ppose 5*m = -4*a + 20, -490*m + 486*m + 16 = -4*a. Factor -2/21*b**2 + 0 + 4/21*b + 2/21*b**m - 4/21*b**3.
2*b*(b - 2)*(b - 1)*(b + 1)/21
Let i(j) = 26 + 0*j**2 + 0*j**2 + 6*j**2 - 8*j**2 - 13*j. Let m be i(-8). Determine w so that m*w - 2 - 1/2*w**2 = 0.
2
Let x(j) = -9*j**3 - j**2 + 446*j + 24. Let m(p) = 35*p**3 + 5*p**2 - 1785*p - 90. Let l(f) = -4*m(f) - 15*x(f). Factor l(g).
-5*g*(g - 9)*(g + 10)
Let l = 2/199525 - 1243838872/2194775. Let n = -566 - l. Factor -2/11*h**2 + n + 0*h.
-2*(h - 2)*(h + 2)/11
Let c = -79 + 81. Solve -9*d - 14 - 9*d - c + 1 - 3*d**2 = 0 for d.
-5, -1
Let v(i) be the second derivative of 12*i + 1/24*i**4 + 35/6*i**3 + 1225/4*i**2 + 2. Find a such that v(a) = 0.
-35
Suppose 6*c - n - 62 = -28, -3*c = -n - 19. Factor 1/4*j**c + 0*j + 243/4*j**3 - 729/4*j**2 - 27/4*j**4 + 0.
j**2*(j - 9)**3/4
Let a be 0/9*5/15. Let k be (2 + (-31)/15)*(a - 9). What is p in 0 - 12/5*p + 12/5*p**2 + k*p**3 - 3/5*p**4 = 0?
-2, 0, 1, 2
Let b = 2239 + -2235. Let i(v) be the first derivative of 13 + 0*v**2 - 6*v**3 + 96*v - 3/4*v**b. Let i(g) = 0. What is g?
-4, 2
Suppose 5*o - 4*x + 3*x = 1492, -898 = -3*o + 2*x. Factor -10*b + 0*b**2 + o - 223 - 3*b**2 - 2*b**2.
-5*(b - 3)*(b + 5)
Let m be -2 + 12 + 0/(-19). Suppose -m = -f - 5*k, 5*f + 2*k - 3 = 1. Factor 4/7*b**3 - 4*b - 24/7*b**2 + f.
4*b*(b - 7)*(b + 1)/7
Let f = 104407 + -104405. Solve -3/5*u**f - 36/5 - 39/5*u = 0 for u.
-12, -1
Let l(q) = -q**3 - 10*q**2 - 10*q - 6. Let j be l(-9). Factor 2 - o**3 + 1 - 5*o**j - 30*o - 18*o**3 + 51*o**2.
-3*(o - 1)**2*(8*o - 1)
Suppose -l = 3*o - 20, -5*l + 16 = -9. Suppose -4*b - 20 = 0, 5*v + 5*b - 6 + 21 = 0. Suppose -1 + 5*f**2 - v*f - 3*f**2 - 4*f + o = 0. What is f?
1, 2
Let r(o) be the first derivative of o**5 - 305*o**4/4 + 445*o**3 + 3605*o**2/2 + 1960*o + 5291. Factor r(z).
5*(z - 56)*(z - 7)*(z + 1)**2
Determine c, given that -2/3*c**3 - 17672/3*c + 0 + 376/3*c**2 = 0.
0, 94
Let g(x) = -3*x - 7. Let n be g(-4). Factor 4*p + 20*p - 779*p**2 + 788*p**2 + p**3 + n + 11.
(p + 1)*(p + 4)**2
Let i(q) = 19*q - 403. Let c be i(31). Let j = c - 184. What is h in -1/5*h**j + 0*h + 1/5 = 0?
-1, 1
Let j(h) be the second derivative of h**4/21 + 212*h**3/21 + 30*h**2 + 3845*h. Find p such that j(p) = 0.
-105, -1
Suppose -q = 5*z - 150, -8*q = -5*q. Suppose 0 = -12*i + 27*i - z. Let 0 - 1/6*h**3 - 49/6*h + 7/3*h**i = 0. What is h?
0, 7
Factor 315/8*k + 33/8*k**2 + 1/8*k**3 + 675/8.
(k + 3)*(k + 15)**2/8
Let n be -17 + -1 + 104/616*132. Determine y so that 2*y**4 + 0*y + 2/7*y**5 + 18/7*y**2 + 0 + n*y**3 = 0.
-3, -1, 0
Let y(z) = -z**3 - z**2 - z + 1. Suppose -12*q = -7*q - 30. Let x be (-208)/24 + q/9. Let a(f) = 10*f**3 + 16*f - 8. Let g(i) = x*y(i) - a(i). Factor g(c).
