v(y). Suppose -3*p**3 + 8*p**2 + z*p**2 - 7*p**2 = 0. What is p?
0, 3
Let d(v) be the first derivative of 4*v**3/3 + 8164*v**2 + 16662724*v - 3604. Factor d(g).
4*(g + 2041)**2
Let r(g) = -11*g**2 + g - 2. Let z(w) = -52*w**2 - 70*w - 262. Let k(d) = 5*r(d) - z(d). Factor k(l).
-3*(l - 28)*(l + 3)
Let l(x) = 17*x**4 - 64*x**3 + 183*x**2. Let a(h) = 155*h**4 - 575*h**3 + 1650*h**2. Let c(j) = -6*a(j) + 55*l(j). Factor c(y).
5*y**2*(y - 11)*(y - 3)
Factor -664/3*f + 1312/3 + 4/3*f**2.
4*(f - 164)*(f - 2)/3
Let g(y) be the third derivative of -6 + 0*y - 1/40*y**6 - 3*y**3 + 3*y**2 - 3/10*y**5 - 11/8*y**4. Factor g(f).
-3*(f + 1)*(f + 2)*(f + 3)
Factor 41*m**2 - 3*m**3 - m**2 + 23*m**3 - 55*m**2 - 31*m**2 + 28*m - 2*m**4.
-2*m*(m - 7)*(m - 2)*(m - 1)
Let o be 22/(5 + 1 - (-13332)/(-2211)). Let l = o + 2219/3. Let -l - 10/3*z - 2/3*z**2 = 0. What is z?
-4, -1
Solve -3/2*n**5 + 345/4*n**3 - 27/2 + 165/4*n**2 + 149/4*n**4 - 79/4*n = 0.
-1, -2/3, 1/2, 27
Let a = -101 + 105. Factor 39929*w + 13057*w - 4*w**a - 6144*w**2 + 12550*w - 262144 + 256*w**3.
-4*(w - 16)**4
Suppose 3*m = -3*m + 12. Let v(b) = 1 + 5*b + 6*b - 15*b**m + 2*b - b**2. Let r(q) = -33*q**2 + 25*q + 3. Let t(k) = -6*r(k) + 15*v(k). Factor t(a).
-3*(a - 1)*(14*a - 1)
Let n = -1893905 - -1893905. Factor 7*u**2 + n*u + 0 - 1/4*u**3.
-u**2*(u - 28)/4
Let y = 9/9452 - -4699/28356. What is d in -2 - y*d**2 - 4/3*d = 0?
-6, -2
Let 26/15*c + 0 + 28/15*c**2 + 2/15*c**3 = 0. Calculate c.
-13, -1, 0
Let n(s) = -37*s**2 + 197*s - 600. Let b(p) = 104*p**2 - 589*p + 1800. Let f(c) = 6*b(c) + 17*n(c). Factor f(t).
-5*(t - 3)*(t + 40)
Let i(n) = n**2 + n + 10. Let k(f) = -47*f**2 - 8471*f - 373817. Let c(r) = i(r) - k(r). Suppose c(w) = 0. Calculate w.
-353/4
Let u(l) = 96*l**3 - 105*l**2 + 876*l + 1008. Let h(q) = -25*q**3 + 26*q**2 - 219*q - 252. Let r(n) = -23*h(n) - 6*u(n). Let r(p) = 0. Calculate p.
-1, 12, 21
Let g(m) be the second derivative of -m**5/20 + 7*m**4/6 - 49*m**3/6 + 18*m**2 - 1575*m. Determine y so that g(y) = 0.
1, 4, 9
Let s(c) be the third derivative of c**7/270 - c**6/27 - 113*c**5/108 + 215*c**4/108 + 28*c**3/9 + 4*c**2 - 233*c - 1. Suppose s(j) = 0. Calculate j.
-7, -2/7, 1, 12
Let p(q) be the second derivative of 0*q**2 + 0*q**3 - 1/12*q**4 - 74*q - 1/6*q**6 - 1 - 3/10*q**5. Factor p(f).
-f**2*(f + 1)*(5*f + 1)
Factor 3/8*s**2 - 2577/8 - 1287/4*s.
3*(s - 859)*(s + 1)/8
Let i(s) = -s**5 - s**4 + s**3 + s**2 + 1. Let g(q) = -4*q**5 + q**4 + 12*q**3 - q**2 - 8*q + 5. Let z(h) = 2*g(h) - 10*i(h). Determine d so that z(d) = 0.
-4, -2, -1, 0, 1
Let n(d) be the first derivative of -d**4 + 184*d**3/3 + 392*d**2 + 800*d - 1005. Find o, given that n(o) = 0.
-2, 50
Let b = -214640 + 3219728/15. Determine a, given that 96/5*a - 194/15*a**2 - b - 2/15*a**4 + 12/5*a**3 = 0.
