*c - 6 - 16*c - 24 - 3*c.
5*(3*c - 2)*(7*c + 3)
Let p(t) be the second derivative of -t**7/168 + 3*t**6/20 - 129*t**5/80 + 115*t**4/12 - 34*t**3 + 72*t**2 + 274*t. Factor p(u).
-(u - 4)**3*(u - 3)**2/4
Solve -c**4 - 32*c**3 + 5*c**4 - 119*c**2 + 179*c**2 = 0.
0, 3, 5
Let q = -1416 + 1420. Factor -12/5*y**2 + 3/5*y**5 + 3/5*y + 18/5*y**3 + 0 - 12/5*y**q.
3*y*(y - 1)**4/5
Suppose -54 + 57*o + 3/4*o**3 - 33/2*o**2 = 0. What is o?
2, 18
Let l be (4 + 6/(-4))/((-95)/(-988)*13). Determine q so that -2*q**l + 2/3 - 5/3*q - q**5 + 4/3*q**4 + 8/3*q**3 = 0.
-1, 1/3, 1, 2
Suppose 2*u = -2*n - 2, 55*n + 22 = 2*u + 51*n. Solve -125/2 - 15/2*p**2 + 1/2*p**u + 75/2*p = 0 for p.
5
Let x(j) be the third derivative of 0 - 14*j**4 + 5*j + 39/10*j**5 - 2/5*j**6 + 1/70*j**7 + 2*j**2 + 49/2*j**3. Factor x(h).
3*(h - 7)**2*(h - 1)**2
Let j(t) = -t**4 - 12*t**3 + t**2 + 6*t + 6. Let z(p) = p**5 - 3*p**4 - 35*p**3 + 3*p**2 + 17*p + 17. Let u(y) = 17*j(y) - 6*z(y). Determine l so that u(l) = 0.
-1, 0, 1/6, 1
Factor -11*i**4 - 21*i**2 + 15*i**4 + 10*i**2 + 71*i**2 - 64*i**3.
4*i**2*(i - 15)*(i - 1)
Let n be 6/(-15)*7/(56/(-12)). Let g = 1111/1835 - 2/367. Factor g*x**5 - 3/5*x**2 - 2/5*x + n*x**3 + 0 + 7/5*x**4.
x*(x + 1)**3*(3*x - 2)/5
Let b be 1 - ((-3241)/(-21) - 2/6). Let k = -609/4 - b. Factor 0 + 0*d - 3/4*d**3 - k*d**2.
-3*d**2*(d + 1)/4
Let s(j) be the second derivative of -1/10*j**5 + 1/6*j**4 - 15 + 1/3*j**3 - j**2 - 2*j. Factor s(q).
-2*(q - 1)**2*(q + 1)
Let q(p) be the second derivative of -10*p**7/21 + 16*p**6/5 - 6*p**5 + 8*p**4/3 + 2*p**3 - 2*p + 18. Suppose q(x) = 0. Calculate x.
-1/5, 0, 1, 3
Solve -25*d**3 - 9*d**2 + 0*d**4 + 5*d**4 - 2*d**2 + 72*d + 48*d + d**2 = 0 for d.
-2, 0, 3, 4
Let m(s) be the third derivative of -s**5/120 + s**4/12 + 8*s**3/3 + 11*s**2 - 5. Factor m(k).
-(k - 8)*(k + 4)/2
Let a(n) = n**2 - 11*n - 1. Let u be a(5). Let r = -29 - u. Solve -10/7*i + 8/7*i**r - 2/7*i**3 + 4/7 = 0.
1, 2
Let o(z) = 5*z**3 - 90*z + 60. Let n(m) = -22*m + 3. Let f be n(-1). Let x(k) = -k**3 + 15*k - 10. Let d(p) = f*x(p) + 4*o(p). Find r such that d(r) = 0.
-2, 1
Let p(t) = -2*t**3 - 36*t**2 - 26*t - 465. Let c be p(-18). Let 0 + 0*l**2 + 0*l + 1/2*l**c = 0. Calculate l.
0
Let v = 2992 - 2990. Let -2/9*w + 0*w**4 - 2/9*w**5 + 4/9*w**3 + 0*w**v + 0 = 0. Calculate w.
-1, 0, 1
Let o(q) be the first derivative of -q**6/160 + 7*q**2/2 + 7. Let p(g) be the second derivative of o(g). Factor p(n).
-3*n**3/4
Suppose -3*q + 30 = -5*n, -5*n - 30 = -0*q - 2*q. Let w be (-3)/(63/12)*n/12. Factor -6/7*u**2 - 6/7*u - 2/7*u**3 - w.
-2*(u + 1)**3/7
Suppose 5*d - 2*y + 24 = 0, 0 = -0*d + 4*d + 4*y + 36. Let m = 8 + d. What is r in -4/3 - m*r - 10/3*r**4 + 14/3*r**2 + 2*r**3 = 0?
