= -a*k + 165. Suppose 64*m + 80*m**4 + 5*m**3 - 32 - 6*m**3 - 16*m**2 - k*m**3 - 74*m**4 = 0. Calculate m.
-2, 2/3, 2
Let t(n) be the first derivative of 146/3*n**3 + 22/5*n**5 - 43/2*n**4 + 32*n - 1/3*n**6 - 56*n**2 + 200. Let t(m) = 0. Calculate m.
1, 4
Let c be 246*(-2)/(-42) - 6/8*160/20. Solve 10/7*x**5 - 170/7*x**2 + c - 86/7*x**4 + 214/7*x**3 - 8/7*x = 0 for x.
-2/5, 1, 2, 5
Let z be 12/(-12 - -8) + 222 + -215. Factor -1/2*i**z - 8 - 12*i + 3*i**3 - 1/2*i**2.
-(i - 4)**2*(i + 1)**2/2
Let w = -751048/237 - -3169. Let q = w - -701/474. Suppose -1/2*s**3 + 3/2*s**2 - q*s + 1/2 = 0. What is s?
1
Let w be 353 + -341 - 398/20 - -8. Solve 1/10 + w*g**2 + 1/5*g = 0 for g.
-1
Let w(m) be the third derivative of -1/12*m**5 - 5/12*m**4 + 0*m + 0 - 78*m**2 + 5/2*m**3. Factor w(x).
-5*(x - 1)*(x + 3)
Let o(d) be the first derivative of -5*d**3/6 + 25*d**2 - 375*d/2 - 4112. Factor o(t).
-5*(t - 15)*(t - 5)/2
Let w(v) be the first derivative of -v**3 - 141*v**2 - 6627*v - 1018. Factor w(r).
-3*(r + 47)**2
Let h be (2 + -2)/(-17) + (-1 - -4). Let v(t) be the second derivative of t**4 + 15*t + 3/5*t**2 + 13/10*t**h + 27/100*t**5 + 0. Factor v(u).
3*(u + 1)**2*(9*u + 2)/5
Let u(b) be the third derivative of 0 + 0*b**3 - 1/30*b**6 - 71*b**2 + 1/3*b**5 - b**4 + 0*b. Factor u(d).
-4*d*(d - 3)*(d - 2)
Let j(m) be the first derivative of 0*m - 26 + 4/5*m**2 - 2/15*m**3 - 2/5*m**4 + 2/25*m**5. Factor j(q).
2*q*(q - 4)*(q - 1)*(q + 1)/5
Let r(l) = -l**2 - 11*l + 1866. Let g be r(-49). Let n(z) be the first derivative of 2 - 16/3*z**3 + 0*z**2 + 0*z + z**g. Suppose n(u) = 0. What is u?
0, 4
Factor -2/13*n**2 + 648/13*n + 1304/13.
-2*(n - 326)*(n + 2)/13
Find h, given that -1969974/7 + 1963098/7*h + 6870/7*h**2 + 6/7*h**3 = 0.
-573, 1
What is i in 30 - 23/2*i + 1/2*i**2 = 0?
3, 20
Let q(l) be the third derivative of 0*l**3 + 1/14*l**7 - 2*l**2 - 1/5*l**6 + 1/5*l**5 + 0*l**4 - 11 - 1/112*l**8 + 0*l. Let q(b) = 0. Calculate b.
0, 1, 2
Let h(n) be the first derivative of -n**4/2 + 10*n**3/3 + 14*n**2 + 340. Factor h(j).
-2*j*(j - 7)*(j + 2)
Let t(r) = 5*r**3 + 43*r**2 + 98*r + 57. Let o be 3/(110/(-25) + 5) + -2. Let d(a) = 40*a**3 + 345*a**2 + 785*a + 455. Let v(s) = o*d(s) - 25*t(s). Factor v(x).
-5*(x + 1)*(x + 3)*(x + 4)
Let l = -58 - -62. Suppose 0 = l*t - 51 + 31. Determine z so that z**5 - 3*z**t - 4*z**4 + 4*z**5 = 0.
0, 2
Let l(i) be the second derivative of 209 - 1/48*i**4 - 1/2*i**2 - i - 1/6*i**3. Solve l(u) = 0 for u.
-2
Suppose 16*h = 12*h - 148. Let w = h - -47. Factor -4*l**2 + 196*l**3 - 201*l**3 - w*l - 11*l**2.
-5*l*(l + 1)*(l + 2)
Let l(s) = -61*s**2 + 69*s + 40. Let r(v) = 54*v**2 - 64*v - 40. Let n(u) = 8*l(u) + 9*r(u). Suppose n(p) = 0. What is p?
