*m + 34. Let h(t) be the first derivative of i(t). Factor h(a).
-a*(a - 2)/3
What is l in -1/4*l**2 - 4 + 17/4*l = 0?
1, 16
Let x be 1/((-9)/(-2 - (-11)/33*-3)). Suppose -50 - x*y**2 - 95/6*y + 1/6*y**3 = 0. Calculate y.
-5, 12
Let u(w) = w**3 + 3*w**2 + 7*w + 9. Let f be u(-3). Let d be f/108 + 2/18. Find c, given that 1/6*c**3 + 0*c + 1/6*c**2 + d = 0.
-1, 0
Let z = -4694 - -98578/21. Let x(w) be the second derivative of 25*w + 1/42*w**4 - 5/7*w**2 + 0 + z*w**3. Suppose x(f) = 0. What is f?
-5, 1
Factor 1300/9*w**2 - 872/3*w + 0 + 4/9*w**3.
4*w*(w - 2)*(w + 327)/9
Let t = -704 + 713. Factor 259*u**3 - t - 18*u**2 - 259*u**3 - 24*u + 3*u**4.
3*(u - 3)*(u + 1)**3
Let -714*j**2 - 4*j**4 + 841 + 45*j**3 - 710*j**2 + 1432*j - 1477*j**3 - 477 + 1064 = 0. What is j?
-357, -1, 1
Let n(x) be the second derivative of 5*x**3/3 - 4*x**2 - 23*x. Let q be n(1). Factor -8*j**2 - 24*j + 36*j + 2*j**3 - 6*j**q.
2*j*(j - 6)*(j - 1)
Let u(p) be the first derivative of -p**8/1176 + p**7/245 - 2*p**5/105 + 87*p**2 + 82. Let s(t) be the second derivative of u(t). Suppose s(j) = 0. What is j?
-1, 0, 2
Let f(n) = -n**2 + 104*n - 679. Let r(h) = -4*h**2 + 312*h - 2036. Let w(a) = 4*a + 8. Let s be w(-4). Let j(p) = s*f(p) + 3*r(p). Factor j(o).
-4*(o - 13)**2
Let o = -34763 + 34767. What is r in -6/7*r**o + 0*r - 3/7*r**5 + 0*r**3 + 0 + 0*r**2 = 0?
-2, 0
Let u(c) = -c**2 + 16*c + 151. Let f be u(-7). Let t be ((-296)/185)/(8/f). Factor -1/3*z**3 - 2/3*z**t + 0 + 0*z.
-z**2*(z + 2)/3
Let k = -266 + 1333/5. Let i(p) be the first derivative of 0*p + 7 + 1/5*p**3 + k*p**2. Solve i(a) = 0 for a.
-2, 0
Let n = 46011/2 + -23004. Determine w, given that 0 - n*w**5 - 48*w**3 - 48*w**2 + 0*w - 15*w**4 = 0.
-4, -2, 0
Let m be ((-7364)/(-8416))/((-21)/(-6)). Factor -529/4 - m*p**2 - 23/2*p.
-(p + 23)**2/4
Let g(v) be the first derivative of -v**4/4 - v**3/3 + v**2 + 182. Let b(m) = 5*m**3 + 32*m**2 + 157*m - 450. Let q(w) = -5*b(w) - 20*g(w). Factor q(i).
-5*(i - 2)*(i + 15)**2
Let s(j) be the second derivative of -8/3*j**3 + 64*j**2 + 1/24*j**4 + 13 + 2*j. Factor s(p).
(p - 16)**2/2
Let j = 4541/13760 - 53/172. Let d = 1301/960 - j. Let -d + 32/9*n**2 + 4/9*n**3 - 2/3*n**5 - 20/9*n**4 + 2/9*n = 0. What is n?
-3, -1, 2/3, 1
Suppose 0*b + 210 = 3*b. Let f = 190 - b. Factor -117*j**4 - 2*j**2 - 4*j**2 + f*j**4 - 3*j**3.
3*j**2*(j - 2)*(j + 1)
Let t(w) be the third derivative of 0*w**3 + 51*w - w**2 + 0*w**4 - 1/945*w**7 + 0 - 1/45*w**5 + 1/108*w**6. Factor t(q).
-2*q**2*(q - 3)*(q - 2)/9
Let j(x) be the first derivative of -x**4/20 - 496*x**3/15 - 61997*x**2/10 - 122018*x/5 - 1973. Factor j(m).
-(m + 2)*(m + 247)**2/5
Let -2/7*h - 6/7*h**3 - 6/7*h**2 - 2/7*h**4 + 0 = 0. What is h?
-1, 0
Find u such that 162/7 - 2/7*u**4 + 96/7*u**2 - 4/7*u**3 - 36*u = 0.
