. Let u(p) = p**3 + 2*p**2 + 3*p. Let t(m) = -2*m**2 - 2*m. Let d(h) = i*t(h) - 4*u(h). Determine r, given that d(r) = 0.
0, 1
Let k(x) be the first derivative of -5*x**3/3 - 20*x**2 + 45*x - 109. Factor k(z).
-5*(z - 1)*(z + 9)
Let h(d) be the third derivative of 0*d**3 - 5*d**2 + 1/168*d**8 + 1/20*d**6 + 0*d + 0 + 1/35*d**7 + 0*d**4 + 1/30*d**5. What is o in h(o) = 0?
-1, 0
Determine f, given that -2028/5*f**3 + 2496/5*f**2 - 99*f + 27/5 = 0.
3/26, 1
Let o(s) = -s - 1. Let z be (2/(-4))/((-12)/(-72)). Let u(x) = -2*x**2 - 7*x - 5. Let p(l) = z*o(l) + u(l). Determine m, given that p(m) = 0.
-1
Suppose -14 = -5*q - 2*n + 6, 5*q - 3*n + 5 = 0. Let y(u) be the first derivative of 1/5*u**q - 1 - 1/5*u**3 + 0*u. What is j in y(j) = 0?
0, 2/3
Let t(m) be the first derivative of -m**3/6 - 45*m**2/4 - 22*m + 93. Determine k, given that t(k) = 0.
-44, -1
Let t(b) be the first derivative of -b**7/3360 - b**6/240 - 3*b**5/160 - 4*b**3 - 4. Let y(g) be the third derivative of t(g). Factor y(p).
-p*(p + 3)**2/4
Let a be (4/48)/(15/60). Factor -1/3*i**2 + 2/3*i - a.
-(i - 1)**2/3
Factor 1/5*u**3 - 3/5*u**2 - 16/5*u - 12/5.
(u - 6)*(u + 1)*(u + 2)/5
Let o be (-210)/(-75)*400/2380. Factor 0*m + 0 + o*m**2 - 2/17*m**3.
-2*m**2*(m - 4)/17
Suppose -2*y + 11 = -3*x, 13 - 1 = 2*y - 4*x. Let a(s) be the first derivative of 5 + 0*s - 8/39*s**3 - 2/65*s**5 + 0*s**2 + 2/13*s**y. Factor a(i).
-2*i**2*(i - 2)**2/13
Let u(h) be the third derivative of h**8/1092 - h**7/1365 - h**6/195 + h**5/130 - 119*h**2. Find x, given that u(x) = 0.
-3/2, 0, 1
Let f(k) be the first derivative of k**6/420 - k**5/105 - 5*k**2 + 7. Let s(p) be the second derivative of f(p). Factor s(i).
2*i**2*(i - 2)/7
Suppose 4*i - z - 13 = 0, 2 = -4*i - 2*z + 24. Determine v, given that -v**5 + 0*v**5 - 5*v**3 + 10*v**i - 4*v**5 = 0.
0, 1
Let a(x) be the third derivative of 0 + 1/48*x**4 + 0*x + 0*x**3 + 1/120*x**5 - 14*x**2. Factor a(n).
n*(n + 1)/2
Let l = 651 + -644. Let i(u) be the second derivative of -1/3*u**3 + 0 + 1/12*u**4 + 0*u**2 + 3/20*u**5 - 1/30*u**6 + 5*u - 1/42*u**l. Factor i(b).
-b*(b - 1)**2*(b + 1)*(b + 2)
Let m(d) be the third derivative of d**8/4480 - d**7/1120 + d**6/960 - d**4/8 + 22*d**2. Let y(c) be the second derivative of m(c). Factor y(r).
3*r*(r - 1)*(2*r - 1)/4
Suppose -57*f + 35 = -136. Let m(p) be the second derivative of -1/3*p**f + 1/4*p**4 + 0 - 7*p + 0*p**2. Factor m(d).
d*(3*d - 2)
Let y(m) = 22*m**3 - 62*m**2 + 874*m - 3446. Let i(c) = 2*c**3 + c**2 + c + 1. Let g(q) = 10*i(q) - y(q). Let g(w) = 0. Calculate w.
12
Suppose -m - 1 = 1. Let i be (-3)/27*(-8 - m). Factor i*h**3 + 8*h - 16/3 - 4*h**2.
2*(h - 2)**3/3
Let c(v) = 10*v**3 + 90*v**2 + 774*v + 2048. Let g(l) = -l**3 + l**2 - l. Let f be (-9)/(-18) - 9/6. Let i(u) = f*c(u) - 6*g(u). Factor i(k).
-4*(k + 8)**3
Suppose 0 = 2*c - 5*p - 21, -4*p + 18 = c + 27. Determine t so that 0*t**2 + 3/7*t**c + 0*t + 0 = 0.
