 8/15*y**6 - 1/3*y**4 - 14*y**2 + 0*y + 1/21*y**8 - 2/7*y**7 - 1/5*y**5 + 0 + 0*y**3. Let r(v) = 0. What is v?
-1/4, 0, 1, 2
Let q(k) be the third derivative of -k**6/40 - 99*k**5/20 - 300*k**4 + 1250*k**3 + 99*k**2. Factor q(b).
-3*(b - 1)*(b + 50)**2
Let a(j) be the second derivative of j**4/4 + 31*j**3/2 + 45*j**2 + 180*j. Solve a(u) = 0.
-30, -1
Let l(j) be the third derivative of j**6/320 + j**5/20 + 7*j**4/64 - 3*j**2 + 10*j. Factor l(v).
3*v*(v + 1)*(v + 7)/8
Let q(h) be the third derivative of h**6/40 + h**5/5 - h**4/8 - 2*h**3 + 2*h**2 + 14. Factor q(r).
3*(r - 1)*(r + 1)*(r + 4)
Let r(f) = -30*f**3 - 85*f**2 + 35*f. Let j(s) = -5*s**3 - 9*s**2 + 6*s. Let h(v) = -v**2. Let u(d) = -5*h(d) - j(d). Let y(x) = -6*r(x) - 35*u(x). Factor y(m).
5*m**2*(m + 4)
Let m(q) be the second derivative of -q**8/2240 - q**7/1260 + 7*q**6/720 - q**5/60 + 13*q**4/12 - 7*q. Let r(u) be the third derivative of m(u). Factor r(t).
-(t - 1)*(t + 2)*(3*t - 1)
Determine q, given that -1/4*q**2 + 1/2*q + 3/4 = 0.
-1, 3
Suppose 3*l = -4*h + 3*h + 23, -5*l + 3*h + 15 = 0. Factor 5*i - i**2 - 8 - 2 + l*i**2.
5*(i - 1)*(i + 2)
Let o(z) be the first derivative of -7*z - 4 - z**2 - 1/2*z**3 - 1/12*z**4. Let c(p) be the first derivative of o(p). Determine a so that c(a) = 0.
-2, -1
Factor -15/7 + 1/7*y**2 + 2*y.
(y - 1)*(y + 15)/7
Suppose -b = 3*b - 20. Suppose 12 = -z - 5*p - 3, 0 = 5*z - b*p - 45. Solve -z*r + r + r - r - 4*r**2 = 0 for r.
-1, 0
Let f = 20 - 18. Suppose 3*h - 20 = 5*x, f*h - 2*x + 1 = 9. Factor k**3 + h + 9/2*k**4 + 0*k**2 + 0*k + 7/2*k**5.
k**3*(k + 1)*(7*k + 2)/2
Solve -9 + 130 + 535*z + 45 + 85 - 10*z**2 + 19 = 0 for z.
-1/2, 54
Let p(v) = -2*v**2 - v**4 - 2*v**3 + 6*v**2 - v**3 - 6*v**2 + 6. Let h(y) = y**2 - 1. Let x(r) = -6*h(r) - p(r). Suppose x(j) = 0. What is j?
-4, 0, 1
Let o = 971 + -967. Find r, given that 1/6*r**3 - 1/6*r + 0 - 1/6*r**2 + 1/6*r**o = 0.
-1, 0, 1
Factor -3/2*f**4 + 0*f**2 + 6*f + 0 - 9/2*f**3.
-3*f*(f - 1)*(f + 2)**2/2
Suppose -4*q = -5*r - 0*r - 4, -r = 0. Suppose -q = -3*i + 5. Let 6 + 0*o - 4*o**i + 3*o + o**2 = 0. Calculate o.
-1, 2
Let j(x) = -2 - 6 + 10 + 3*x - 4*x**2 - 1. Let a be (-2)/4 + (-45)/(-6). Let q(k) = 3*k**2 - 2*k - 1. Let u(w) = a*q(w) + 5*j(w). Factor u(i).
(i - 1)*(i + 2)
Let q(p) be the second derivative of 3/2*p**4 + 2*p**3 + p + 3/2*p**2 + 1/10*p**6 + 3/5*p**5 + 0. Factor q(b).
3*(b + 1)**4
Let u(j) be the third derivative of j**9/3780 + j**8/560 + 23*j**4/24 - 32*j**2. Let l(z) be the second derivative of u(z). Suppose l(d) = 0. Calculate d.
-3, 0
Let c = 289 - 283. Let g(h) be the second derivative of 0 + c*h - 1/78*h**4 + 0*h**2 + 1/39*h**3. Find s such that g(s) = 0.
0, 1
Let n(l) = l**3 - l**2 - l + 1. Let u(f) = -5*f**3 + 5*f**2 - 10. Suppose -15 = -5*z + 35. Let i(g) = z*n(g) + u(g). Factor i(w).
