4
Let n(s) be the third derivative of s**6/30 - 10*s**5/3 + 97*s**4/6 - 32*s**3 + 1500*s**2. Determine u so that n(u) = 0.
1, 48
Let w(v) be the first derivative of -v**3/15 + 117*v**2/5 + 47*v + 1036. Factor w(f).
-(f - 235)*(f + 1)/5
Let h = -17333/4 + 4334. Suppose -3*n + 3*p = -9, -2*n + 9 = -p - 2*p. Find a, given that -h*a + 3/8*a**2 + n = 0.
0, 2
Let s(j) be the second derivative of j**6/90 - 23*j**5/60 + 43*j**4/36 - 7*j**3/6 - 511*j + 2. Solve s(v) = 0.
0, 1, 21
Let k(p) be the third derivative of -p**6/900 - p**5/60 - p**4/15 - 25*p**3/6 - 5*p**2 + 4. Let g(b) be the first derivative of k(b). Factor g(x).
-2*(x + 1)*(x + 4)/5
Let r = 3711 + -3705. Let s(t) be the second derivative of t + 0 + 1/5*t**r + 1/2*t**4 - 11/10*t**5 - 6*t**2 + 11/3*t**3. Solve s(a) = 0 for a.
-1, 2/3, 1, 3
Let c be (-930)/124*(-36)/135. Solve -12/7*q + 0 - 2/7*q**c + 12/7*q**3 + 2/7*q**4 = 0.
-6, -1, 0, 1
Let x(f) be the first derivative of -f**4/8 + 9*f**2/4 - 1975. Determine i so that x(i) = 0.
-3, 0, 3
Let b = 103 + -87. Factor 20*j**2 - 52*j + 113*j - 53*j + b*j**3 + 4*j**4.
4*j*(j + 1)**2*(j + 2)
Let g(d) be the third derivative of -4*d**2 - 1/16*d**4 + 0 + 0*d + 7/320*d**6 + 3/40*d**5 - d**3 + 1/560*d**7. Factor g(p).
3*(p - 1)*(p + 2)**2*(p + 4)/8
Let u(c) be the second derivative of 2*c**6/45 - 2*c**5/5 - c**4 + 28*c**3/9 - 41*c + 7. Find r, given that u(r) = 0.
-2, 0, 1, 7
Factor 378075/2 + 1/6*j**2 + 355*j.
(j + 1065)**2/6
Suppose 15*o - 12*o = 93. Let v = o - 12. Factor -8*l + v*l**4 - 3*l**2 - 16*l**3 - 15*l**4 + 12*l**2 + 11*l**2.
4*l*(l - 2)*(l - 1)**2
Let y = 106/215 - 4/43. Let u = 1201083/5 + -240207. Find x such that u*x**2 + y*x**3 + 1024/5 + 384/5*x = 0.
-8
Let t(k) = k**2 - 2*k - 2. Suppose 0 = 2*s - 5*o - 3 - 0, 18 = -s - 4*o. Let h be t(s). Factor -77*z**3 - 256*z - 20*z**4 - 288*z**2 - h - 18 - 51*z**3.
-4*(z + 2)**3*(5*z + 2)
Let x(g) be the second derivative of -2*g**6/5 + 8*g**5/5 - g**4 - 4*g**3/3 - 68*g - 6. Factor x(b).
-4*b*(b - 2)*(b - 1)*(3*b + 1)
Let -72/7 + 3/7*o**3 + 18/7*o**2 - 57/7*o = 0. What is o?
-8, -1, 3
Let h(t) be the second derivative of 2*t**7/945 - 2*t**5/135 + 2*t**3/27 - 21*t**2 + 28*t. Let w(c) be the first derivative of h(c). Factor w(i).
4*(i - 1)**2*(i + 1)**2/9
Let a(l) be the second derivative of 2/3*l**6 + 8*l + 5/42*l**7 + 2 + 0*l**2 + 0*l**4 + 3/4*l**5 + 0*l**3. Suppose a(f) = 0. Calculate f.
-3, -1, 0
Let y(o) = -4*o**2 - 36*o + 64. Let k(j) = -j. Let s(i) = 2*i**2 - 4*i - 1. Let z(r) = 5*k(r) - s(r). Let d(l) = y(l) - 4*z(l). Factor d(u).
4*(u - 5)*(u - 3)
Let b be (-14)/77 - 897/(-33). Find j, given that -4*j**3 + 9*j + 3*j**2 + 7*j**3 - b*j**2 + 12*j = 0.
0, 1, 7
Let t = 808 - 829. Let h be ((-14)/t - 1)/(20/(-12)). Solve 0*p + 0 - 2/5*p**3 - h*p**4 - 1/5*p**2 = 0.