0
Solve 4*d**2 - 1667 - 9*d - d**2 + 1667 = 0 for d.
0, 3
Let z(d) be the third derivative of d**5/60 - d**4/24 - d**3/3 - 66*d**2. Let z(y) = 0. What is y?
-1, 2
Let o(w) = -w**5 + 3*w**3 + 2*w**2 + 2*w. Let m(y) = 2*y**5 - y**4 - 7*y**3 - 4*y**2 - 5*y. Let g(b) = 2*m(b) + 5*o(b). Factor g(u).
-u**2*(u - 1)*(u + 1)*(u + 2)
Let r = -1493 + 1495. Solve -32*o - 4*o**r - 1/6*o**3 - 256/3 = 0 for o.
-8
Suppose 5*x + 3 = 6*x. Factor 7*b**2 + 20*b**x - 16*b + 3*b**2 - 10 + b - 5*b**5.
-5*(b - 2)*(b - 1)*(b + 1)**3
Determine n so that -6*n**3 - 300/7 - 207/7*n**2 - 60*n - 3/7*n**4 = 0.
-5, -2
Let g(m) be the third derivative of m**5/6 + 25*m**4/8 + 35*m**3/6 - 2*m**2 + 2*m. Factor g(t).
5*(t + 7)*(2*t + 1)
Let j be (6 - 2)*30/8. Suppose -3*d + 3*u = -j, -2*d + u + 6 = -4. Determine h, given that 12*h**4 - 8*h**4 - 5*h**2 + h**2 - 10*h**3 + 10*h**d = 0.
-1, -2/5, 0, 1
Let k(z) be the third derivative of 11*z**2 + 2/945*z**7 + 0*z**3 + 1/3024*z**8 + 0*z + 1/216*z**4 + 0 + 1/135*z**5 + 1/180*z**6. Determine r so that k(r) = 0.
-1, 0
Let j be (-19)/5*(-16 - -17) - -4. Solve 1/5*q**4 + 0 - 1/5*q - j*q**2 + 1/5*q**3 = 0.
-1, 0, 1
Suppose -5*b - 45 + 43 = -p, 4*b - 4*p + 8 = 0. What is d in -4/3*d**3 + 0*d - d**2 + b - 1/3*d**4 = 0?
-3, -1, 0
Let d(h) be the third derivative of -605*h**5/54 + 55*h**4/27 - 4*h**3/27 - 95*h**2 + 3. Let d(y) = 0. Calculate y.
2/55
Let p = -51 + 93. Solve -5*k**4 - 5*k**3 + p*k**2 + 0*k**3 - 32*k**2 = 0.
-2, 0, 1
Let o(s) = s**3 + 4*s**2 + 4*s + 2. Let z be o(-2). Suppose -3*g - g = 4*x - 4, -4*x - z = -2*g. Factor 1/3*p**4 + p**3 + x*p + 0 + 2/3*p**2.
p**2*(p + 1)*(p + 2)/3
Let i be ((-28)/49)/(9/(-63)) + -3 + 1. Factor -4/3 - 4/3*u - 1/3*u**i.
-(u + 2)**2/3
Let a(r) be the third derivative of 0*r + 9*r**2 + 0 + 1/228*r**4 - 2/57*r**3 + 1/570*r**5. Factor a(p).
2*(p - 1)*(p + 2)/19
Let x(f) be the third derivative of f**5/150 + 5*f**4/4 + 74*f**3/15 + 882*f**2. Factor x(q).
2*(q + 1)*(q + 74)/5
Factor 17/4*z**2 + 3/4*z + 5/4*z**3 - 9/4.
(z + 1)*(z + 3)*(5*z - 3)/4
Let f(a) = 5*a - 17. Let y be f(7). Let p be 3/y + 28/(-24) + 4. Factor 1/3*n**4 + 0*n**2 + 0*n + 0 + 1/3*n**p.
n**3*(n + 1)/3
Let y(g) = 2*g - 1. Let c be y(3). Factor 9 + c + 5*z + z**2 + 0 - 8.
(z + 2)*(z + 3)
Let l(a) be the first derivative of 1/10*a**4 - 2/5*a + 13 - 1/5*a**2 + 2/15*a**3. Let l(j) = 0. Calculate j.
-1, 1
Let z be (-99)/(-45) - (-22)/(-110). Factor 0 + 2/5*f**3 - 8/5*f**z - 8/5*f + 2/5*f**4.
2*f*(f - 2)*(f + 1)*(f + 2)/5
Let w(l) = -6*l**2 + 4*l - 2. Suppose -3*v + 4*v = 1. Suppose v + 4 = -z. Let n(s) = 7*s**2 - 5*s + 3. Let b(p) = z*w(p) - 4*n(p). Factor b(c).