-9, 1, 3
Solve 2/3*a**2 - 148 + 218/3*a = 0 for a.
-111, 2
Let n(z) be the second derivative of -z**7/3360 - 41*z**6/960 + 21*z**5/80 - 47*z**4/2 - 2*z + 11. Let p(u) be the third derivative of n(u). Factor p(x).
-3*(x - 1)*(x + 42)/4
Suppose 32/13 - 12/13*f - 2/13*f**2 = 0. Calculate f.
-8, 2
Suppose 19371 - 19019 = 32*y. Let h(f) be the third derivative of y*f**2 + 0 + 4/33*f**4 - 1/330*f**5 - 64/33*f**3 + 0*f. Determine o, given that h(o) = 0.
8
Let g(j) be the third derivative of 5/2*j**3 + 12*j**2 + 0 + 0*j + 1/72*j**4 - 1/1080*j**6 + 0*j**5. Let l(v) be the first derivative of g(v). Factor l(u).
-(u - 1)*(u + 1)/3
Let q be (2009/(-196))/(2/(-8)). Let o = 41 - q. Determine n, given that 2/9*n + o - 2/9*n**2 = 0.
0, 1
Let j be 0*4/(-12)*1 + 6. Suppose -j*c + 2*c + 3*y = -12, -c = 4*y + 16. Factor 0*r**2 - 2/3*r**4 + c + 0*r**3 + 0*r - 2*r**5.
-2*r**4*(3*r + 1)/3
Let n(p) be the second derivative of p**6/180 - 83*p**5/60 + 2351*p**4/24 - 3403*p**3/9 + 1681*p**2/3 - 235*p - 2. Let n(j) = 0. What is j?
1, 82
Suppose -52 - 5*s**2 + 121*s + 282 + 218*s - 234*s = 0. Calculate s.
-2, 23
Let v(x) = x**3 - 44*x**2 - 39*x - 268. Let r be v(45). Suppose 4*s - 4*i - 26 + r = 0, 4*s + i - 9 = 0. Factor 0 + 0*w - s*w**2 + 3/2*w**3.
3*w**2*(w - 2)/2
Let h(b) = 2*b**2 - 1. Let r(n) = 7*n**2 + 164*n - 167. Let u(j) = 12*h(j) - 3*r(j). Factor u(y).
3*(y - 163)*(y - 1)
Factor 115*d - 1/3*d**2 - 344/3.
-(d - 344)*(d - 1)/3
Let q = 281 + -277. Suppose 110*o + 5*r = 111*o - 20, -4*o + q*r + 16 = 0. Factor o - 1/7*x**2 + 3/7*x.
-x*(x - 3)/7
Suppose -28*o - 55*o - 37*o + 414 = 18*o. Factor 0 - 1/6*n**o + 0*n + 28/3*n**2.
-n**2*(n - 56)/6
Let y(t) = 33*t**3 + 5*t + t**4 + 64*t + 9*t**4 + 87*t**2 - t**4 + 18. Let l(b) = b**4 + b**2 - b - 1. Let s(g) = 6*l(g) - y(g). Determine n so that s(n) = 0.
-8, -1
Let o(w) = -10*w**2 - 25*w + 10. Let v(d) = -d**3 + 40*d**2 + 95*d - 38. Let y(c) = 19*o(c) + 5*v(c). Suppose y(u) = 0. What is u?
0, 2
Factor -3120*c**3 + 1554*c**3 + 90*c + 1562*c**3 + 274*c - 360*c**2.
-4*c*(c - 1)*(c + 91)
Let l(w) be the second derivative of -w**6/210 + 93*w**5/140 - 2297*w**4/84 + 2085*w**3/14 - 2025*w**2/7 + 8242*w. Find f such that l(f) = 0.
1, 2, 45
Determine r, given that -3827/3*r**2 + 1604/3*r + 1426/3*r**3 + 268 - 7/3*r**4 = 0.
-2/7, 1, 2, 201
Determine x, given that -2*x**2 - 86/13*x - 60/13 = 0.
-30/13, -1
Let z(r) = -172*r**3 + 97940*r**2 + 46240712*r + 92090024. Let i(j) = -80*j**3 + 45203*j**2 + 21341867*j + 42503088. Let g(w) = -28*i(w) + 13*z(w). Factor g(p).
4*(p + 2)*(p + 941)**2
Suppose 47455 + 86*j**2 + 2127*j - 43213 - 83*j**2 = 0. What is j?
-707, -2
Let m(z) be the first derivative of -5*z**4/4 + 440*z**3/3 - 5250*z**2 + 35280*z - 1377. Suppose m(v) = 0. What is v?