5*w*(w - 2)*(w + 1)
Let a = 3235 + -3231. Find u such that 32/23*u**2 + 24/23*u**3 + 32/23 - 10/23*u**a - 96/23*u = 0.
-2, 2/5, 2
Let f(d) = 40*d + 1 - 36*d - 2 - d**2. Let k(j) = 2*j**2 - 4*j + 2. Let g(s) = 4*f(s) + 3*k(s). Let g(a) = 0. Calculate a.
-1
Let n(a) = -37*a**3 + 71*a**2 - 38*a + 10. Let s be 9/(5 - 42/12). Let l(k) = 2*k**3 - k**2 - k + 1. Let d(y) = s*l(y) - n(y). Factor d(w).
(w - 1)*(7*w - 2)**2
Let f(l) = -10*l**3 - 45*l**2 + 135*l + 85. Let c(n) = 6*n**3 + 23*n**2 - 68*n - 42. Let m(r) = -5*c(r) - 2*f(r). Solve m(g) = 0.
-4, -1/2, 2
Let b = -706/7 + 722/7. Find n such that -b*n**2 + 0*n - 24/7*n**3 + 0 + 36/7*n**4 - 10/7*n**5 = 0.
-2/5, 0, 2
Let j(u) be the third derivative of -7/20*u**5 - u**3 + 0*u - 10*u**2 + 0 + 9/8*u**4. Factor j(g).
-3*(g - 1)*(7*g - 2)
Let z(d) = 10*d**3 - 78*d**2 - 180*d - 86. Let l(h) = 9*h**3 - 79*h**2 - 180*h - 87. Let c(i) = 6*l(i) - 5*z(i). Factor c(k).
4*(k - 23)*(k + 1)**2
Let i(v) be the third derivative of -v**8/1092 + v**7/455 + 3*v**2 + v. Factor i(z).
-2*z**4*(2*z - 3)/13
Suppose 34*a - 57*a = -26*a. Let t(w) be the second derivative of -1/60*w**6 - 1/6*w**3 + a*w**5 + w + 0 + 0*w**2 + 1/8*w**4. Factor t(f).
-f*(f - 1)**2*(f + 2)/2
Let v(c) be the third derivative of -c**8/1176 + c**6/210 - c**4/84 + 202*c**2. Determine s, given that v(s) = 0.
-1, 0, 1
Let c = 31 - 22. What is p in 11*p + 2 + p**2 + 0*p - c*p + p = 0?
-2, -1
Let f(z) be the first derivative of -92/15*z**3 + 16/25*z**5 + 0*z - 12/5*z**2 - 14 + z**4. Let f(g) = 0. Calculate g.
-3, -1/4, 0, 2
Let o(i) be the first derivative of 40 - 1/2*i**2 + 6/5*i + 1/15*i**3. Determine p so that o(p) = 0.
2, 3
Let i(z) = -2*z - 36. Let w be i(-19). Find g such that -2*g**3 + 5*g**w - 9*g**2 + 6*g**3 = 0.
0, 1
Suppose 2/3*m**3 - 2/3*m - 4/3 + 4/3*m**2 = 0. Calculate m.
-2, -1, 1
Let g(y) be the third derivative of 1/150*y**5 + 0*y**3 + 0*y**4 + 0 + 1/840*y**8 - 45*y**2 - 1/525*y**7 + 0*y - 1/300*y**6. Factor g(q).
2*q**2*(q - 1)**2*(q + 1)/5
Suppose 63*f = 1356 - 1167. Solve 24/5*j - 12/5*j**2 - 16/5 + 2/5*j**f = 0 for j.
2
Let k(i) be the third derivative of i**7/560 - 17*i**5/160 - 9*i**4/16 - 5*i**3/4 + 3*i**2 - 7*i. Determine b, given that k(b) = 0.
-2, -1, 5
Let d be ((-25)/(-10))/((-1)/(-2)). Let -p**3 - 8*p**d + 20*p**5 - p**2 - 11*p**5 + p**4 = 0. Calculate p.
-1, 0, 1
Let g(a) be the second derivative of -2*a**6/15 - 3*a**5/5 + a**4 + 22*a**3/3 + 12*a**2 - 245*a. Factor g(v).
-4*(v - 2)*(v + 1)**2*(v + 3)
Let q = -18 - -17. Let u = 2 - q. Factor -6*r**2 + 3*r**3 + u*r**4 + 4*r - 4*r.
3*r**2*(r - 1)*(r + 2)
Factor -12*s**4 + 24*s**5 - 600*s**3 - 720*s**2 - 29*s**5 + 127*s**4.