-1, 0
Let m(k) be the second derivative of k**6/135 - k**5/9 - 85*k**4/54 - 170*k**3/27 - 32*k**2/3 - 4*k + 541. Determine j so that m(j) = 0.
-3, -2, -1, 16
Let k(i) be the second derivative of 2*i**7/75 - i**6/30 - 2*i**5/75 + 47*i**2/2 + 4*i + 7. Let d(h) be the first derivative of k(h). Factor d(q).
4*q**2*(q - 1)*(7*q + 2)/5
Suppose 0 = 31*r - 7160 + 7005. Let q(s) be the third derivative of 0*s - 27/4*s**3 + 0 - 1/120*s**r + 3/8*s**4 - 35*s**2. Factor q(m).
-(m - 9)**2/2
Factor -908*d**2 + 1772*d + 1230*d - 2584882 + 826405 + 907*d**2 - 494524.
-(d - 1501)**2
Suppose v + 9*v = -v. Let x be 0/(2 + v/(-9)). Factor x - u**2 - 2/3*u.
-u*(3*u + 2)/3
Let c = 120926 + -967407/8. Factor 1/4*z**2 + 1/8*z**3 + c*z + 0.
z*(z + 1)**2/8
Let l be (4 + -2)*((-3)/2)/3. Let s be (6 - 0 - 37)/(l - 0). Find t, given that -9*t**2 + s*t**3 - 19*t**3 + 5 - 12*t + 7 - 3*t**4 = 0.
-1, 1, 2
Let p = -21020 + 21027. Let l(w) be the first derivative of -12*w - 2/3*w**3 - 32 - p*w**2. Suppose l(b) = 0. Calculate b.
-6, -1
Let f(z) be the third derivative of 25/12*z**4 + 0*z + 0 - 7/12*z**5 - 1/24*z**6 - 88*z**2 + 40/3*z**3. Solve f(u) = 0.
-8, -1, 2
Suppose -2*u = -10*u + 16. Factor 18*i - 14*i**u - 13*i**2 + 29*i**2 + 18*i + 162.
2*(i + 9)**2
Suppose -p = -2 - 10. Suppose 0 = -7*q - 2*q + p*q. Factor 0*g**2 + q*g + 0 + 2/5*g**3 - 2/5*g**4.
-2*g**3*(g - 1)/5
Let j(c) be the first derivative of -9*c**6/16 + 99*c**5/8 - 669*c**4/8 + 190*c**3 - 192*c**2 + 90*c + 1634. Suppose j(d) = 0. Calculate d.
2/3, 1, 6, 10
Let g be (-14398)/481*55/(-4400). Let z = g - -2/2405. Solve z*m**4 - 3/8*m**3 + 3/2*m - 3/2*m**2 + 0 = 0.
-2, 0, 1, 2
Let v(r) = 9*r + 43. Let b be v(-3). What is a in 4*a**4 + b*a**3 + 37*a**2 - a**4 + 14*a**3 + 8*a**2 + 2*a**4 = 0?
-3, 0
Let f(b) be the second derivative of -b**6/30 + 23*b**5/10 - 191*b**4/4 + 506*b**3/3 - 242*b**2 + 504*b - 1. Factor f(x).
-(x - 22)**2*(x - 1)**2
Let c(k) be the first derivative of k**3/3 - 320*k**2 + 102400*k - 654. Let c(b) = 0. What is b?
320
Let y(a) be the first derivative of 3/2*a**4 + 6*a**2 + 1/5*a**5 + 4*a - 49 + 13/3*a**3. Find m such that y(m) = 0.
-2, -1
Let b(i) be the third derivative of -i**5/75 + i**4/5 + 112*i**3/3 - i**2 - 886. Factor b(m).
-4*(m - 20)*(m + 14)/5
Suppose -6*k - 28 = -100. Let -t + 12*t - k + t**3 + 5*t - 7*t**2 = 0. What is t?
2, 3
Let r = 75 - 73. Suppose 2*d + 2 = t, -3*t + 8 = 3*d + r. Factor 5*n**2 + 54*n - 55*n + 4*n**3 + 3*n**3 + n**t.
n*(n + 1)*(7*n - 1)
Let l be ((-20)/(-2))/(64*64/2048) - 5. What is i in -1/5*i**4 + 0*i + l + i**3 - 6/5*i**2 = 0?
0, 2, 3
Let v(b) be the second derivative of -b**4/6 + 281*b**3/3 + 282*b**2 - 6405*b. Factor v(r).
-2*(r - 282)*(r + 1)
Suppose 4*k - 191 + 199 = 0, -5*r + 5*k + 110 = 0. Let f be (-79)/(-4) + (-3)/(-12). Solve 5*h**3 - 3*h**3 - 16*h**2 + 26*h**3 + r*h**3 - f*h**5 - 12*h**4 = 0.