-10, -2
Let a = 2420279/2 - 1210107. Suppose -64*b**2 + 1 + a*b**3 + 61/2*b = 0. What is b?
-2/65, 1
Let x(o) be the first derivative of 2*o**5/75 + 4*o**4 + 160*o**3 + 383. Factor x(a).
2*a**2*(a + 60)**2/15
Let m(w) = w**3 + 16*w**2 - 278*w - 3739. Let y be m(16). Factor 3/5*j**y + 0*j + 3*j**4 + 21/5*j**3 + 9/5*j**2 + 0.
3*j**2*(j + 1)**2*(j + 3)/5
Factor 2*x - 92 + 2*x**2 + 42*x - 29*x + 27*x.
2*(x - 2)*(x + 23)
Determine u, given that -2/5*u**3 - 4*u**2 + 27/5*u + 6/5*u**4 - 1/5*u**5 - 2 = 0.
-2, 1, 5
Let k(z) = -255*z**2 + 68*z + 8. Let b(i) = 265*i**2 - 67*i - 8. Let a(c) = -12*b(c) - 10*k(c). Factor a(r).
-2*(7*r - 2)*(45*r + 4)
Suppose 0 = -13*w - 260 + 169. Let l be 42/(-12) + 4 - 0/w. Factor l*i**2 - 5/2*i + 2.
(i - 4)*(i - 1)/2
Let w(p) be the second derivative of 2/15*p**3 - 1/120*p**4 - 3 - 20*p - 7/20*p**2. Let w(r) = 0. What is r?
1, 7
Let s = -671 - 47. Let j = s - -10784/15. Suppose -8/5*o + 8/15 + j*o**3 - 6/5*o**2 = 0. What is o?
-1, 2/7, 2
Suppose -552 = 6*j - 12*j. Let u be 11/(165/(-10)) + j/3. Solve -8*f**2 + f**2 - u*f**3 - 10*f**2 - 6*f - 9*f**4 - 10*f**2 = 0 for f.
-2, -1, -1/3, 0
Let w(k) be the second derivative of -5*k**4/12 + 25*k**3/2 + 1750*k**2 + 4294*k. Factor w(l).
-5*(l - 35)*(l + 20)
Suppose -6 = -t + l, 6*l - 11 = -3*t + 2*l. Factor 108*g**2 + 12*g + 38*g**3 + 24*g**4 + 4*g**t + 10*g**3 - 68*g**2.
4*g*(g + 1)**3*(g + 3)
Let p(m) be the second derivative of -5*m**7/84 + 13*m**6/12 + 17*m**5/8 - 895*m**4/8 + 180*m**3 + 1215*m**2 - 7*m - 57. Suppose p(o) = 0. What is o?
-6, -1, 2, 9
Factor -864 + 114*g**2 + 9*g**2 - 684*g - 3*g**4 + 51*g**2 + 18*g**2 + 9*g**3.
-3*(g - 6)**2*(g + 1)*(g + 8)
Let q(n) be the second derivative of -n**5/4 - 55*n**4/12 + 892*n. Determine o so that q(o) = 0.
-11, 0
Let p = 287 + -285. Let f(q) = q**2 + 2. Let o(h) = -h**2 + 26*h + 165. Let y(i) = p*o(i) + 4*f(i). Factor y(a).
2*(a + 13)**2
Let b(d) be the first derivative of -2*d**5 + 0*d + 10/3*d**3 + 37 - 5/6*d**6 + 5/4*d**4 + 0*d**2. Determine z so that b(z) = 0.
-2, -1, 0, 1
Let g(h) be the first derivative of h**4/14 + 100*h**3/21 + 369*h**2/7 + 3933. Let g(w) = 0. What is w?
-41, -9, 0
Let o be (-46)/(-3) + 288/(-216). Let m(h) be the first derivative of 0*h**3 - 1/3*h**2 + 4/9*h + 1/18*h**4 - o. Factor m(c).
2*(c - 1)**2*(c + 2)/9
Let y(o) be the first derivative of 1/25*o**4 - 2/25*o**3 + 2/125*o**5 + 30 + 8/25*o - 4/25*o**2. Factor y(v).
2*(v - 1)**2*(v + 2)**2/25
Let q(l) be the second derivative of -l**6/60 + 5*l**5/6 - 8*l**4/3 - 77*l**3/6 - 212*l. Let b(n) be the second derivative of q(n). Factor b(x).
-2*(x - 16)*(3*x - 2)
Determine r, given that 3*r**5 + 22929*r + 9*r**4 - 9*r**2 - 35*r**3 - 22935*r + 38*r**3 = 0.
