t r(k) be the third derivative of 1/18*k**6 + 0*k**4 + 10*k**2 - 5/144*k**8 + 0 + 0*k + 0*k**3 + 1/45*k**5 + 11/630*k**7. Find f such that r(f) = 0.
-2/5, -2/7, 0, 1
Let j(u) be the first derivative of -u**6/33 + 2*u**5/11 - 9*u**4/22 + 14*u**3/33 - 2*u**2/11 + 192. Factor j(g).
-2*g*(g - 2)*(g - 1)**3/11
Let x(n) be the first derivative of -5*n**4/28 - 8*n**3/21 - n**2/14 + 2*n/7 + 78. Suppose x(d) = 0. Calculate d.
-1, 2/5
Determine t so that 32/5 - 74/5*t**2 + 8*t**3 - 76/5*t + 6/5*t**4 = 0.
-8, -1, 1/3, 2
Let v(p) be the second derivative of -2*p**6/15 - p**5 - 3*p**4 - 14*p**3/3 - 4*p**2 - 56*p. Factor v(z).
-4*(z + 1)**3*(z + 2)
Suppose 4*q - 13 = 11. Suppose -5*r = -q*r + 2. Let 0 + 0*d + 2/7*d**5 - 2/7*d**r + 2/7*d**4 - 2/7*d**3 = 0. What is d?
-1, 0, 1
Let s(b) be the first derivative of -b**5/45 + 7*b**4/36 - 16*b**3/27 + 2*b**2/3 - 290. Factor s(h).
-h*(h - 3)*(h - 2)**2/9
Let d(y) be the first derivative of -12 - 5/2*y**3 - 6*y - 3/8*y**4 - 6*y**2. Factor d(x).
-3*(x + 1)*(x + 2)**2/2
Let a = -5/1708 - -20521/8540. Suppose a*w**3 - 8/5 - 12/5*w + 4/5*w**2 + 4/5*w**4 = 0. Calculate w.
-2, -1, 1
Suppose 5*w = d - 5*d + 13, 0 = 4*d - 8. Let p be (52/(-12) - -3 - -1) + w. Factor -2/3*o**3 - 2/3*o**4 + 2/3*o**2 + 0 + p*o.
-2*o*(o - 1)*(o + 1)**2/3
Let r(y) be the first derivative of 8/15*y**3 + 6*y + 7/30*y**4 + 5 + 1/5*y**2. Let m(c) be the first derivative of r(c). Find z, given that m(z) = 0.
-1, -1/7
Factor -10/7*u + 4/7 - 2*u**2.
-2*(u + 1)*(7*u - 2)/7
Suppose -8 = -3*z - z. Factor -i**5 + i**5 - z*i**5 + 4*i**5.
2*i**5
Factor -44/9*t**3 - 4/9*t**5 + 16/3*t**4 + 0 + 0*t**2 + 0*t.
-4*t**3*(t - 11)*(t - 1)/9
Let p(s) = s**3 + s**2 - s. Let l be p(0). Suppose -6*b + b + 15 = l. Factor 3*o**4 + b*o**3 - 2*o**3 - 3*o**3.
o**3*(3*o - 2)
Let y(z) = 8 - 2 + 105*z + 7*z**3 + z**2 - 99*z. Let f(m) = -13*m**3 - 2*m**2 - 11*m - 11. Let h(c) = -6*f(c) - 11*y(c). Factor h(x).
x**2*(x + 1)
Let t = -53423/36 - -1484. Let w(x) be the second derivative of 3*x + 25/6*x**2 + t*x**4 + 0 + 5/9*x**3. Factor w(j).
(j + 5)**2/3
Let l(n) = 4*n**2 + 39*n + 32. Let y(m) = -5*m**2 - 42*m - 33. Let p(i) = 4*l(i) + 3*y(i). Solve p(o) = 0.
-29, -1
Suppose 8*v + 206 = -18. Let q = -28 - v. Factor -h**2 + q - 1/4*h.
-h*(4*h + 1)/4
Let v = 82 + -77. Let f(r) be the first derivative of 0*r - v + 1/9*r**3 + 1/6*r**2. Factor f(w).
w*(w + 1)/3
Let a be 6/(-57) + 726/38. Factor -15*g - 32*g**2 + a*g**2 + 10 + 2 + 16*g**2.
3*(g - 4)*(g - 1)
Suppose -18 = -4*u - 2. Let r(s) be the first derivative of -1/2*s**u - 2*s + 2/3*s**3 + s**2 - 3. Suppose r(n) = 0. What is n?
-1, 1
Factor 24*k**2 - k**3 - 31*k + 59*k - 3*k**2 - 76*k - 2*k**3 + 36.
