 + 906. Let f(n) = 4*n**2 + 186*n + 176. Let q(a) = a**2 + 3*a + 1. Let i(u) = b*q(u) + f(u). Determine g so that i(g) = 0.
-1, 85
Suppose 0 = -4*r - 4*m - 12, 5*r + 4*m - 4 + 14 = 0. Factor -r*l**3 + 7*l**2 - 55*l**2 + 0*l**3.
-2*l**2*(l + 24)
Suppose 219 - 1535 = -178*u - 480*u. Factor -4*s + 2/5*s**u + 18/5.
2*(s - 9)*(s - 1)/5
Let 1312*y + 92*y**4 - 80*y**3 - 240 + 1838*y**2 + 201*y**3 + 605*y**3 - 28*y**5 + 6*y**3 - 3706*y**2 = 0. What is y?
-5, 2/7, 1, 6
Let a(w) be the second derivative of w**5/20 - w**4/3 - 5*w**3 - 6*w**2 - 115*w. Let g be a(8). What is q in -g*q - 8/3 + 20/3*q**2 = 0?
-2/5, 1
Let 3*o**2 - 203 - 30*o + 98*o - 10 + 142*o = 0. What is o?
-71, 1
Let f(c) be the third derivative of -c**6/30 - c**5 + 37*c**4/6 + 34*c**3 + 29*c**2 - 2*c - 7. Factor f(j).
-4*(j - 3)*(j + 1)*(j + 17)
Suppose -5*a + 726 = -a - 2*m, -3*a = -m - 544. Let x = -181 + a. Determine c, given that -10/13*c**4 + 18/13*c**3 + 4/13*c + 2/13*c**5 - 14/13*c**2 + x = 0.
0, 1, 2
Let r(o) be the second derivative of o**4/6 + 32*o**3/3 + 231*o**2 + 6445*o. Factor r(v).
2*(v + 11)*(v + 21)
Let s(g) be the second derivative of -g**5/10 - 73*g**4/6 + g**3/3 + 73*g**2 - 12*g + 56. Let s(a) = 0. Calculate a.
-73, -1, 1
Let p(k) be the second derivative of -21/20*k**5 - 2 + 2*k - 9*k**2 - 13/2*k**3 + 13/2*k**4. Factor p(x).
-3*(x - 3)*(x - 1)*(7*x + 2)
Suppose -7*b = -3*t - 8*b + 353, 0 = 2*b + 8. What is d in 623*d**5 + 9*d - 625*d**5 + 32*d**2 - 32*d**4 + t*d - 126*d**3 = 0?
-8, -1, 0, 1
Let t(c) be the third derivative of c**6/720 - 7*c**5/120 + c**4 - 9*c**3 - c**2 + 2516. Factor t(u).
(u - 9)*(u - 6)**2/6
Suppose 115*t + 271 - 4335 + 154 = 0. Let l(h) be the third derivative of 0 - 7/15*h**5 + 0*h + 0*h**3 - 49/12*h**4 - t*h**2 - 1/60*h**6. Factor l(p).
-2*p*(p + 7)**2
Let g(p) be the second derivative of -p**5/12 - 205*p**4/36 - 290*p**3/9 - 190*p**2/3 + 333*p. Suppose g(y) = 0. Calculate y.
-38, -2, -1
Let f = 9706547033/46516550082 + -5/4550631. Let s = f - -1/538. Factor -2/19*w**2 - s*w + 0.
-2*w*(w + 2)/19
Suppose 2/7*a**2 + 724/7*a + 65522/7 = 0. Calculate a.
-181
Let 352*c**3 - 3978*c**2 + 106*c**4 - 1066*c**3 - c**5 + 360*c**2 - 168*c**4 - c**5 - 6804*c = 0. Calculate c.
-9, -7, -6, 0
Let x = 10328 - 10326. Let i(n) be the first derivative of -n**5 + 38 - 50*n**x - 40*n - 30*n**3 - 35/4*n**4. Find p such that i(p) = 0.
-2, -1
Suppose -u - 40 - 16 = -3*o, 2*o + 4*u = 56. Suppose -7*d**3 - 6*d**3 + 18*d - 5*d**3 + o*d**3 - 20*d**2 = 0. What is d?
0, 1, 9
Let f be (-961)/(-2170) - 160/(-448). Factor 1372/5 + 84/5*g**2 - f*g**3 - 588/5*g.
-4*(g - 7)**3/5
Let g be 2/(-1)*(-27 - 3). Suppose 92 + g = 4*z. Let -z*a + 4*a**2 + 3*a + 0*a**2 + 3*a + 64 = 0. What is a?
4
Suppose 0 = -15*j - 9 + 39. Suppose j*f - 6*f + 4 = 0. Suppose f + 0*a - 1/4*a**2 = 0. What is a?
