. Let q(k) be the first derivative of -3 + a*k + 2/27*k**3 - 7/9*k**2. Determine j, given that q(j) = 0.
1, 6
Let v(c) = -26*c - 986. Let z be v(-38). Let u(b) be the first derivative of -10/7*b**z - 4/21*b**3 - 10 - 16/7*b. Factor u(i).
-4*(i + 1)*(i + 4)/7
Suppose 0 = -4*n - k + 4 - 1, -3*k = 3*n + 9. Suppose 0 = -2*q - q + 2*r + 3, 0 = 2*q - n*r. Solve -162*p**2 - 43*p**3 + 174*p**2 - 5*p**q + 21*p**4 = 0 for p.
0, 2/7, 2
Factor 24*a + 48 - 303 - 84*a + 10*a**3 + 100*a**2 + 75*a**2 + 130*a.
5*(a - 1)*(a + 17)*(2*a + 3)
Let i(a) = 3*a**4 - 9*a**3 - 12*a**2 + 6*a - 6. Let r(z) = -1 + 176*z**2 + z - 4 - 177*z**2 + z**4 + 4. Let x(l) = -i(l) + 6*r(l). Factor x(n).
3*n**2*(n + 1)*(n + 2)
Suppose -3*w + w = m - 16, -2*w = 4. Suppose -f = -11*f + m. Determine l so that -4*l**3 - 55*l + f + 2*l**5 + 2*l**4 + 116*l - 4*l**2 - 59*l = 0.
-1, 1
Let g be ((-217)/21 - -7)*(-4)/10. Let n(m) be the third derivative of 1/6*m**4 + 0*m + 0 + 1/15*m**5 - g*m**3 + 8*m**2. Factor n(s).
4*(s - 1)*(s + 2)
Let d(h) be the second derivative of -1/4*h**5 + 0*h**2 + 1/4*h**4 + 1/42*h**7 + 0 + 0*h**3 + 1/30*h**6 + 137*h. Solve d(q) = 0.
-3, 0, 1
Let n = 69712 - 69710. Find t, given that 27/4*t**n - 3/4*t**3 + 0 - 27/2*t = 0.
0, 3, 6
Suppose 15*p = 9*p + 132. Factor -i**4 + p*i + 34*i**3 - 4 - 30*i**2 - 9*i**4 - 34*i**2 + 22*i**2.
-2*(i - 1)**3*(5*i - 2)
Let z(v) = -2*v**3 + v - 9*v + 6*v - 2 + 2*v**2 - 3*v. Let c(u) = -u**3 + u**2 - 5*u - 1. Let m(t) = -7*c(t) + 6*z(t). Factor m(q).
-5*(q - 1)**2*(q + 1)
Let a(h) be the third derivative of 0 + 3*h**2 + 31/108*h**4 + 58/27*h**3 - 22*h + 1/270*h**5. Factor a(z).
2*(z + 2)*(z + 29)/9
Let z = 4930 - 834. Factor 11*q**2 + 16*q**2 - 43*q**2 - z + 15*q**2 - 136*q + 8*q.
-(q + 64)**2
Let p(x) = x**2 + 3*x + 1. Let u(j) = -16*j**2 - 144*j - 12. Let g(z) = 12*p(z) + u(z). Factor g(i).
-4*i*(i + 27)
Suppose 8872*q = 8869*q - 5*w + 65, 0 = 2*q - 4*w + 8. Solve 16/3*p + 8/9 + 50/9*p**3 + q*p**2 = 0.
-1, -2/5
Let a(m) be the second derivative of -86*m - 8/3*m**2 + 1/5*m**5 - 2/3*m**3 + 0 + 1/45*m**6 + 7/18*m**4. Solve a(g) = 0.
-4, -2, -1, 1
Let h be (-44)/(-24) - 1 - (-15)/(-18). Let n(u) be the first derivative of 0*u**4 - 2/15*u**5 + 2/9*u**3 + h*u + 6 + 0*u**2. Factor n(l).