-3*(k - 3)*(k - 2)**2
Suppose 3*y + y = r - 20, -2*y = 10. Let p(g) be the first derivative of 0*g**2 + r*g**5 - 3 + 4/21*g**3 + 3/14*g**4 + 0*g - 1/21*g**6. What is b in p(b) = 0?
-1, 0, 2
Let l(f) be the third derivative of -f**6/120 + f**4/8 - f**3/3 - 19*f**2. Let u(r) be the first derivative of l(r). Factor u(v).
-3*(v - 1)*(v + 1)
Factor 1/2*i**2 + 0 - 1/4*i**5 + i**4 + 0*i - 5/4*i**3.
-i**2*(i - 2)*(i - 1)**2/4
Let y(m) be the third derivative of 250/3*m**3 + 0 - 13*m**2 + 25/2*m**4 + m**5 + 1/30*m**6 + 0*m. Factor y(k).
4*(k + 5)**3
Let g(y) be the first derivative of -2*y**3/15 + y**2/5 + 12*y/5 - 6. Suppose g(f) = 0. Calculate f.
-2, 3
Factor 13/5*i - 12/5 - 1/5*i**2.
-(i - 12)*(i - 1)/5
Let -2/9*d**4 + 4/9*d - 10/9*d**2 + 0 + 8/9*d**3 = 0. Calculate d.
0, 1, 2
Let k be 7 + (9 - (-7 + 14)). Let p(h) be the third derivative of 0*h - 1/9*h**4 - k*h**2 + 0 - 1/180*h**5 - 8/9*h**3. Factor p(b).
-(b + 4)**2/3
Let x(s) = 7*s**2 - 4*s**3 + 11 + 5*s**3 - 7*s - 2*s**3 - 3. Let v be x(6). Factor -7*i**2 + 24*i + 8 + 16*i**v + i**2.
2*(i + 2)*(5*i + 2)
Let p(k) = k**2 - 20*k + 2. Let l be p(20). Let 4*h**4 + 0*h**3 + 2*h**5 + 3*h**3 - 203*h**l - 5*h**3 + 199*h**2 = 0. Calculate h.
-2, -1, 0, 1
Let r(a) be the second derivative of 4/3*a**3 - 2*a**2 + 15*a - 1/3*a**4 + 0. Find n such that r(n) = 0.
1
Suppose -120*n = -101*n - 57. Let b(v) be the first derivative of -1/2*v**2 + n + 0*v - 1/4*v**4 + 2/3*v**3. Find m such that b(m) = 0.
0, 1
Let z(p) be the second derivative of -8*p**7/21 - 2*p**6 + 88*p**5/5 - 7*p**4 + 292*p. Suppose z(w) = 0. What is w?
-7, 0, 1/4, 3
Let l(x) be the first derivative of 0*x + 0*x**2 + 4/15*x**3 + 21 + 121/25*x**5 + 11/5*x**4. Solve l(y) = 0 for y.
-2/11, 0
Let f(o) = -4*o**2 - 32*o + 44. Let v(i) = i**2 - i - 1. Let n(m) = -f(m) - 8*v(m). Let n(p) = 0. What is p?
1, 9
Let k(v) be the second derivative of 2*v**3 + 0 - 11/12*v**4 - 1/42*v**7 - 9*v - 2*v**2 + 1/10*v**6 + 1/20*v**5. Solve k(r) = 0.
-2, 1, 2
Factor -6936/7*v - 78608/7 - 2/7*v**3 - 204/7*v**2.
-2*(v + 34)**3/7
Find i, given that 0*i**2 + 6*i**2 - 10*i**2 - 6 + 14 - 3*i - i = 0.
-2, 1
Let c(h) be the first derivative of -5*h**3/9 + 25*h**2/3 - 15*h - 56. Factor c(p).
-5*(p - 9)*(p - 1)/3
Let x = -3/133 - -17698/399. Let f = -611/15 + x. Factor -4/5 - 14/5*g**2 - f*g.
-2*(g + 1)*(7*g + 2)/5
Let w be 25/60*4*3. Suppose 10*o + w*o = -6*o. Solve -2/3*y**5 + 2/3*y**3 + 0*y**2 + 0*y**4 + o*y + 0 = 0 for y.
-1, 0, 1
Let q(x) be the third derivative of -x**6/600 - 17*x**5/100 + 7*x**4/8 - 53*x**3/30 - 294*x**2. Factor q(t).
-(t - 1)**2*(t + 53)/5
Let n(d) = 5*d**3 + 5*d**2 - 134*d + 120. Let f(o) = -o. Let p(j) = -4*f(j) + n(j). Factor p(h).
5*(h - 4)*(h - 1)*(h + 6)
Let b(x) be the third derivative of 1/3*x**4 - x**2 + 0*x + 0 + 0*x**3 + 1/15*x**5. Let b(l) = 0. Calculate l.