-2*c*(c - 2)**2
Suppose -4*g - 3 + 11 = 0. Let f be ((-169)/(-4056) + (-73)/216)*(-12)/16. Factor -f + 2/9*h**g + 2/9*h**3 - 2/9*h.
2*(h - 1)*(h + 1)**2/9
Let o(u) = -u**2 + 37*u + 49. Let h be o(38). Let j(y) = 2*y**2 - 1. Let b be j(1). Factor 9 - b - h*z + 9*z - 4*z**3 - 18*z + 16*z**2.
-4*(z - 2)*(z - 1)**2
Let x(z) be the second derivative of -z**4/3 + 178*z**3/3 + 465*z. Suppose x(v) = 0. Calculate v.
0, 89
Let y(p) = p**3 - 7*p**2 + p - 3. Let f be y(7). Suppose -3*s + 2*x - 1 = 0, -4*s - f*x = -7 - 25. Factor 2*n + 9*n**3 - 14*n**3 - 3*n + 6*n**s.
n*(n - 1)*(n + 1)
Let b(j) be the second derivative of -j**9/2520 + j**8/840 - j**7/1260 - 41*j**4/12 - 7*j. Let d(n) be the third derivative of b(n). Find v such that d(v) = 0.
0, 1/3, 1
Let y(n) be the second derivative of -n**7/42 + n**6/30 + n**5/4 - 5*n**4/12 - 2*n**3/3 + 2*n**2 - 760*n. Solve y(r) = 0.
-2, -1, 1, 2
Let n(c) be the first derivative of -115 + 15*c - 25/4*c**4 + 5/2*c**2 - 35/3*c**3. Factor n(i).
-5*(i + 1)**2*(5*i - 3)
Let m = -291 - -295. Let q be 55 + -53 - 6/m. Factor -q - 7/4*y**3 + 2*y**2 + 13/4*y.
-(y - 2)*(y + 1)*(7*y - 1)/4
Suppose 5*f - 5 = -5*l, -14*l = -9*l + f - 9. Suppose n + 4 = l*w + 5*n, w - 3*n - 2 = 0. Factor w*b + b + 357*b**3 + 4 + b - 358*b**3 - b**2.
-(b - 2)*(b + 1)*(b + 2)
Let i(m) be the third derivative of 1/12*m**4 - 2*m + 1/420*m**7 + 0*m**3 - 1/80*m**6 + 0*m**5 + 31*m**2 + 0. Factor i(u).
u*(u - 2)**2*(u + 1)/2
Let w(s) be the third derivative of 2*s**7/105 - 13*s**6/30 + 23*s**5/15 - 11*s**4/6 + 132*s**2 - 3. Factor w(z).
4*z*(z - 11)*(z - 1)**2
Let j be 42804/29 + -3*2. Let w = j - 1468. Factor 6/5 + 2/5*h**w + 8/5*h.
2*(h + 1)*(h + 3)/5
Let w(y) = -y - 2. Let v be w(-4). Let t = -40520758/11 + 3683706. Find c, given that -1/11*c**4 + 27/11 + 0*c - 18/11*c**v - t*c**3 = 0.
-3, 1
Let n(q) = 529*q + 3705. Let b be n(-7). Let o(p) be the first derivative of -5/3*p**4 - 8/3*p**3 + 9 - 2/5*p**5 - 2/3*p - b*p**2. Let o(m) = 0. What is m?
-1, -1/3
Let k(z) be the third derivative of -1/40*z**4 - 1/560*z**8 + 0*z**3 - 2/175*z**7 - 3/100*z**6 - 1/25*z**5 + 0*z + 14*z**2 + 0. Factor k(s).
-3*s*(s + 1)**4/5
Suppose -5*g + 19 - 4 = 0. Let -19*x**3 + 60*x - 75*x**4 + 63*x**2 + 12 - 64*x**3 + 23*x**g = 0. Calculate x.
-1, -2/5, 1
Let m(h) be the third derivative of 0 - 1/45*h**7 + 0*h - 13/36*h**6 - 22/9*h**3 - 35/36*h**4 + 43/30*h**5 + 57*h**2. Determine f so that m(f) = 0.
-11, -2/7, 1
Let f(c) be the second derivative of 5/48*c**4 - 3/4*c**3 + 35*c + 0*c**2 + 0. Suppose f(i) = 0. Calculate i.
0, 18/5
Let q be (-2*2/20)/((-6)/60). Let 27*h - 329 + 41*h + 131 + h**2 + 37*h - 4*h**q = 0. What is h?
2, 33
Suppose -34 = -4*p - p - 4*q, -4*q - 8 = -2*p. Suppose -p*j + 46 = 28. Factor -11/5*w**2 - 7*w - 5 - 1/5*w**j.