-5*s**2*(s - 12)**2*(s + 1)
Factor t**3 + 25/3*t**2 + 0 - 6*t.
t*(t + 9)*(3*t - 2)/3
Let i(v) = -3*v**2 + 60*v - 84. Let l(y) = -6*y**2 + 126*y - 168. Let n(t) = -5*i(t) + 2*l(t). Let n(c) = 0. What is c?
2, 14
Let p(l) be the second derivative of -l**6/70 + 33*l**5/140 + l**4/28 - 11*l**3/14 + 2*l - 3. Find z such that p(z) = 0.
-1, 0, 1, 11
Let d(p) be the first derivative of 37 + 3/20*p**5 - 3/2*p**2 + 3/4*p**4 + 3/4*p**3 - 3*p. What is h in d(h) = 0?
-2, -1, 1
Let l(t) be the second derivative of t**8/420 + t**7/210 - 5*t**3/3 + 5*t. Let p(s) be the second derivative of l(s). What is i in p(i) = 0?
-1, 0
Factor 18/5 - 6/5*d**3 + 6*d**2 - 42/5*d.
-6*(d - 3)*(d - 1)**2/5
Let y be (-7)/14 - -3*6/20. Factor 6/5*g**4 + 2/5*g**2 - y*g**5 + 0*g + 0 - 6/5*g**3.
-2*g**2*(g - 1)**3/5
Let i(k) = 5*k**4 + k**3 - 11*k**2 - 7*k - 6. Let h(f) = f**4 - 2*f**2 - f - 1. Let g(p) = 6*h(p) - i(p). What is a in g(a) = 0?
-1, 0, 1
Suppose -33*r + 31*r**3 + 672*r**2 + 2079 + 1993*r + 4*r**4 - 707 + 32*r**3 + 25*r**3 = 0. Calculate r.
-7, -1
Let v be (3/(-13))/((-54)/702). Determine l, given that -4/3*l**v - 4/3*l**2 + 8/3*l + 0 = 0.
-2, 0, 1
Let q(s) = -9*s**2 + 21*s + 6. Let f = -24 - -37. Let x(p) = 19*p**2 - 44*p - 13. Let j(h) = f*q(h) + 6*x(h). Factor j(w).
-3*w*(w - 3)
Let j be ((-81)/(-18) + -7)/((-3)/6). Let 9/2*d**4 - 41/2*d**2 + 7/2*d**j - 2 - 19/2*d**3 - 12*d = 0. What is d?
-1, -2/7, 2
Factor 0 - 1/6*k - 2/3*k**2.
-k*(4*k + 1)/6
Let k(x) be the second derivative of -x**7/1260 + x**6/360 - 13*x**4/12 + 8*x. Let g(s) be the third derivative of k(s). Find l such that g(l) = 0.
0, 1
Let y(q) be the first derivative of -31 - 80/3*q**2 - 125/3*q**5 - 16/3*q - 200/3*q**3 - 250/3*q**4. Factor y(i).
-(5*i + 2)**4/3
Suppose 0 = -22*l + 48 - 4. Let n(b) be the first derivative of -1/7*b**4 + 2/21*b**3 - 5 + 5/7*b**l + 4/7*b. Solve n(x) = 0.
-1, -1/2, 2
Let q be 2/7 + (-284)/(-84) + -3. Let n(o) be the third derivative of -q*o**3 + 4*o**2 - 1/10*o**5 + 7/12*o**4 + 0*o + 0. Suppose n(d) = 0. What is d?
1/3, 2
Let o(d) be the second derivative of -3*d**5/20 - 12*d**4 - 384*d**3 - 6144*d**2 + 82*d. Factor o(g).
-3*(g + 16)**3
Suppose 4*s + 4*m - 20 = 0, -2*s = -5*m + 6 + 5. Suppose 3*f = 5*u - 24, -s*u = -0*f - 4*f - 18. Factor -3*j**3 - 8*j**2 + 7*j**3 + 2*j + u*j - j.
4*j*(j - 1)**2
Determine r, given that -2*r**3 - 158*r - 22 + 54 + 40 + 42 + 46*r**2 = 0.
1, 3, 19
Let b(k) = -2*k**3 + k**2 - k. Let q(s) = -3*s**4 + 29*s**3 + 113*s**2 + 163*s + 66. Let r(c) = 4*b(c) + q(c). Factor r(t).
-3*(t - 11)*(t + 1)**2*(t + 2)
Solve 126*y**4 - 49/6*y**5 - 10*y - 178/3*y**2 + 0 - 97/2*y**3 = 0.
-2/7, 0, 1, 15
Let g(q) = 5*q**2 + 9*q + 8. Let r(o) = 9*o**2 + 17*o + 15. Let s = -2 + 6. Let v(x) = s*r(x) - 7*g(x). What is f in v(f) = 0?
-4, -1
