 c = 444 - 440. Let r(t) be the first derivative of 0*t + 0*t**3 + 2/5*t**5 + 1/2*t**2 - 3/4*t**c + 8. What is k in r(k) = 0?
-1/2, 0, 1
Suppose -10*q + 12*q - 8 = 0. Suppose -44 = -q*i + 28. Factor 0*z + 4*z**4 - i*z**2 + z - 2*z + 24*z**2 - 9*z**3.
z*(z - 1)**2*(4*z - 1)
Let z(p) = -5*p + 113. Let c be z(22). Factor -118*a**3 - 116*a**3 + 235*a**3 + c*a**2 + 2*a.
a*(a + 1)*(a + 2)
Let z(w) = 2*w - 17. Let n be z(11). Suppose -4 = n*u - 7*u. Factor 5*l + 5*l + u*l - 9*l**3 - 3*l**4.
-3*l*(l - 1)*(l + 2)**2
Suppose 0 = 5*t + 2*o - 36, 17*t = 27*t + 3*o - 59. Factor 4/3 + 2/3*j**4 + 2/3*j**3 - 2/3*j - 2*j**t.
2*(j - 1)**2*(j + 1)*(j + 2)/3
Suppose -260*g = -2752 + 672. Let i(q) be the first derivative of 9 - 4/3*q**3 + g*q**2 - 12*q. Factor i(u).
-4*(u - 3)*(u - 1)
Let -24*m**2 - 27*m**2 + 3*m**2 + 12*m**2 - 80*m + 4 - 5*m**2 = 0. Calculate m.
-2, 2/41
Let m(o) be the third derivative of -o**5/270 - 4*o**4/9 + 100*o**3/27 - 332*o**2 + 2*o. Suppose m(d) = 0. What is d?
-50, 2
Let d(k) = k**2 + 547*k - 14295. Let q be d(25). Factor 0*t + 0 - 1/2*t**4 + 2/3*t**2 + 0*t**3 + 1/6*t**q.
t**2*(t - 2)**2*(t + 1)/6
Let u(v) be the first derivative of v**5 + 0*v**2 + 0*v + 90 - 25/2*v**4 + 80/3*v**3. Factor u(t).
5*t**2*(t - 8)*(t - 2)
Let d be (((1*-1)/1)/((-1013)/4052))/1. Solve 0*w**2 - 1/5*w**d + 2/5*w**3 - 2/5*w + 1/5 = 0.
-1, 1
Let m be (-28)/7 - 3/3*-6. Factor -14 - 17*l**m - 18 + 13*l**2 + 8 - 20*l.
-4*(l + 2)*(l + 3)
Let c = 587/2586 - 26/431. Let h(s) be the first derivative of -c*s**2 + 0*s - 21 + 1/12*s**4 - 1/9*s**3 + 1/15*s**5. Determine x so that h(x) = 0.
-1, 0, 1
Let y be (-3 + 1361/5)/(72/10). Let o = y - 332/9. Find i such that o*i**2 - 7/2 - 3*i = 0.
-1, 7
Factor 312*v**2 + 0*v + 3/2*v**3 + 0.
3*v**2*(v + 208)/2
Let l be 360/210*(-3)/(3 - (-54)/(-14)). Let v(a) be the second derivative of 1/56*a**7 + 0*a**5 - 2*a**3 + 1/10*a**l + a - 1 + 0*a**2 - a**4. Factor v(d).
3*d*(d - 2)*(d + 2)**3/4
Let b(o) = -4 + 8*o**2 + o**3 + 3 - 2 + 0*o**2 + 6*o. Let z be b(-7). Factor -z*t - 3*t + 4*t - 12*t**2 - 5*t + 4*t**4.
4*t*(t - 2)*(t + 1)**2
Let z = -450 - -793. Suppose z = q + 6*q. Find g, given that -3*g**2 - q*g**3 + 3*g - 3*g - 3*g**4 + 55*g**3 = 0.
0, 1
Let t be (16*57/(-152))/(-12) - (-1)/(-1 + 2). Factor 3/2*j**3 - 24*j + t*j**2 + 30.
3*(j - 2)**2*(j + 5)/2
Suppose 0 = h + 4*f - 19, -20 = -5*h - f - 1. Let -h*j**4 - 177*j**3 - 3420*j**2 + 24000 - 7737*j - 16056*j + 3393*j = 0. What is j?
-20, 1
Let j(y) be the second derivative of -74*y - 3/80*y**5 - 11/8*y**3 + 9/4*y**2 - 1 + 3/8*y**4. Suppose j(o) = 0. What is o?
1, 2, 3
Let m = 118808 - 118805. What is p in -24/7 + 10/7*p**5 - 26/7*p**4 - 128/7*p - 162/7*p**m - 230/7*p**2 = 0?