-(w + 1)*(w + 5)**2/5
Let m(t) be the second derivative of -t**5/10 - 47*t**4/6 - 475*t**3/3 + 1875*t**2 + 756*t. Suppose m(o) = 0. What is o?
-25, 3
Solve -3/4*t**3 + 321/4*t**2 - 68229/4 - 7353/4*t = 0.
-7, 57
Let v(h) = -81*h**2 + 15*h + 1011. Let n(z) = -5*z**2 + z + 64. Let s(r) = 33*n(r) - 2*v(r). Factor s(m).
-3*(m - 6)*(m + 5)
Suppose -2*g**2 - 63 - 65/2*g = 0. Calculate g.
-14, -9/4
Suppose 5*d - 28 = 3*d + 5*k, 0 = 3*d + 3*k. Let u be (-6)/20*(5 - 80/d). Determine n so that -u*n - 1/2*n**5 + 0 + 6*n**2 - 2*n**4 + n**3 = 0.
-3, 0, 1
Let r(p) be the first derivative of -21*p**5/5 + 927*p**4/8 - 11*p**3 + 3825. Factor r(q).
-3*q**2*(q - 22)*(14*q - 1)/2
Let s(c) be the first derivative of -c**4/4 + 7*c**3/2 - 15*c**2 - 110*c + 50. Let u(l) be the first derivative of s(l). Factor u(o).
-3*(o - 5)*(o - 2)
Let y = -413 - -412. Let o be 108/162*(y + 1 - -6). Let 2/3*x**o + 2/3*x**3 + 0*x + 1/6*x**5 + 0*x**2 + 0 = 0. Calculate x.
-2, 0
Let i(c) = c**3 - 26*c**2 + 51*c - 68. Let w be i(24). Let g(t) be the first derivative of -w - 3/11*t**2 - 2/33*t**3 + 0*t. Determine y so that g(y) = 0.
-3, 0
Factor -15/2 + 1/4*o**2 - 13/4*o.
(o - 15)*(o + 2)/4
Let m be (50 + 2376/(-48))/(3*(-1)/(-12)). Suppose 0 + 27*n**4 - 1/3*n - 33*n**3 + 19/3*n**m = 0. What is n?
0, 1/9, 1
Suppose 30 = 17*p - 11*p. Solve 8*i**4 + 8 - 16*i**2 + 4*i**3 - 7*i + p*i + 8*i**5 - 6*i**5 - 4*i**5 = 0.
-1, 1, 4
Let m be 1*4 - (15 - 56). Let j = 49 - m. Find w, given that -4*w**2 - 3*w**2 + 5 - 5*w - j*w**2 + w**2 = 0.
-1, 1/2
Let g be ((-5)/(-8) + (-15)/(-40))*-3. Let k(o) = o**2 - 2*o - 12. Let a be k(g). Suppose 4/9*b**2 + 2/9*b + 2/9*b**a + 0 = 0. What is b?
-1, 0
Suppose 2*m - 4*z = 6, -7 = -4*m - z + 5. Let v(w) be the second derivative of 0*w**2 + 0 + 1/30*w**4 - 18*w - 2/15*w**m. Determine y, given that v(y) = 0.
0, 2
Let h(w) = -14*w**2 - 63582 - 2*w**3 + 3*w**3 - 2*w + 10*w + 63472. Let z be h(14). Let -4/7*t**z + 0*t - 2/7*t**3 + 0 + 2/7*t**4 = 0. Calculate t.
-1, 0, 2
Factor 225*x**2 - 8*x**3 + 196*x**2 - 431*x**2 + 28*x + 6*x**3.
-2*x*(x - 2)*(x + 7)
Find r such that 1279*r**2 - 639*r**2 - 390 - 643*r**2 - 201*r = 0.
-65, -2
Let q = 1697/231 + -1/77. Let d = 88264 - 88260. Find s such that d*s**4 + 0 - q*s**3 + 8/3*s - 8/3*s**2 = 0.
-2/3, 0, 1/2, 2
Suppose 3*a - 8*k = -5*k + 27, 3*k = -2*a - 17. Let v(m) be the first derivative of 2*m**a + 7/2*m + 1/6*m**3 + 35. Determine q so that v(q) = 0.
-7, -1
Let h(v) be the first derivative of 5*v**3/3 - 61*v**2 + 48*v - 1028. Factor h(z).
(z - 24)*(5*z - 2)
Factor -1/2*f**2 + 152*f - 11552.
-(f - 152)**2/2
Suppose -5*a - 3*l = -16, 5*a - 13 + 1 = -l. Find c, given that 38*c**2 - 2 + 6*c**3 + 6*c - 12*c**2 - 16*c**a - 12*c - 8*c**4 = 0.
-1, -1/4, 1
Let g = 70615 +