 5*g**4 + 28*g**3 + 19*g**2 - 4*g. Let b(m) = -3*m**4 - 18*m**3 - 12*m**2 + 3*m. Let l(x) = n*b(x) + 5*u(x). Solve l(q) = 0 for q.
-1, 0, 1, 4
Suppose -6*v = -9*v + 471. Let -148*x**3 - 90 - v*x**3 + 340*x**3 + 10*x**2 - 315*x = 0. What is x?
-3, -2/7, 3
Suppose -748*h + 1893 - 344 = -1443. Find y, given that 0 - 3*y**2 - 3/2*y**5 + 0*y**3 + 3*y**h + 3/2*y = 0.
-1, 0, 1
Let r(v) be the first derivative of -72*v**2 + 0*v - 96 - 368/3*v**3 - 5*v**4. Let r(b) = 0. Calculate b.
-18, -2/5, 0
Suppose 415*t - 151*t = 0. Let d(m) be the third derivative of t*m - 11*m**2 - 1/4*m**4 + 11/20*m**5 + 0 + 0*m**3 + 2/35*m**7 - 13/40*m**6. Factor d(l).
3*l*(l - 2)*(l - 1)*(4*l - 1)
Suppose 5970 = 964*u + 3159 - 11649. Factor -1/3*y**2 + 46/3 - u*y.
-(y - 1)*(y + 46)/3
Find x, given that 4/7*x**2 + 792/7 + 276/7*x = 0.
-66, -3
Let b(c) be the first derivative of 3*c**5/10 + 93*c**4/2 - 6614. Let b(x) = 0. Calculate x.
-124, 0
Let u(r) = 14*r**2 + 6624*r + 6746. Let i(d) = -5*d**2 - 2208*d - 2251. Let g(l) = -17*i(l) - 6*u(l). Factor g(n).
(n - 2209)*(n + 1)
Let y(o) = -3*o**3 + 10016*o**2 - 6693364*o + 1490388162. Let q(d) = 35*d**3 - 120190*d**2 + 80320370*d - 17884657945. Let x(v) = 2*q(v) + 25*y(v). Factor x(p).
-5*(p - 668)**3
Let r = 87 - 69. Suppose -t = 5*f - 33, -3*f + r = -f + 2*t. Suppose -10*a + 0 + f - 9*a**2 - 7*a + 2*a = 0. What is a?
-2, 1/3
Let n be 29 + -24 - (5 - 2). Factor 0*r**2 - r**2 - 4*r + 10*r**2 + 10 + 19*r - 4*r**n.
5*(r + 1)*(r + 2)
Suppose -104 - 100 = -51*r. Find x such that 2*x**3 - x**r + 2*x**4 - 1072*x**2 + x**4 - 6*x**3 + 1074*x**2 = 0.
0, 1
Let c(k) be the second derivative of 0*k**5 + 17/2*k**2 + 1/60*k**6 + 0 - 1/4*k**4 + 14*k - 2/3*k**3. Let v(i) be the first derivative of c(i). Factor v(h).
2*(h - 2)*(h + 1)**2
Factor -2*o**2 + 728*o - 16611848 - 2062*o - 10194*o.
-2*(o + 2882)**2
Suppose -10*b = -15*b + 20. Suppose 0 = 4*a - 20, b*r - 25 = 3*r - 5*a. Factor r + 0*i**2 - 8*i + 4 + 4*i**2.
4*(i - 1)**2
Let o be (12/(-9))/((-8)/36). Suppose 4*j - o = 6. Factor 6*z**j - 8 + 360*z - 372*z - 2*z**3.
4*(z - 2)*(z + 1)**2
Let w(f) = 12*f**2 - 14*f - 152. Let d be w(-7). Let x = d - 532. Solve 0*k - 2*k**x + 0 - 2/3*k**3 = 0.
-3, 0
Let q = -34 + 152. Let i be -6 + q/8 + 1/4. Determine p so that -5 + 1 - 8*p - p**3 + 8*p - 6*p**2 - i*p = 0.
-4, -1
Let t be (-2)/((-25)/(-4 - -9)). Let a be ((486/24)/(-9))/(6/(-8)). What is c in -2/5*c**a + 2/5*c**2 + 0 + 2/5*c - t*c**4 = 0?
-1, 0, 1
Factor -50/3*f + 2/3*f**3 + 5*f**2 - 125/6 - 1/6*f**4.
-(f - 5)**2*(f + 1)*(f + 5)/6
Let m(q) be the first derivative of -5*q**3/3 - 165*q**2 + 680*q + 1513. Factor m(l).
-5*(l - 2)*(l + 68)
Let f(y) be the third derivative of 2*y + 7/18*y**3 - 1/180*y**5 + 10*y**2 + 1/12*y**4 + 0. Factor f(c).