-1, -2/5, 1
Let l(w) be the third derivative of -w**8/1008 + w**7/126 + w**6/72 - 5*w**5/36 - 5*w**4/9 - 8*w**3/9 + 17*w**2. Solve l(s) = 0.
-1, 4
Suppose -107*w - 44 = -118*w. Let o(y) be the third derivative of 1/80*y**5 + 1/480*y**6 + 5*y**2 + 0*y + 1/48*y**w + 0 + 0*y**3. Solve o(q) = 0.
-2, -1, 0
Let u(a) = -37*a + 14. Let y be u(2). Let z be -2 + 1 + y/(-44). Factor -z + 4/11*f**2 + 2/11*f**3 - 2/11*f.
2*(f - 1)*(f + 1)*(f + 2)/11
Suppose 9*g + 24 - 51 = 0. Let k(a) be the second derivative of 0*a**2 - 1/66*a**4 + a + 1/165*a**6 - 1/110*a**5 + 0*a**g + 0 + 1/231*a**7. Factor k(b).
2*b**2*(b - 1)*(b + 1)**2/11
Let w(b) be the second derivative of b**8/5040 + b**7/1680 - b**5/720 - 17*b**3/6 + 27*b. Let a(k) be the second derivative of w(k). Factor a(x).
x*(x + 1)**2*(2*x - 1)/6
Let g(q) = -q**2 + q + 1. Let u(y) = -144*y + 514. Let i(a) = 29*a - 103. Let m(x) = -14*i(x) - 3*u(x). Let c(p) = 2*g(p) + m(p). Let c(b) = 0. What is b?
7
Factor 432/5 + 4/5*w**2 - 436/5*w.
4*(w - 108)*(w - 1)/5
Let m(a) = 3*a**2 - 6*a. Let n(j) be the second derivative of -j**4/4 + 5*j**3/6 + j. Let c = 8 + -5. Let r(k) = c*n(k) + 4*m(k). Let r(z) = 0. What is z?
0, 3
Let w(h) be the first derivative of h**4/6 - 2*h**3/3 + 2*h**2/3 + 27. Factor w(u).
2*u*(u - 2)*(u - 1)/3
Let g(k) be the second derivative of k**7/840 + k**6/180 + 4*k**3 - 2*k. Let r(y) be the second derivative of g(y). Factor r(a).
a**2*(a + 2)
Let p(c) = 5*c**5 + 3*c**4 - 8*c**3 - 28*c**2 - 20*c - 2. Let o(a) = 12*a**5 + 6*a**4 - 17*a**3 - 56*a**2 - 38*a - 5. Let d(z) = -2*o(z) + 5*p(z). Factor d(y).
y*(y - 3)*(y + 2)**3
Let l(h) be the first derivative of -1/30*h**5 + 1/540*h**6 - 7 + 0*h + 1/4*h**4 - 1/3*h**3 + 0*h**2. Let r(z) be the third derivative of l(z). Factor r(y).
2*(y - 3)**2/3
Let l(f) be the second derivative of -f**5/20 - 7*f**4/12 + 20*f**3/3 - 22*f**2 + 207*f. Let l(o) = 0. Calculate o.
-11, 2
Suppose 22 = 4*b - 2*p, 3*b - 3*p - 36 + 21 = 0. Let s(y) be the second derivative of 1/30*y**3 + 3/20*y**2 + 0 - b*y - 1/120*y**4. Factor s(c).
-(c - 3)*(c + 1)/10
Let j(z) = z**2 - 5*z - 50. Let m be j(10). Determine t, given that m + 0*t + t**4 - 1/2*t**5 + 1/2*t**3 - t**2 = 0.
-1, 0, 1, 2
Let l be (-8)/(-12)*(-12)/8. Let i(x) = x**2 - 3*x - 2. Let u be i(l). Factor -1/3*k**u - 3 - 2*k.
-(k + 3)**2/3
Determine g so that 14*g**2 + 55*g**5 - 16*g**5 - 14*g**4 - 15*g - 40*g**5 + 16*g**3 = 0.
-15, -1, 0, 1
Determine t so that 8/17*t**3 - 16/17*t**2 + 260/17*t**4 + 0*t + 126/17*t**5 + 0 = 0.
-2, -2/7, 0, 2/9
Let w(r) be the second derivative of r**6/15 - 4*r**5/5 + 5*r**4/2 + 8*r**3/3 - 16*r**2 + r + 24. Factor w(x).
2*(x - 4)**2*(x - 1)*(x + 1)
Let o(t) be the second derivative of t**5 + 0*t**2 - 1/3*t**6 + 0 + 0*t**3 + 10/3*t**4 - 42*t - 5/42*t**7. Factor o(r).