-1, -2/5, 6
Let y be 5 - 175/(-49) - (-3)/7. What is p in y*p - 4*p**2 + 3*p - 16 + 2*p**2 = 0?
2, 4
Let n be 1099 - -3 - (11 - 15). Let p = n + -1102. Factor 2/3*d**3 + 0*d - 2/3*d**p + 0 + 0*d**2.
-2*d**3*(d - 1)/3
Let -13005 - 265/2*p**3 - 15065/4*p**2 - 13515*p - 5/4*p**4 = 0. What is p?
-51, -2
Let y(u) = 0*u**2 + 2*u**2 + 4 + 12 - 4 - 10*u. Let o(b) = -b**2 + 2*b. Let w(r) = -3*o(r) - y(r). Suppose w(m) = 0. Calculate m.
-6, 2
Let f(z) = -11*z**2 + 359*z - 90. Let j(y) = -98*y**2 + 3232*y - 810. Let x(p) = -52*f(p) + 6*j(p). Factor x(s).
-4*(s - 45)*(4*s - 1)
Let f(q) = 2*q**2 + 102*q - 200. Let i(w) = 8*w**2 + 412*w - 802. Let l(g) = 18*f(g) - 4*i(g). Solve l(v) = 0.
-49, 2
Solve 121*b**3 - 10*b + 6 + 41*b**3 - 54*b**5 + 62*b**5 - 32*b**4 - 94*b**2 - 40*b**5 = 0 for b.
-3, -1/4, 1/4, 1
Let w(v) be the third derivative of -v**6/40 - 5*v**5/2 - 643*v**4/8 - 297*v**3 + v**2 - 6547. Solve w(o) = 0 for o.
-27, -22, -1
Let u(d) be the first derivative of -d**3/9 - 3836*d**2/3 - 14714896*d/3 + 2400. What is o in u(o) = 0?
-3836
Suppose -22*l + 13*l + 24 = 3*r, 3*r = 2*l + 13. Let d(c) be the second derivative of 0 - 1/4*c**4 - 8*c + 0*c**2 + 0*c**3 + 3/20*c**r. Solve d(y) = 0 for y.
0, 1
Let u = 207009 - 1035043/5. Determine b so that 6/5*b - 2/5 + u*b**3 - 6/5*b**2 = 0.
1
Let h(f) be the second derivative of f**7/3024 - 5*f**6/108 + f**4/3 + f**3/3 + 15*f + 4. Let g(r) be the third derivative of h(r). Factor g(v).
5*v*(v - 40)/6
Suppose 6*q + 158 = 4*j + 5*q, -162 = -4*j - q. Factor j*c**2 - 100 - 25*c - 16*c**4 + 4*c**2 + 51*c - 48*c**3 + 94*c.
-4*(c - 1)**2*(2*c + 5)**2
Suppose 9*d - 2*v - 16 = 5*d, -4*d + 5*v = -22. Factor 399*s**5 + 3*s**2 + 0 - 3*s**4 - 3*s**d - 396*s**5 + 0.
3*s**2*(s - 1)**2*(s + 1)
Let d(a) = 4*a**2 - 160*a - 47. Let l be d(40). Let z(o) = -o**3 - 46*o**2 + 51*o + 190. Let j be z(l). Let 0 + 2/3*h**j - 2/3*h**3 + 0*h = 0. Calculate h.
0, 1
Let g be -2*(-2)/(-4)*23. Let k = g - -25. Let 8*c + 10*c**3 - 26*c**k + 2 + 4 + 2 = 0. What is c?
-2/5, 1, 2
Let j(i) be the first derivative of -7/9*i**3 + 222 + 0*i + 1/15*i**5 - 2/3*i**2 + 5/24*i**4. Solve j(k) = 0 for k.
-4, -1/2, 0, 2
Suppose -7*c + n - 11136 = -11152, 4*c - 3*n = 14. Factor 36/5*y - 42/5*y**c + 16/5*y**3 - 2.
2*(y - 1)**2*(8*y - 5)/5
Let t = -8 + 3. Let x be 11*(2 + -22)/t. Solve -12*u**2 - 9*u**2 + x*u - 9 - 83*u + 9*u**2 = 0 for u.
-3, -1/4
Let o = -18231/2 - -9406. Let a = o - 290. Factor -1/2*n**2 + 2 - 2*n + a*n**3.
(n - 2)*(n - 1)*(n + 2)/2
Let h(m) be the first derivative of 3/28*m**4 + 8/21*m**3 + 52 - 15/14*m**2 + 4/7*m. Determine o, given that h(o) = 0.
-4, 1/3, 1
Let a be (-30)/6 + (5 - -3). Factor 110*n**2 + 50*n**4 - 5*n**5 - 35*n - 132*n**3 + 3*n**3 + 9*n**a.