1, 8
Let v be (-9)/(-18)*(331 + 3). Factor 39*j**2 + 3*j**4 - v*j + 49*j + 46*j + 30*j**3.
3*j*(j - 1)*(j + 3)*(j + 8)
Let n(w) be the third derivative of -7/18*w**4 + 0 + 111*w**2 + 1/135*w**5 + 40/27*w**3 + 0*w. Let n(z) = 0. Calculate z.
1, 20
Suppose -7*v + 9423 = -601. Let i = -1430 + v. Factor -1/4*a**i - 1/2*a + 0.
-a*(a + 2)/4
Factor 2*p**2 - 3017*p - 7 - 31 - 188 + 3241*p.
2*(p - 1)*(p + 113)
Let j(v) = 4*v - 42 - v + 15 + 40 + 13. Let n be j(-8). Suppose -2 - 1/2*c**2 - n*c = 0. Calculate c.
-2
Let c(t) be the first derivative of 5*t**3/3 - 745*t**2/2 + 6747. Determine p so that c(p) = 0.
0, 149
Suppose 3*g = -5*c + 88, -1 + 9 = 4*c. Let r be g/4 + -1 + 6/(-12). Factor -8*h**2 - 2 + 2*h - r*h**3 + 10 + 2*h + h**3.
-4*(h - 1)*(h + 1)*(h + 2)
What is u in -129/5*u + 3/5*u**2 - 54 = 0?
-2, 45
Let y = -606 + 906. Let r be y/400*8/2. Factor -w - w**4 + 4/3*w**5 + 17/3*w**2 - 13/3*w**r - 2/3.
(w - 1)**3*(w + 2)*(4*w + 1)/3
Let w(v) be the third derivative of -v**5/75 - 14*v**4/5 + 704*v**3/15 - 4*v**2 + 120*v. Factor w(z).
-4*(z - 4)*(z + 88)/5
Let r be 120/(-400) - (92/(-240) + 0). Let x(f) be the first derivative of r*f**2 + 0*f + 5/36*f**3 + 6. Solve x(a) = 0 for a.
-2/5, 0
Let o be 72/28 - 20/(-14). Let v(c) be the third derivative of 1/60*c**6 + 0*c + 0 - 3*c**3 + 18*c**2 + 1/6*c**5 + 1/4*c**o. Factor v(w).
2*(w - 1)*(w + 3)**2
Let -100*b**4 - 10*b**3 - 79284 + 28*b**4 + 79284 + 33*b**5 + 72*b**2 - 11*b**3 - 12*b = 0. What is b?
-1, 0, 2/11, 1, 2
Let o(j) = -j**3 - 9*j**2 + 9*j - 6. Let y be o(-10). Suppose 0 = -y*f + 6 + 2. Factor 12*v**3 + 0*v**3 - f*v**4 + 6*v**4 - 10*v**3.
2*v**3*(2*v + 1)
Let r = -3 + 6. Suppose 8*n = -r + 35. Let 2*v**5 + 3*v**n + 11*v**3 - 11*v**3 - v**4 = 0. Calculate v.
-1, 0
Let d(j) be the second derivative of -j**5/20 - 5*j**4/2 - 203*j**3/6 + 117*j**2 - j - 754. Factor d(b).
-(b - 1)*(b + 13)*(b + 18)
Let f(p) be the third derivative of -p**7/840 + p**6/360 + p**5/120 - p**4/24 - 29*p**3/3 - 3*p**2 + 9. Let d(j) be the first derivative of f(j). Factor d(o).
-(o - 1)**2*(o + 1)
Let u(g) be the first derivative of -3*g**4/4 - 19*g**3 - 72*g**2 + 540*g - 7976. Factor u(p).
-3*(p - 2)*(p + 6)*(p + 15)
Let l(q) be the third derivative of -q**6/140 - 34*q**5/35 - 1445*q**4/28 - 9826*q**3/7 - 6383*q**2. Factor l(v).
-6*(v + 17)**2*(v + 34)/7
Let c(n) be the third derivative of 0*n**3 - 1/672*n**8 + 0*n**4 - 9*n**2 - 31/420*n**7 + 3 - 15/8*n**5 + 0*n - 17/16*n**6. Let c(h) = 0. Calculate h.
-15, -1, 0
Let l(y) be the first derivative of y**5/10 + 3*y**4/4 - 8*y**3/3 + 1489. Factor l(p).
p**2*(p - 2)*(p + 8)/2
Let j = 242206 - 242203. Factor -j*f**2 + 27/2 - 3/4*f**3 + 9/4*f.
-3*(f - 2)*(f + 3)**2/4
Let o(c) be the third derivative of -6*c**2 + 0*c**3 + 1/15*c**5 + 0 + 2*c + 0*c**4 - 1/60*c**6. Factor o(p).