-5*r**2*(r - 2)*(r + 2)**2
Solve 10*b**2 + 2*b**2 + 2*b**2 - 18*b**2 - 136*b = 0 for b.
-34, 0
Let b(p) = 2*p - 12. Let l be b(7). Factor -2 - 60*s**l - 1 - 9*s + 63*s**2 + 9.
3*(s - 2)*(s - 1)
Let y(x) be the second derivative of 1/35*x**6 - 18*x + 1/147*x**7 + 1/42*x**4 + 3/70*x**5 + 0 + 0*x**2 + 0*x**3. Determine m, given that y(m) = 0.
-1, 0
Let h = 4082/15 + -272. Find d, given that 32/15 + 16/15*d + h*d**2 = 0.
-4
Let v(o) = 5*o + 39. Let b be 27/(-4) - (-4)/(-16). Let l be v(b). What is c in 2*c**3 + 0 + 4/3*c**2 + 0*c + 2/3*c**l = 0?
-2, -1, 0
Let o(g) be the first derivative of 4/75*g**5 + 29 + 19/5*g**2 + 20/9*g**3 + 17/30*g**4 + 12/5*g. Suppose o(t) = 0. What is t?
-3, -2, -1/2
Let r = 47 - 47. Let 9*c + 4 - 8*c**2 + 5*c**3 + 4*c**4 + 3*c**3 - 4*c**5 + r*c**3 - 13*c = 0. Calculate c.
-1, 1
Let r(j) be the third derivative of 5*j**8/336 - j**7/21 - j**6/3 + 2*j**2 + 31. Factor r(l).
5*l**3*(l - 4)*(l + 2)
What is u in -2/11*u**3 + 8/11*u - 2/11*u**4 + 8/11*u**2 + 0 = 0?
-2, -1, 0, 2
Determine d, given that 20/7*d**4 + 0 + 12/7*d**2 - 2/7*d - 24/7*d**3 - 6/7*d**5 = 0.
0, 1/3, 1
Suppose 5*q + 36 = -q. Let f be 24/9 - (-2 + q/(-9)). Factor l**2 - l**f + 0*l**3 + 1/2*l - 1/2*l**5 + 0.
-l*(l - 1)*(l + 1)**3/2
Let h(o) be the first derivative of -3*o**5/4 + 5*o**4/3 + 10*o**3/3 - 48*o - 22. Let w(u) be the first derivative of h(u). Factor w(k).
-5*k*(k - 2)*(3*k + 2)
Suppose -22*a - 42 = -16*a. Let u(l) = 4*l**2 + 21*l - 23. Let q(r) = 3*r**2 + 14*r - 15. Let z(j) = a*q(j) + 5*u(j). What is o in z(o) = 0?
2, 5
Let m(c) be the first derivative of -3*c**7/14 - c**6/10 + 3*c**5/10 + 8*c + 1. Let v(y) be the first derivative of m(y). Factor v(g).
-3*g**3*(g + 1)*(3*g - 2)
Suppose i = 3*r - 12, 0 = -4*i - 7 - 5. Let -18 - 1 - 92*h - 3*h**r - 5 + 56*h - 18*h**2 = 0. Calculate h.
-2
Suppose -24 = o - 0*v - 5*v, 0 = 3*o - 2*v + 7. Find q, given that o - q**2 + 2*q**2 + q**2 - 3*q**2 = 0.
-1, 1
Let v(c) be the first derivative of c**4/22 + 12*c**3/11 + 17*c**2/11 - 179. Find s, given that v(s) = 0.
-17, -1, 0
What is b in -6 - 42/5*b**3 + 39/5*b + 3/5*b**5 + 6/5*b**4 + 24/5*b**2 = 0?
-5, -1, 1, 2
Let v(i) be the third derivative of 0*i - 1/12*i**5 - 1/2*i**4 - 2/3*i**3 + 0 + 1/12*i**6 + 1/168*i**8 + 12*i**2 + 3/70*i**7. Determine a so that v(a) = 0.
-2, -1, -1/2, 1
Let q be (-2)/(-4 - 70/(-20)). Let a(k) be the first derivative of 4/3*k**2 - 32/9*k**3 + 10/3*k**5 + 5/6*k**4 + 0*k - q. Suppose a(o) = 0. What is o?
-1, 0, 2/5
Suppose 15*o + 2 = 32. Let c(i) be the first derivative of -o*i + 2/3*i**3 - 7 + 0*i**2. Suppose c(g) = 0. Calculate g.
-1, 1
Determine t so that 8/9*t**2 + 4/9*t - 8/9*t**3 - 4/9*t**4 + 4/9*t**5 - 4/9 = 0.
-1, 1
Factor -136/3*t - 40/3*t**2 - 2/3*t**3 - 128/3.
-2