-2*l**2*(l - 1)*(l + 1)/3
Let q be 20 + -41 - 1/((-14)/322). Factor 0 + 3*g + 3/2*g**q.
3*g*(g + 2)/2
Let c(o) be the third derivative of 0*o**4 - 147*o**2 + 0*o**6 - 1/735*o**7 + 0*o**5 + 0*o + 0 + 0*o**3 - 1/1176*o**8. Factor c(v).
-2*v**4*(v + 1)/7
Let i(t) be the first derivative of 1/21*t**3 - 110 + 2025/7*t + 45/7*t**2. Factor i(w).
(w + 45)**2/7
Let d be 2*(2 - 3)*78/(-52). Factor -r**4 - 4 + 2*r + 400*r**3 - 402*r**d - r**4 + 6*r**2.
-2*(r - 1)**2*(r + 1)*(r + 2)
Suppose 8*s = 10*s + 3*m - 9, m = -4*s + 13. Let k be 12/s + 7 + -9. Let 0*v**3 - 6*v**2 + 4*v**k + v**3 + 6*v**4 - 2*v**4 - 3*v**5 = 0. What is v?
-2/3, 0, 1
Let x(g) be the first derivative of -g**7/420 - g**6/40 - g**5/24 - 71*g**2 + 139. Let a(k) be the second derivative of x(k). Solve a(d) = 0.
-5, -1, 0
Let o be (-47)/6110*-325 + (-6)/(-4). Factor -57/2*f + 3/2*f**5 - 39*f**2 - 15/2 - 21*f**3 - 3/2*f**o.
3*(f - 5)*(f + 1)**4/2
Let y(z) be the third derivative of 0*z**3 - 1/48*z**5 - 3/64*z**4 - 1/960*z**6 + 0*z + 0 + 126*z**2. Factor y(d).
-d*(d + 1)*(d + 9)/8
Suppose -2*u = 4*d - 24, 5*d = 5*u - 12 - 48. Suppose d - 26/5*m**4 - 8/5*m + 74/5*m**3 - 8*m**2 = 0. Calculate m.
-2/13, 0, 1, 2
Let j be ((-22)/(-44))/(4/(-6))*(-20)/3. Let u(z) be the third derivative of 0 + 0*z + 7/36*z**4 + 1/90*z**j + 10/9*z**3 - 20*z**2. Find k such that u(k) = 0.
-5, -2
Let z = 137837 - 413509/3. Determine u so that 0 + 0*u - 4/3*u**3 - 2/3*u**2 - z*u**4 = 0.
-1, 0
Let l(t) be the second derivative of t**4/28 + 344*t**3/7 + 177504*t**2/7 + 3*t - 531. Factor l(q).
3*(q + 344)**2/7
Let x(r) be the first derivative of -r**3/9 - 1511*r**2/3 - 2283121*r/3 + 1359. Factor x(v).
-(v + 1511)**2/3
Suppose -16 = -29*c + 21*c. Factor 78*z + 12*z**2 - 19*z**c - 57 - 20*z + 41.
-(z - 8)*(7*z - 2)
Let y(k) = -4*k**4 - 47*k**3 - 9*k**2 + k + 8. Let r(t) = -9*t**4 - 108*t**3 - 19*t**2 + t + 16. Let g(a) = -3*r(a) + 7*y(a). Factor g(x).
-(x - 1)*(x + 2)**3
Let s(a) be the first derivative of -2*a**3/45 + 4342*a**2/15 - 9426482*a/15 - 7137. Suppose s(i) = 0. What is i?
2171
Factor 1207801/5 - 2198/5*g + 1/5*g**2.
(g - 1099)**2/5
Let u(w) = w + 1. Let n(i) = i**2 - 4*i + 1. Let y be n(7). Suppose -3 = -y*q + 19*q. Let a(s) = -5*s**2 + 23*s - 32. Let g(h) = q*a(h) + 2*u(h). Factor g(f).
-5*(f - 3)*(f - 2)
Find n, given that -28566 + 249/2*n**2 + 3/2*n**3 + 1932*n = 0.