-2, 2
Let c(g) be the third derivative of g**6/60 - g**5/10 + g**4/6 + 5775*g**2. Determine f so that c(f) = 0.
0, 1, 2
Suppose 6*z + 367 = 379. Factor -59*w + 4*w**z + 72*w - 37*w.
4*w*(w - 6)
Let x(p) be the second derivative of -4/27*p**3 + 2/27*p**4 + 1/90*p**5 + 0 - 1/135*p**6 + 0*p**2 + 24*p. Factor x(d).
-2*d*(d - 2)*(d - 1)*(d + 2)/9
Let j(d) be the second derivative of -1/6*d**3 + 0 - 2/3*d**2 - 105*d + 1/36*d**4. Factor j(n).
(n - 4)*(n + 1)/3
Let u(k) = 1428*k - 152792. Let p be u(107). Suppose 14/9*t**3 + 4*t + 1/9*t**p + 19/3*t**2 - 12 = 0. What is t?
-6, -3, 1
Let v = 1288135/115494 + 258/19249. Factor v + 2/3*o**2 - 269/6*o.
(o - 67)*(4*o - 1)/6
Let o = 91595/99 - 8338/9. Let h = o - -977/627. Let 0 + 8/19*g**2 - h*g - 2/19*g**3 = 0. Calculate g.
0, 1, 3
Suppose -4*r + 1963 = -20*d + 15*d, 0 = -4*d + r - 1577. Let w be 9/((-495)/d) + -7. Solve 2*k**3 + w*k**5 - 16/11 - 24/11*k + 12/11*k**4 + 4/11*k**2 = 0.
-2, -1, 1
Let l(b) = 2*b**3 + 30*b**2 + 22*b - 7. Let n be l(-14). Let f be (-18)/(-56)*n/66. What is y in -f*y**3 - 9/8*y**2 + 81/8 + 27/8*y = 0?
-3, 3
Let d(x) be the third derivative of -19/25*x**5 - 8/15*x**3 - 14/15*x**4 + 56*x**2 - 6/25*x**6 + 0*x + 0. Find f such that d(f) = 0.
-2/3, -1/4
Let b(u) be the first derivative of -21/20*u**4 + 3/10*u**6 + 0*u**2 - 88 - 6/25*u**5 - 2/5*u**3 + 0*u. What is z in b(z) = 0?
-1, -1/3, 0, 2
Suppose -310997*w = -310974*w - 69. Suppose 4/5 + w*c**2 + 1/5*c**4 - 7/5*c**3 - 13/5*c = 0. What is c?
1, 4
Let d(h) be the third derivative of 1/450*h**5 - 7*h**2 + 1/3*h**3 + 0 + 0*h + 2/45*h**4. Let d(g) = 0. What is g?
-5, -3
Solve -2960*b**2 - 16*b**4 - 262*b**3 - 241*b**3 - 1584 - 343*b**3 - 1608*b**2 + 42*b**3 - 7428*b = 0.
-44, -3, -1/4
Let c be (4 + -10)*(-3)/(-1620)*-12. Find i such that -c*i**3 + 2/15*i + 2/5*i**2 - 2/5 = 0.
-1, 1, 3
Let m = 6508 - 6506. Let j(c) be the third derivative of -1/300*c**6 + 0*c**5 + 0 + 0*c**4 + 0*c**3 + 1/560*c**8 + 0*c - 7*c**m - 1/1050*c**7. Factor j(t).
t**3*(t - 1)*(3*t + 2)/5
Let p(m) = 7*m**3 - 796*m**2 + 3*m + 9. Let b(y) = -25*y**3 + 3182*y**2 - 11*y - 33. Let z(c) = -6*b(c) - 22*p(c). Find o such that z(o) = 0.
-395, 0
What is c in 0 + 15/4*c**2 + 0*c + 3/8*c**3 = 0?
-10, 0
Let q = -222 + 224. Factor -105*k - 5*k**q - 3008 + 18*k - 113*k + 1008.
-5*(k + 20)**2
Let a be (0 + 7)/(-7)*-233. Suppose 73*f - 140 - 34*f**2 - 55*f**3 - a*f + 12 + 53*f**3 = 0. What is f?
-8, -1
Let m be 1/18 - ((9 - 13) + 175/45). Let u(p) be the first derivative of -9 - 1/10*p**5 + 1/2*p**4 - p**2 + m*p**3 + 0*p. Factor u(c).
-c*(c - 4)*(c - 1)*(c + 1)/2
Factor -1972/11 + 90*h - 2/11*h**2.
-2*(h - 493)*(h - 2)/11
Let o(z) be the first derivative of -11/4*z**4 - 12 + 3*z**2 + 0*z - 31/3*z**3. Solve o(n) = 0 for n.