2*(c - 1)*(c + 1)
Let q(z) = z**3 + 11*z**2 + 18*z - 70. Let t be q(-7). Suppose -y = y. Factor t*a - 2/9*a**2 + 0 + 2/9*a**4 + y*a**3.
2*a**2*(a - 1)*(a + 1)/9
Suppose -2 = 2*d - 60*d - 2. Suppose 2/3*f**5 + 0*f**2 + 2*f**4 + d + 0*f + 4/3*f**3 = 0. Calculate f.
-2, -1, 0
Let o(a) be the second derivative of 0*a**2 - 1/2*a**4 + 1/5*a**6 + 0 + 11*a + 2/3*a**3 - 1/10*a**5 - 1/21*a**7. Find l such that o(l) = 0.
-1, 0, 1, 2
Let g be 12/16 - (-5)/4. Suppose 7*s - 2*s**g - 16*s - s**3 + 10*s + 2*s**3 = 0. What is s?
0, 1
Let s(p) be the third derivative of 16*p**2 - 1/120*p**6 + 0*p**5 + 0*p**3 + 0*p**4 + 0*p + 0 - 1/210*p**7. Factor s(c).
-c**3*(c + 1)
Factor 4/5*t**3 + 32*t + 144/5 + 52/5*t**2.
4*(t + 2)**2*(t + 9)/5
Let j(q) = -q**4 - q - 1. Let w(s) = -6*s**4 - 11*s**3 - 22*s**2 - 23*s - 10. Let m(k) = -12*j(k) + 3*w(k). Suppose m(b) = 0. What is b?
-2, -3/2, -1
Let a(r) be the second derivative of -r**5/70 + 47*r**4/42 + 16*r**3/7 - 182*r - 4. Determine u so that a(u) = 0.
-1, 0, 48
Suppose 0 = 46*r - 62*r + 48. Let o(a) be the first derivative of -2/3*a**r + 2*a**2 + 7 - 2*a. Solve o(d) = 0.
1
Let k be 1 + (-1908)/162 + 11. Factor 4/9*t**2 - k*t**3 + 0*t + 0.
-2*t**2*(t - 2)/9
Let t(r) = -19*r**2 - 54*r - 22. Let b(q) = -75*q**2 - 216*q - 87. Let m(x) = -2*b(x) + 9*t(x). Factor m(k).
-3*(k + 2)*(7*k + 4)
Let a(q) be the third derivative of -q**6/540 - q**5/180 + 5*q**3/2 - 12*q**2. Let g(f) be the first derivative of a(f). Let g(m) = 0. What is m?
-1, 0
Let f = -607/5 - -4254/35. Let o(b) be the second derivative of -11/42*b**3 - f*b**2 - 1/7*b**4 + b + 0 + 9/140*b**5. Factor o(z).
(z - 2)*(3*z + 1)**2/7
Let d(i) = -7*i**3 - 16*i**2 + 23*i + 3. Let l(g) = 15*g**3 + 32*g**2 - 47*g - 7. Let k(f) = 7*d(f) + 3*l(f). Factor k(c).
-4*c*(c - 1)*(c + 5)
Let d = -55/104 - -751/1248. Let c(v) be the third derivative of 1/48*v**5 + 0 + 1/8*v**3 - 2*v**2 - 1/480*v**6 + 0*v - d*v**4. Factor c(n).
-(n - 3)*(n - 1)**2/4
Let c(r) be the first derivative of r**5/120 + r**4/8 + 3*r**3/4 - 11*r**2/2 - 12. Let k(y) be the second derivative of c(y). Factor k(v).
(v + 3)**2/2
Let v(u) be the second derivative of -3/140*u**5 + 1/14*u**3 - 10*u + 0 - 1/28*u**4 + 3/14*u**2. Solve v(g) = 0.
-1, 1
Let q(c) be the first derivative of c**4/20 - 17*c**3/15 + 8*c**2 - 64*c/5 + 44. Factor q(b).
(b - 8)**2*(b - 1)/5
Let o(u) be the first derivative of -u**4/20 + u**3/2 - 6*u**2/5 - 4*u + 47. Let p(x) be the first derivative of o(x). Let p(w) = 0. Calculate w.
1, 4
Let d be 10/(100/90) - 9. Factor 0 + 0*i + 0*i**3 - 2/15*i**4 + d*i**2.
-2*i**4/15
Suppose 3*d + 386 = 104. Let f = d - -850/9. Factor -f*g**2 + 2/9*g**3 + 0*g + 0 + 2/9*g**4.
2*g**2*(g - 1)*(g + 2)/9
What is s in 