-(c - 7)*(c + 1)/3
Let x be -1*3 + (-54)/(-6) + 19. Solve -28*t**2 + 8*t + x*t**3 - 12*t**3 + 7*t**4 - 15*t**3 + 2 - 2 = 0 for t.
-2, 0, 2/7, 2
Let s be ((-24)/28)/((-6)/448). Factor 49*o + 31*o - 16*o + 68 - 72*o**2 - s*o**3 + 4*o**4.
4*(o - 17)*(o - 1)*(o + 1)**2
Factor -71*h**2 + 252*h + 13068 - 2232*h - 87*h**2 + 30*h**3 - 98*h**2 + 3*h**4 - 65*h**2.
3*(h - 6)**2*(h + 11)**2
Let z(d) be the first derivative of -d**5 - 20*d**4 + 290*d**3/3 + 40*d**2 - 285*d + 615. Determine f so that z(f) = 0.
-19, -1, 1, 3
Let j(p) be the third derivative of p**6/360 + 7*p**5/30 + 9*p**4/8 - 486*p**3 + 18*p**2 - 12. Factor j(n).
(n - 12)*(n + 27)**2/3
Suppose 0 = 3*s - 4*h + 15, 36*h + 13 = -4*s + 39*h. Let a be (-1 - s)*5*3/(-15). Factor -2/5*n**4 + 18/5*n + 14/5*n**3 - 6*n**2 + a.
-2*n*(n - 3)**2*(n - 1)/5
Let r = 514217/5 + -102841. Factor 0 + 16/5*k**3 - r*k + 44/5*k**2.
4*k*(k + 3)*(4*k - 1)/5
Let f(g) be the first derivative of 38*g - 1/2*g**4 + 34/3*g**3 + 114 + 37*g**2. Factor f(h).
-2*(h - 19)*(h + 1)**2
Let t(b) = 8*b**3 - 74*b**2 - 122*b + 1272. Let q be t(9). Solve q*n**2 - 44*n + 121/3 = 0 for n.
11/6
Let t be 2*5 + (1 + -3 - -1). What is n in -3*n**2 - 5*n**4 + t*n + 18*n**2 + n = 0?
-1, 0, 2
Suppose -4*s + 4*f = -2512, 3*s - f - 1250 = 640. Find x such that x - s*x**4 + 3*x**2 - x**3 + 1249*x**4 - 621*x**4 = 0.
-1, -1/3, 0, 1
Suppose 0*b - 4*b = 8, -4*v + b = -174. Let l = -41 + v. Determine p so that p**3 - 15*p + 7 + 10*p**2 - 17 + l*p**3 + 12*p**3 = 0.
-1, -2/3, 1
Let w(d) be the first derivative of -d**6/120 + d**5 - 50*d**4 + 5*d**3/3 - 27. Let s(o) be the third derivative of w(o). Factor s(v).
-3*(v - 20)**2
Let r = -393 - -377. Let q be r/(-104) + 24/351. Determine w so that -14/9*w - 2/3 - q*w**3 - 10/9*w**2 = 0.
-3, -1
Let y(s) be the second derivative of 5*s**7/126 + 23*s**6/15 + 209*s**5/60 + 2*s**4/3 - 26*s**3/9 + 4387*s. Solve y(h) = 0.
-26, -1, 0, 2/5
Let l = 2239/70 - 317/10. Let s(m) be the first derivative of 4/7*m**3 - 16 - 16/7*m + 8/7*m**2 - l*m**4 - 4/35*m**5. Determine x so that s(x) = 0.
-2, 1
Let k(g) be the second derivative of 10*g - 1/10*g**2 - 1/20*g**4 - 1/10*g**3 - 2 - 1/100*g**5. Factor k(b).
-(b + 1)**3/5
Suppose 4*o = -7 - 13. Let l be (-2)/o + 115/25. Suppose -l*n - n - n + 2*n**2 + 5*n = 0. What is n?
0, 1
Suppose -4*c - 214*d + 211*d = 0, 0 = c - 2*d + 11. Let v(x) = -x**3 - 4*x**2 - 12*x - 27. Let o be v(c). Factor 2/11*k**4 + 0 + o*k - 2/11*k**3 - 4/11*k**2.
2*k**2*(k - 2)*(k + 1)/11
Let f(u) be the second derivative of -u**8/1344 + u**7/420 - u**5/120 + u**4/96 + 205*u**2/2 - 221*u + 1. Let h(t) be the first derivative of f(t). Factor h(v).
-v*(v - 1)**3*(v + 1)/4
Suppose -4*q + 156 = 3*k + 174, -6*q - 46 = -5*k. Factor 272/3*y - 9248/3 - 2/3*y**k.