-3, 0, 2/11
Let v(m) be the first derivative of -48 + 1/4*m**4 - 1/18*m**6 + 2/15*m**5 - 4/9*m**3 - 2/3*m**2 + 0*m. Solve v(l) = 0 for l.
-1, 0, 2
Let u(z) = 17*z**2 - 152*z + 153. Let x(d) = 80*d**2 - 762*d + 766. Let w(a) = -28*u(a) + 6*x(a). Factor w(g).
4*(g - 78)*(g - 1)
Let i(c) = -c**2 - 33*c + 10. Let x be i(-20). Suppose x*h**2 + 61236 - 1093*h + 4888*h + 1090*h + 3215*h + 19764 + 3*h**3 = 0. What is h?
-30
Let i(o) = o + 19. Let q be i(-17). Find c, given that -20*c**3 - 24 + 4*c**4 + 46*c**2 - 45*c**2 + 20*c + 19*c**q = 0.
-1, 1, 2, 3
Let d be -4 + 4 + 7 + 31226/39. Let n = -803 + d. Find b, given that -n*b - 2/3*b**2 - 20/3 = 0.
-5, -2
Factor -12*z**2 + 24*z + 0 + 3/2*z**3.
3*z*(z - 4)**2/2
Let n = 631 - 619. Solve 25*i**2 + 22*i**3 - n - 59*i - 13*i**2 + i + 36*i**2 = 0.
-3, -2/11, 1
Let i = 66083/3 + -330319/15. Factor 0 - 36*h**3 - 50*h - 2/5*h**5 - 80*h**2 - i*h**4.
-2*h*(h + 1)*(h + 5)**3/5
Let m(i) = -7*i**3 + 162*i**2 + 1434*i + 4308. Let d(n) = 23*n**3 - 488*n**2 - 4301*n - 12922. Let v(h) = 6*d(h) + 19*m(h). Factor v(r).
5*(r + 6)*(r + 12)**2
Suppose k + 7*k = 40. Suppose -k*l + 11 = -4. Determine t, given that -156*t**2 - 4*t**5 + 212*t**2 + 48*t**l + 20*t - 1 + 8*t**4 + 1 = 0.
-1, 0, 5
Let i = -357 + 373. Let m(v) be the first derivative of -2/15*v**5 - 1/6*v**4 + 2/9*v**3 + 1/3*v**2 + 0*v - i. Suppose m(c) = 0. What is c?
-1, 0, 1
Let u(p) be the first derivative of -p**3/6 - 21*p**2/4 - 10*p - 1152. Factor u(v).
-(v + 1)*(v + 20)/2
Let p(b) = 586*b**2 - 1167*b**2 + 583*b**2 + 23*b + 15. Let j be p(-11). Find z such that -2/23*z**j + 6/23*z**3 - 12/23 - 14/23*z + 6/23*z**2 = 0.
-1, 2, 3
Suppose 0 = 7*s - 20*s + 559. Suppose -43*x + s + 86 = 0. Solve 0*a**x - 1/3*a - 1/6*a**4 + 1/2*a**2 + 0 = 0.
-2, 0, 1
Factor 13/6*n**2 + n**3 - 7*n + 0 - 1/6*n**4.
-n*(n - 7)*(n - 2)*(n + 3)/6
Let 254 - 739 + 176*y - 635 - 752 - y**2 - 3*y**2 = 0. Calculate y.
18, 26
Suppose -18*m - 51 = -35*m. Let j be (2 + (-208)/91)/((-1)/m). Factor -1/7*r**5 - j*r**4 - 12/7*r**2 - 13/7*r**3 - 4/7*r + 0.
-r*(r + 1)**2*(r + 2)**2/7
Let t = 516 + -492. Factor -110 + 110 - 4*y**4 - 20*y**3 - t*y**2.
-4*y**2*(y + 2)*(y + 3)
Suppose 4*a = 2*z + 20, 13*a - 5 = 18*a + 5*z. Find m such that 0*m + 0 + 4/7*m**5 - 48/7*m**2 - 32/7*m**a + 4/7*m**4 = 0.
-2, 0, 3
Let r(n) = 13*n. Let y(b) = 18*b. Let x(q) = -7*r(q) + 5*y(q). Let p(c) = -5*c**2 - 247*c - 3125. Let i(t) = p(t) + 3*x(t). Factor i(o).
-5*(o + 25)**2
Suppose -4 = t + 3*s, 12*t + 12 = 13*t - s. Let g(x) be the first derivative of x**4 + t*x - 2*x**2 + 12 - 8/3*x**3. Factor g(p).
4*(p - 2)*(p - 1)*(p + 1)
Let o(h) be the second derivative of h**4/6 - 7*h**3/6 + 5*h**2 - 8*h.