-5*n*(n - 7)*(n - 1)**3
Let l(n) be the first derivative of -5*n**3/12 + 40*n**2 - 435*n + 1826. Factor l(w).
-5*(w - 58)*(w - 6)/4
Suppose 0 = 3*g + 5*f - 123, -3*g - 34 + 115 = -2*f. Let q(o) be the third derivative of 0 + 6/5*o**3 + 0*o + g*o**2 - 4/75*o**5 - 3/10*o**4. Factor q(n).
-4*(n + 3)*(4*n - 3)/5
Let i(u) be the first derivative of 4*u**3/3 - 130*u**2 + 256*u + 886. Determine z so that i(z) = 0.
1, 64
Let c(x) be the third derivative of -x**7/168 + x**5/24 + 39*x**3/2 + 10*x**2 + 8. Let m(l) be the first derivative of c(l). Factor m(f).
-5*f*(f - 1)*(f + 1)
Let n(a) = a**3 - 2*a**2 - 4*a + 3. Let f be n(-3). Let k be (-155)/f + (-3)/(-18). Factor -k*b**2 - 4/3*b**3 - 4/3 - 14/3*b + 2/3*b**5 + 4/3*b**4.
2*(b - 2)*(b + 1)**4/3
Let z be 1/(-2) - 2/(-4). Suppose 2583*r - 665 - 2285 = 1868 + 2931. Factor r*s - 3/2*s**3 - 3/2*s**2 + z.
-3*s*(s - 1)*(s + 2)/2
Let x(s) be the first derivative of s**3/18 - 5*s**2/12 - s + 288. Let x(t) = 0. What is t?
-1, 6
Factor 4/7*f**4 + 32400/7 + 376/7*f**3 + 9556/7*f**2 + 33840/7*f.
4*(f + 2)**2*(f + 45)**2/7
Let o = 90895 - 272683/3. Factor 0 - 2/3*u + o*u**3 - 1/6*u**2 + 1/6*u**4.
u*(u - 1)*(u + 1)*(u + 4)/6
Let o(h) be the second derivative of h**5/4 - 5*h**4/12 - 110*h**3/3 + 210*h**2 + h + 1654. Factor o(v).
5*(v - 6)*(v - 2)*(v + 7)
Let c(o) be the first derivative of -o**4/12 + 8*o**3/9 - 7*o**2/2 + 6*o - 501. Factor c(w).
-(w - 3)**2*(w - 2)/3
Let b(u) be the first derivative of -u**3/3 - 43*u**2/2 + 44*u - 27. Let y(l) = 4*l**2 + 216*l - 220. Let z(p) = 16*b(p) + 3*y(p). Find f, given that z(f) = 0.
-11, 1
Suppose -34 = -k - 22. Let v = k + -8. Let 15*r**2 - 2 + v*r**4 - 10 - 7*r**4 = 0. What is r?
-2, -1, 1, 2
Let w(g) = -2*g**5 - g**4 + g**3 - g**2 - g + 1. Let d(n) = 11*n**5 - 75*n**4 + 1594*n**3 + 85*n**2 - 1595*n - 5. Let f(p) = -d(p) - 5*w(p). Factor f(z).
-z*(z - 40)**2*(z - 1)*(z + 1)
Let p(j) be the third derivative of -j**6/120 + 3*j**5/2 - 879*j**2. Factor p(b).
-b**2*(b - 90)
Let r be ((-3)/4)/((-12)/8). Let l = 53190 - 53186. Factor -r*k**l + 0 + 1/4*k**5 + 1/4*k**3 + 0*k + 0*k**2.
k**3*(k - 1)**2/4
Let b(q) = q**3 - 5*q**2 - 32*q - 22. Let l be b(9). Let t be (11 + (-407)/55)/(l/10). Factor 58/7*r**4 + 0 + 30/7*r**2 - 66/7*r**3 - 4/7*r - t*r**5.
-2*r*(r - 1)**3*(9*r - 2)/7
Let n = 2249 + -2245. Let w(l) be the first derivative of -4/9*l**3 - 1/3*l**2 + 1/5*l**5 + 1/6*l**n - 5 + 1/3*l. What is j in w(j) = 0?
-1, 1/3, 1
Let f = 22 + -20. Let t(g) = -g**2 + 11*g - 8. Let q(j) = 21*j - 13*j**2 + 13*j - 33 + 10*j**2 + 11*j. Let l(b) = f*q(b) - 9*t(b). Let l(s) = 0. Calculate s.
1, 2
Let n = -386 + 488. Let d be (-34)/n - 7/(-3). Determine h, given that 2/9*h**3 + 2/9*h**4 - 8/9*h + 16/9 - 4/3*h**d = 0.
-2, 1, 2
Suppose 24 = 3*l - 5*h + 127, l + 5*h + 1 = 0. Let f be (-2 + (-3)/2)*13/l. Factor -5/2