-2, 0, 2/5, 1
Determine i, given that 51*i - 6 - 2*i**4 - 16*i + 44*i - 65*i**5 + 138*i**4 - 2*i - 130*i**2 - 12*i**3 = 0.
-1, 6/65, 1
Let w be (-3 - (2 + 96/(-22)))*4/168*-12. Factor -2/11 + 0*u + w*u**2.
2*(u - 1)*(u + 1)/11
Factor -1462*f - 196/3*f**2 - 2/3*f**3 + 6936.
-2*(f - 4)*(f + 51)**2/3
Suppose 10/11 - 102/11*g + 20/11*g**2 = 0. Calculate g.
1/10, 5
Find v such that -7/2*v**2 - 17/3 - 359/6*v = 0.
-17, -2/21
What is b in 59 - 51*b**2 + 19*b**3 - 148*b**3 - 471*b + 9*b**4 + 497*b**2 + 37*b**2 + 49 = 0?
1/3, 1, 4, 9
Let g(u) be the third derivative of -1/24*u**5 + 0*u + 1/90*u**6 + 0 - 15*u**2 + 1/24*u**4 + 19/6*u**3. Let f(x) be the first derivative of g(x). Factor f(z).
(z - 1)*(4*z - 1)
Let m(y) be the first derivative of y**6/12 + 9*y**5/20 - 11*y**4/8 + 5*y**3/6 + 38*y + 121. Let h(t) be the first derivative of m(t). What is x in h(x) = 0?
-5, 0, 2/5, 1
Suppose 4*x = -v - v + 54, 3*x = 4*v + 57. Find a such that -x*a + 3*a**3 + 6 - 6*a**2 + 0 + 18*a**2 - 6*a**3 = 0.
1, 2
Let u = 1605 + -1607. Let h be (22/11 - 132/64)*u. Factor 2*c**3 - 125/8 - h*c**4 - 45/4*c**2 + 25*c.
-(c - 5)**3*(c - 1)/8
Let b(x) be the first derivative of x**4/4 - 25*x**3/3 + 72*x**2 - 8018. Suppose b(w) = 0. What is w?
0, 9, 16
Suppose -6 = -15*x + 54. Solve v**4 + 12*v + 15*v**3 + 463*v**2 - 487*v**2 - 4*v**x = 0 for v.
0, 1, 2
Let w(i) be the second derivative of 1/10*i**5 + 92*i + 0 + 17/6*i**4 + 19*i**2 - 37/3*i**3. Factor w(q).
2*(q - 1)**2*(q + 19)
Factor 2*l**3 - 70*l + 1225/2 - 33*l**2 + 1/2*l**4.
(l - 5)**2*(l + 7)**2/2
Suppose -24 = 2*k - 28. Determine m, given that -26*m**2 + 60 + k*m**3 + 36 - 2*m - 70 = 0.
-1, 1, 13
Let c(n) be the second derivative of n**7/280 + 7*n**6/120 + 7*n**5/20 + n**4 + n**3/2 + 6*n**2 + 110*n. Let s(x) be the second derivative of c(x). Factor s(a).
3*(a + 1)*(a + 2)*(a + 4)
What is y in -7*y**4 + 2*y**5 - 5*y**4 - 3*y**5 + 51*y - 132*y**2 + 188*y**3 + 16*y**2 - 110*y**3 = 0?
-17, 0, 1, 3
Let u(d) be the first derivative of d**3/2 + 489*d**2/2 + 79707*d/2 + 2083. Factor u(w).
3*(w + 163)**2/2
What is u in 10*u**4 + 254 + 82 + 520*u + 174*u**3 + 74018*u**2 - 74750*u**2 = 0?
-21, -2/5, 2
Let m(f) = f**2 + 3*f - 29. Let c be m(-9). Let l = 16 - 14. Solve -2 + 6 + 2*i**l - 14*i - 5*i + c*i = 0 for i.
-2, -1
Solve 268*m**3 - 27*m**2 - m**5 - 267*m**2 - 42*m**4 + 69*m**3 + 0*m**5 = 0.
-49, 0, 1, 6
Solve 187531 + 14*n**2 - 22*n**2 - 663631 + 4*n**2 - 2760*n = 0.
-345
Factor -8/3*y**2 + 0 - 7/3*y - 1/3*y**3.
-y*(y + 1)*(y + 7)/3
Suppose 0 = -3*m - 3*w - 10 + 61, m = 2*w + 29. Factor -78 + 31 + 10 + m + p**2.
(p - 4)*(p + 4)
Factor 312