-2, -1, 0, 1
Let g be 4 + 2*(-5)/10 + 1. Suppose 50*i + 4*b = 53*i - 1, g*b = -4*i + 20. Solve -2/5*m**4 + 2/5*m**2 - 4/5*m + 0 + 2*m**i - 6/5*m**5 = 0.
-1, 0, 2/3, 1
Let j(s) be the second derivative of -s**7/399 + 4*s**6/285 - 3*s**5/95 + 2*s**4/57 - s**3/57 - 24*s - 5. What is p in j(p) = 0?
0, 1
Factor -2554*y - 5*y**2 + 13*y**2 - 2770*y - 9*y**2 - 10601536 - 1188*y.
-(y + 3256)**2
Factor -11*n + 1036*n - n**4 + 1290*n**3 + n**2 - 2315*n**3.
-n*(n - 1)*(n + 1)*(n + 1025)
Let y(p) = 5*p**2 - 37*p - 24. Let l be y(8). Determine b, given that l + 12/7*b**3 + 0*b - 2/7*b**4 - 18/7*b**2 = 0.
0, 3
Let r(a) = 3*a**3 + 5*a**2. Let c(d) = -924*d + 11*d**3 + 20*d**2 + 924*d. Let o(l) = -2*c(l) + 9*r(l). Factor o(q).
5*q**2*(q + 1)
Let w(j) be the second derivative of -11/4*j**3 - 3/2*j**2 + 2 - 9/8*j**4 - j. Find y such that w(y) = 0.
-1, -2/9
Let q(x) be the first derivative of 4487*x**3/6 + 324*x**2 + 2*x + 1891. Factor q(f).
(7*f + 2)*(641*f + 2)/2
Suppose -79 - 77 = -11*c - 134. Let m(a) be the first derivative of 0*a - 8*a**3 + 0*a**c + 4 - 3/4*a**4. What is q in m(q) = 0?
-8, 0
Factor 16/11 + 20/11*a**2 - 2/11*a**3 - 34/11*a.
-2*(a - 8)*(a - 1)**2/11
Suppose 107*s + 467*s + 16 = 16. Let w(n) be the first derivative of 2/11*n**3 - 1/2*n**4 + 0*n**2 + s*n + 20 - 8/55*n**5. Let w(l) = 0. Calculate l.
-3, 0, 1/4
Let x(r) be the third derivative of 0 + 1/120*r**6 + 20*r**2 + 0*r + 9/2*r**4 + 2/3*r**3 + 3/10*r**5. Let f(p) be the first derivative of x(p). Factor f(b).
3*(b + 6)**2
Let v(r) be the first derivative of -r**3/7 + 45*r**2/2 + 1308*r/7 - 2035. Find p such that v(p) = 0.
-4, 109
Let x(h) be the third derivative of 0*h**3 + 3/100*h**6 - 9/100*h**5 + 18*h**2 + 0*h + 0*h**4 - 1/350*h**7 - 1. What is j in x(j) = 0?
0, 3
Let 0 + 778/11*t**2 + 140/11*t - 108/11*t**4 + 642/11*t**3 = 0. Calculate t.
-5/6, -2/9, 0, 7
Let s(z) be the second derivative of -z**7/6 + z**6/10 + 386*z + 1. Determine b, given that s(b) = 0.
0, 3/7
Let s(u) be the third derivative of -11*u**7/180 + 283*u**6/240 - 2717*u**5/360 + 665*u**4/48 - 25*u**3/18 + u**2 - 502. What is y in s(y) = 0?
2/77, 1, 5
Let x(d) = -d**4 - 88*d**3 - 387*d**2 + 490*d. Let f(w) = -25*w**4 - 2370*w**3 - 10450*w**2 + 13230*w. Let m(o) = 2*f(o) - 55*x(o). Solve m(c) = 0 for c.
-14, -7, 0, 1
Factor -210635 + 81939 + 549*w**2 + 570*w**2 + 61169 - 312480*w - 246073 - w**3.
-(w - 560)**2*(w + 1)
Let j(s) be the third derivative of -s**6/24 + 269*s**5/2 - 5375*s**4/8 + 4030*s**3/3 - 1648*s**2. What is r in j(r) = 0?
1, 1612
Let f(l) be the third derivative of -l**6/24 + 47*l**5/12 + 2407*l**2. Factor f(m).
-5*m**2*(m - 47)
Let v(r) = -3987483*r**2 - 33863*r - 72. Let n(h) = -5981224*h**2 - 50792*h - 108. Let l(i) = 5*n(i) - 8*v(i). Factor l(o).
4*(706*o + 3)**2
Factor 1023/4*w**2 + 0 - 27/2*w**3 + 57/4*w.
-3*w*(w - 19)