4, 42
Let l(f) = -4*f**3 + 1. Let w be l(-1). Suppose -37*s + 489 - 193 = 0. Find m, given that -4*m**2 + 0*m**2 + s + w*m**2 - 3*m**2 = 0.
-2, 2
Let a(f) = -f**3 - f**2 + f + 1. Suppose 12 = 4*y + 8. Let g(u) = -125*u**4 + 865*u**3 - 2130*u**2 + 2365*u - 995. Let d(n) = y*g(n) + 15*a(n). Factor d(l).
-5*(l - 2)**2*(5*l - 7)**2
Let k(y) be the first derivative of y**5/15 - 3*y**4 + 34*y**3/3 - 30*y**2 - 96. Let c(t) be the second derivative of k(t). Find x, given that c(x) = 0.
1, 17
Let d be 32 + -40 - (-40)/(-150)*8/((-64)/260). Factor 20/3 + d*g**2 - 14/3*g.
2*(g - 5)*(g - 2)/3
Find m such that 0 - 2/3*m**5 + 8/3*m - 16/3*m**2 + 2*m**3 + 4/3*m**4 = 0.
-2, 0, 1, 2
Let o = -6636107/9 + 737355. Factor 350/3*m + 2/9*m**3 + o*m**2 + 196.
2*(m + 2)*(m + 21)**2/9
Suppose 5*s + j = 7*s - 16, -j + 12 = 5*s. Let f(u) be the first derivative of -3*u**3 + 3/8*u**s - 6*u + 27/4*u**2 + 31. Find c, given that f(c) = 0.
1, 4
Let c(d) = -d**3 + 15*d**2 + 3*d. Let t be c(15). Let l = -38 + t. Solve w**3 - 6*w - l*w**3 + 15*w**2 - w**3 + w**3 = 0 for w.
0, 1/2, 2
Let u(i) = i**2 - 2*i + 1. Let w(c) = -5*c**4 + 7*c**3 - 5*c**2 + 9*c - 6. Let r(t) = -40*u(t) - 5*w(t). Determine s, given that r(s) = 0.
-1, 2/5, 1
Suppose n - t = -25, 4*n - 50 = t - 153. Let x = n - -28. Factor -192 - 144*j - 32*j**x - j**3 - j**2 - 2*j**3 - 3*j**2.
-3*(j + 4)**3
Let h(g) = -g**3 - 2*g**2 + g. Let y be h(1). Let n be (-96 - -102) + (y - 1). Factor 2/3*d**2 + 1/3*d + 0*d**n - 2/3*d**4 + 0 - 1/3*d**5.
-d*(d - 1)*(d + 1)**3/3
Let l(y) be the third derivative of -32*y**6/15 - 208*y**5/15 - 185*y**4/6 - 100*y**3/3 + 4*y**2 - 2. Factor l(f).
-4*(f + 2)*(8*f + 5)**2
Factor -1/2*c**3 + 23/2*c**2 - 11*c + 0.
-c*(c - 22)*(c - 1)/2
Let v(h) be the second derivative of -3*h**4/4 - 100*h**3/3 + 9025*h**2/2 + 184*h. Let g(o) = 2*o**2 + 2*o. Let m(u) = 5*g(u) + v(u). Find t such that m(t) = 0.
95
Factor 2481/2*b + 3/4*b**2 + 2051787/4.
3*(b + 827)**2/4
Suppose 33*v + r = 37*v - 26, -5*r - 34 = 4*v. Suppose 2160/7*g + 1728/7 + 468/7*g**2 + 37/7*g**3 + 1/7*g**v = 0. Calculate g.
-12, -1
Let t = -98/55 - -24/11. Let v be ((-25)/(-15))/((-35)/(-63)). Factor 2*a**2 + 8/5 + t*a**v + 16/5*a.
2*(a + 1)*(a + 2)**2/5
Let w(y) = 14*y**3 - 13*y**2 - 7*y. Let h(u) = -5*u**3 + 4*u**2 + 2*u. Suppose -147 = -g - 20*g. Let z(b) = g*h(b) + 2*w(b). Let z(j) = 0. What is j?
0, 2/7
Determine k, given that 5/2*k**2 - 1325/2*k + 0 = 0.
0, 265
Let y(j) = -j**3 + 14*j**2 - 2*j + 34. Let i be y(14). Let h be 1 + ((-30)/i - -8). Let -2/7*p**2 + 6/7*p**5 + 0 - 2*p**h + 0*p + 10/7*p**3 = 0. What is p?
0, 1/3, 1
Suppose -68*q = 203*q + 112*q. Factor -26/5*x**3 + 0 + q*x**2 - 2/5*x**4 + 0*x.
-2*x**3*(x + 13)/5
Let m(t) be the