-2, 0
Let b(c) be the third derivative of 7*c**7/15 + 217*c**6/60 + 2*c**5 - 23*c**4/3 + 16*c**3/3 - 82*c**2. Factor b(y).
2*(y + 1)*(y + 4)*(7*y - 2)**2
Solve -24*s + 2/3*s**2 - 74/3 = 0 for s.
-1, 37
Let v be 13 - 4554/322 - 39/(-28). Let 9/4 - 5/2*z + v*z**2 = 0. What is z?
1, 9
Let y(a) be the third derivative of 10*a**2 + 0 + 1/40*a**4 + 0*a - 1/1050*a**7 + 0*a**3 + 1/60*a**5 + 1/600*a**6. Factor y(n).
-n*(n - 3)*(n + 1)**2/5
Let j = 4 - 2. Suppose -4*r - 7 = -23. Determine y, given that -j + 0*y**r + 4*y**2 + 4*y**4 - 6*y**4 = 0.
-1, 1
Let g(s) = 2*s**3 + 213*s**2 + 1986*s - 4840. Let t(b) = -15*b**3 - 1490*b**2 - 13900*b + 33880. Let k(r) = 20*g(r) + 3*t(r). Factor k(c).
-5*(c - 2)*(c + 22)**2
Let l(f) be the second derivative of -f**6/150 + f**4/20 - f**3/15 + 2*f + 18. Factor l(b).
-b*(b - 1)**2*(b + 2)/5
Let b(n) = -7*n + 8*n**2 - 2*n**2 - 5 - 6*n**2 - n**2. Let l be b(-5). Factor 0 + 2 - l + 3*z**2.
3*(z - 1)*(z + 1)
Let t be -2 + ((-3)/7 - (-180)/28). Suppose -p + 4 = 3*v, -17 = 4*v - t*p - 1. Factor 6/11*y**3 + v - 2/11*y**4 + 0*y - 4/11*y**2.
-2*y**2*(y - 2)*(y - 1)/11
Let r(l) be the second derivative of 0 - 1/60*l**4 - 2/5*l**2 + 14*l + 1/6*l**3. Factor r(f).
-(f - 4)*(f - 1)/5
Factor -2/5*i**2 + 30*i - 292/5.
-2*(i - 73)*(i - 2)/5
Let k(n) be the third derivative of n**8/840 + 2*n**7/525 - n**6/150 - 4*n**5/75 - 7*n**4/60 - 2*n**3/15 + 6*n**2 + 3*n. Determine w, given that k(w) = 0.
-1, 2
Let v(z) be the second derivative of z**6/30 + z**5/5 - 9*z**4/4 + 19*z**3/3 - 8*z**2 - 223*z - 2. Factor v(o).
(o - 2)*(o - 1)**2*(o + 8)
Suppose -q + 4*l + 3 = -6, 27 = 3*q - 5*l. Suppose 20 = 14*a - q*a. Let -6*b + b**2 + 1 + 2*b + a*b + 2*b = 0. What is b?
-1
Let x(n) be the first derivative of n**6/24 + 3*n**5/20 - n**4/16 - 7*n**3/12 + n + 66. Suppose x(s) = 0. Calculate s.
-2, -1, 1
Let j(l) be the first derivative of 5*l**3/3 + 85*l**2/2 - 90*l - 64. Factor j(r).
5*(r - 1)*(r + 18)
Suppose -8*d = -13*d - 2*n + 25, 2*n = 5*d - 5. Suppose y - 3*j = -3, 3*j - 3 = d*y - y. Factor y + 1/6*u - 1/6*u**2.
-u*(u - 1)/6
Let h(d) = -d**3 - 2*d**2 - 2*d - 1. Let k be h(-2). Factor 3*t**2 + 0*t**2 - 6*t**k - 411*t**4 + 414*t**4 + 0*t**2.
3*t**2*(t - 1)**2
Let c(i) be the second derivative of -i**7/14 + 7*i**6/10 + 2*i + 60. Solve c(k) = 0.
0, 7
Factor 14/5*m + 0 + 2/5*m**3 - 16/5*m**2.
2*m*(m - 7)*(m - 1)/5
Factor -16/5*m**2 + 4*m + 24/5.
-4*(m - 2)*(4*m + 3)/5
Let r(c) be the second derivative of c**6/90 - 7*c**5/60 + 5*c**4/18 - 82*c + 2. What is n in r(n) = 0?
0, 2, 5
Factor 28/17 + 2/17*k**2 + 30/17*k.
2*(k + 1)*(k + 14)/17
Let p(b) be the second derivative of 3*b**5/20 - 31*b**3/2 + 45*b**2 + 478*b. Factor p(s).
3*(s - 5)*(s - 1)*(s + 6)
Factor -32*x - 768 - 1/3*x**2.
-(x + 48)**2