r/7 - 4269. Factor t(o).
2*(o + 2)*(o + 4)*(o + 8)/7
Suppose -3*m - 379 = -127. Let n = -80 - m. Suppose -40*o**4 - 46*o**4 + 122*o**4 - 41*o**n = 0. What is o?
0
Let u be 2/6*(-24)/4 + -487. Let f = u + 492. What is b in -2/9*b**f + 2/3*b - 4/9 + 0*b**2 = 0?
-2, 1
Let j be 0 + ((-50)/30 - 15816/(-7479)). Let c = j + -1/277. Factor -70/9*l**4 - 25/9*l**5 + 0 - 23/3*l**3 - 28/9*l**2 - c*l.
-l*(l + 1)**2*(5*l + 2)**2/9
Let v = -578 + 580. Suppose 5*j + v*f = 42, -j + 3*f + 9 = 4*f. Factor 32/3*w + 8/3*w**3 + 1/3*w**4 + j*w**2 + 16/3.
(w + 2)**4/3
Let w(t) be the second derivative of t**6/40 - 21*t**5/10 - t**4/16 + 7*t**3 + 2089*t. Factor w(h).
3*h*(h - 56)*(h - 1)*(h + 1)/4
Let z be (-63)/(-24)*(-167 + 172). What is t in -3/4 - 51/8*t**2 - z*t = 0?
-2, -1/17
Let m = -26752 + 26793. Let o(n) be the first derivative of -12*n + 5*n**2 + 2/3*n**3 - m. What is i in o(i) = 0?
-6, 1
Suppose 20*j - 540 - 2740 = 0. Factor 33*s**2 - j*s**4 + 18*s**3 + 18*s + 85*s**4 + 82*s**4.
3*s*(s + 1)*(s + 2)*(s + 3)
Suppose 98*j - 27 = 125*j. Let g be 7/28*3 + j/4. Factor 0*y + y**4 + 0 - 3/2*y**5 + g*y**3 + 0*y**2.
-y**3*(y - 1)*(3*y + 1)/2
Suppose 57*k + 134*k - 948 = 33*k. Let y(p) be the second derivative of 0 + k*p + 0*p**2 + 2/3*p**3 - 1/6*p**4. Factor y(v).
-2*v*(v - 2)
Factor 238*l + 176*l - 124*l**2 - 50*l + 24.
-4*(l - 3)*(31*l + 2)
Determine d, given that 3/8*d**2 + 27/8 - 15/4*d = 0.
1, 9
Let s(l) be the first derivative of -l**6/60 + l**5/10 - l**4/6 + 39*l**2 - 52. Let d(c) be the second derivative of s(c). Factor d(a).
-2*a*(a - 2)*(a - 1)
Let x(r) be the first derivative of -16*r**5/5 + 140*r**4 + 2500*r**3/3 - 70*r**2 - 624*r - 1012. Find n, given that x(n) = 0.
-4, -1/2, 1/2, 39
Let u = 1586 - 1571. Suppose 2*f + 6 = -u*d + 20*d, 0 = -3*f - 9. Factor 0*g - 2/9*g**3 + d - 14/9*g**2.
-2*g**2*(g + 7)/9