-2*p**2*(p - 2)
Let r(f) = -3*f + 12. Let v be r(5). Let q be v - -82*(4 - 8)/(-4). Solve 127*j + 0*j**4 - 21*j**3 - q*j + 0*j**4 - 3*j**4 - 24*j**2 = 0.
-4, 0, 1
Let 0 + 71/7*m**3 + 38/7*m + 15/7*m**4 + 93/7*m**2 - 1/7*m**5 = 0. What is m?
-2, -1, 0, 19
Let z(q) = -q**3 + 14*q**2 - 4*q + 28. Let p be z(14). Let r be (-12)/p - (-248)/(-840). Let 0 - r*d**3 + 8/15*d**2 - 8/15*d**4 + 2/15*d = 0. Calculate d.
-1, -1/4, 0, 1
Let b(d) be the third derivative of 97/30*d**5 + 15*d**2 + 1/105*d**7 + 64/3*d**3 + 12*d**4 + d + 3/10*d**6 + 0. Factor b(k).
2*(k + 1)**2*(k + 8)**2
Suppose 96/17 - 608/17*s + 448/17*s**2 - 40/17*s**3 - 22/17*s**4 = 0. What is s?
-6, 2/11, 2
Let t(d) = -102*d**2 + 2*d - 9. Let m be t(2). Let i = 831/2 + m. Factor -i*g - 1/2*g**3 - 1 - 2*g**2.
-(g + 1)**2*(g + 2)/2
Let c(d) = 15*d**2 + 924*d + 70227. Let g(a) = 94*a**2 + 5546*a + 421362. Let y(r) = -19*c(r) + 3*g(r). Factor y(n).
-3*(n + 153)**2
Let a be 60/(-15) - 722/(-120) - (7 + -5). Let s(n) be the second derivative of -22*n + 0 - a*n**4 - 2/15*n**3 + 0*n**2. Solve s(h) = 0.
-4, 0
Let m(d) be the second derivative of -11*d - 4*d**3 - 36*d**2 - 1/6*d**4 + 0. Solve m(s) = 0 for s.
-6
Suppose 9588/7*o - 12/7 - 1915203/7*o**2 = 0. What is o?
2/799
Let i(u) be the first derivative of 10/9*u**3 + 1/6*u**4 + 4 + 2*u**2 + 0*u. Factor i(w).
2*w*(w + 2)*(w + 3)/3
Let i(g) = g**3 + 2*g**2 + g - 1. Let h(u) = -882*u**3 - 1756*u**2 - 866*u + 6. Let j(y) = -h(y) + 2*i(y). Factor j(t).
4*(t + 1)**2*(221*t - 2)
Let k(a) = -14*a**2 - 15*a**2 + 41*a**2 - 19*a**2 - 8 - 3*a. Let c(h) = 2*h**2 - h + 1. Let u(w) = -15*c(w) - 5*k(w). Let u(d) = 0. What is d?
-5, -1
Let v = 81110 - 81108. What is x in 4/3*x**v - 8/3*x - 4 = 0?
-1, 3
Let s(t) be the third derivative of -t**7/28 - 227*t**6/80 + 15*t**5/4 + 139*t**4/4 + 46*t**3 - 497*t**2. Let s(m) = 0. What is m?
-46, -1, -2/5, 2
Suppose 51*q = 24 + 231. Suppose 0 = -35*k + 40*k + q, m + k = 2. Factor 0 - 1/4*w**4 - 3/4*w**m + w**2 + 0*w.
-w**2*(w - 1)*(w + 4)/4
Let n(w) be the first derivative of -2*w**3/63 + 136*w**2/21 - 536*w/21 - 3087. Factor n(y).
-2*(y - 134)*(y - 2)/21
Factor -38*s**2 + 78*s**2 + 2*s**4 - s**4 - 36*s - 18*s**3 + 5*s**3.
s*(s - 9)*(s - 2)**2
Let v = -22 - -25. Factor -19*b**v - 95*b + 100*b**2 - 43 - 16*b**3 - 35 + 108.
-5*(b - 1)**2*(7*b - 6)
Let j = -297 + 299. Factor -3*q**3 + 24 + 0*q**j - 150*q + 0*q**2 + 6*q**2 + 180*q - 3*q**2.
-3*(q - 4)*(q + 1)*(q + 2)
Factor -4*o**2 - 138*o + 4 + 0 + 0*o**2 + 74*o + 62*o + 2*o**3.
2*(o - 2)*(o - 1)*(o + 1)
Let u be ((-2070)/1656)/((-5)/16). Let -159/2*j**2 - 39/4*j**u - 87/2*j**3 - 255/4*j - 75/4 - 3/4*j**5 = 0. What is