-2*(y - 68)**2/3
Let j(w) = -3*w**3 + 2*w + 1. Let v be j(-1). Suppose 3*c = -3*z - 213 + 147, 4*c - 3*c + 79 = 18*z. Suppose 2/3*p**z - 2/3*p - 2/3 + 2/3*p**v = 0. What is p?
-1, 1
Suppose 146 - 602 = -4*w. Let c be (-206)/(-310) - w/1767. Factor c*u**4 + 0*u - 3/5*u**2 + 0 + 0*u**3.
3*u**2*(u - 1)*(u + 1)/5
Suppose 0 = o - m - 4, 3*o - 65 = -2*o - 4*m. Let d(v) = -v**2 - 6*v - 3. Let s be d(-5). Find l such that o - 14*l**3 + 17*l**s + 7*l**2 + 3 + 8*l + 42*l = 0.
-1, -2/7, 3
Factor 796*s - 1593/2 + 1/2*s**2.
(s - 1)*(s + 1593)/2
Suppose 867 = 28*r - 27*r. Factor -47*c - 64*c + 60*c**2 + 54 + r*c**3 - 870*c**3.
-3*(c - 18)*(c - 1)**2
Factor -16 - 11*y - 10 + 1 - 2*y**2 + 28 - 17.
-(y + 2)*(2*y + 7)
Let o(q) be the first derivative of -q**4/10 + 10*q**3/3 - 66*q**2/5 - 90. Let o(f) = 0. What is f?
0, 3, 22
Factor -375 - 26*t**2 + 21*t**2 - 122*t + 20*t - 38*t.
-5*(t + 3)*(t + 25)
Let r(i) be the first derivative of i**6/18 - 4*i**5 + 435*i**4/4 - 1350*i**3 + 7290*i**2 - 17496*i + 804. Factor r(c).
(c - 18)**3*(c - 3)**2/3
Suppose 2*k = k. Let h(q) = q**3 + 15*q**2 - 30*q + 68. Let o be h(-17). Let -2 - 45*m + k*m**3 - 19 - 27*m**2 - 3*m**3 + o = 0. Calculate m.
-7, -1
Let i(a) = -3*a**4 + 7*a**3 + 7*a**2 - 27*a + 10. Let m(y) = -48*y**4 + 111*y**3 + 111*y**2 - 429*y + 156. Let x(v) = 33*i(v) - 2*m(v). Solve x(t) = 0.
-2, 1, 3
Suppose 0 = 14779*a - 14789*a. Let s(t) be the first derivative of -3/2*t**4 - 1/2*t**6 + 0*t + 9/5*t**5 + a*t**3 + 0*t**2 + 33. Factor s(n).
-3*n**3*(n - 2)*(n - 1)
What is t in -4/7*t**3 + 0*t + 0*t**2 - 2/7*t**4 + 0 = 0?
-2, 0
Let j(i) be the second derivative of -58956/5*i**2 - 51/10*i**4 + 22 - 1734/5*i**3 + 2*i - 3/100*i**5. Factor j(g).
-3*(g + 34)**3/5
Let j(g) = 1. Let h(p) = 6*p**2 + 0*p**2 - 18 - 2*p + 6*p + 2*p**3. Let a(s) = -2*h(s) - 36*j(s). Let a(z) = 0. What is z?
-2, -1, 0
Let a(d) = 15*d - 115. Let u be a(8). Suppose u*x + 3 = -4*b, -23 + 8 = -4*b + x. Let p + 0 - 1/2*p**5 + 3/2*p**b + 5/2*p**2 - 1/2*p**4 = 0. Calculate p.
-1, 0, 2
Suppose 31*p = 69*p - 34*p. Suppose -z + 13 - 11 = p. Factor 0 + 2*y**z + 8/5*y + 2/5*y**3.
2*y*(y + 1)*(y + 4)/5
Let m(j) be the second derivative of -j**4/12 + 264*j**3 - 313632*j**2 - 3587*j. Factor m(x).
-(x - 792)**2
Let i = 32343 + -32341. Find o, given that 5/2*o**i + 1/4*o**3 + 0 + 9/4*o = 0.
-9, -1, 0
Let 17/6*j - 1/6*j**2 - 1/6*j**3 - 5/2 = 0. Calculate j.
-5, 1, 3
Suppose 194417/5*t**2 - 356*t + 4/5 + 806404/5*t**3 = 0. What is t?
-1/4, 2/449
Suppose -14 = 53*k - 60*k. Let h(a) = -6*a - a + 2*a + 4*a + 1 + a**2. Let m(s) = -8*s**2 + 4*s - 3. Let t(g) = k*m(g) + 14*h(g). Solve t(q) = 0 for q.
-4, 1
Let h(u) be the second derivative of -1/80*u**6 - 272*u + 0 + 0*u**3 + 1/28*u**7 - 27/40*u**5 + 0