-46, 9
Solve -372*y**2 - 323*y**2 - 2 - 250*y - 641*y - 223*y - 277*y = 0 for y.
-2, -1/695
Let l(k) be the third derivative of -k**6/600 + k**4/10 + 17*k**3/2 + 12*k**2 - 2. Let j(u) be the first derivative of l(u). Factor j(b).
-3*(b - 2)*(b + 2)/5
Let n be 1 - 1/(-6 - -7). Suppose 11*r = -n*r + 66. Find a, given that 18 + 1/2*a**2 - r*a = 0.
6
Let p(i) be the third derivative of -i**8/36960 - i**7/396 + 103*i**4/24 - i**3/3 + 2*i**2 + 169*i. Let s(b) be the second derivative of p(b). Factor s(v).
-2*v**2*(v + 35)/11
Find q such that 1/4*q**2 - 27/2 + 25/4*q = 0.
-27, 2
Let i(q) be the second derivative of 0*q**3 + 1 + 0*q**2 - 1/80*q**5 + 1/24*q**4 - q. Find g such that i(g) = 0.
0, 2
Let j(p) be the second derivative of p**5/60 + 173*p**4/36 + 343*p**3/18 + 57*p**2/2 - 2*p - 186. Determine r so that j(r) = 0.
-171, -1
Suppose 379*q - 2446 = -537*q - 307*q. Factor 0 + 1/3*i**q + i.
i*(i + 3)/3
Let m be 160/(-1600) + 42/20. Factor -2/15*j**3 - 24/5 + 4/15*j**m + 2*j.
-2*(j - 3)**2*(j + 4)/15
Let q(s) be the first derivative of s**5/100 + 2*s**4/5 + 24*s**3/5 - 47*s + 90. Let y(t) be the first derivative of q(t). Find k, given that y(k) = 0.
-12, 0
Let a(k) be the first derivative of -4*k**5 - 16*k**2 + 12*k - 176 + 8/3*k**3 + 8*k**4. Determine n, given that a(n) = 0.
-1, 3/5, 1
Let j(g) be the third derivative of -g**9/211680 + g**7/4410 + 11*g**5/10 - 75*g**2. Let k(w) be the third derivative of j(w). Factor k(i).
-2*i*(i - 2)*(i + 2)/7
Let x = -4561 + 4563. Let l(v) be the third derivative of 0 - 14*v**x + 0*v**4 + 0*v - 1/210*v**5 - 1/210*v**6 - 1/735*v**7 + 0*v**3. Factor l(p).
-2*p**2*(p + 1)**2/7
Factor 3*w**5 + 2259*w**3 - w**5 + 8323*w**2 - 228*w**4 + 4901*w**2 + 2425*w**3 + 6728*w + 1582*w**3.
2*w*(w - 58)**2*(w + 1)**2
What is x in -22/5*x**4 + 0*x + 4/5*x**2 + 8/5*x**5 + 0 + 2*x**3 = 0?
-1/4, 0, 1, 2
Let m(v) be the third derivative of -v**6/120 - v**5/4 - 19*v**4/12 - 4*v**3 - 1006*v**2. Factor m(h).
-(h + 1)*(h + 2)*(h + 12)
Let y(u) = -50*u**4 + 25*u**3 + 70*u**2 - 20*u - 10. Let m(h) = 3*h**4 - 2*h**3 + h**2 + 1. Let g(n) = -10*m(n) - y(n). Solve g(s) = 0 for s.
-2, 0, 1/4, 2
Let m(y) be the first derivative of -7*y**5/5 + 139*y**4/2 - 412*y**3 - 2092*y**2 - 1088*y - 5469. Solve m(n) = 0 for n.
-2, -2/7, 8, 34
Suppose 0*q - 2*q = 3*w + 121, 4*q + 207 = w. Let c = 58 + q. Determine f, given that 76*f - 6*f**c + f**5 - 61*f - 40*f**2 + 30*f**3 = 0.
-3, 0, 1
Let c(l) be the second derivative of 15/8*l**3 + 1/4*l**5 + 5/4*l**2 + 5/4*l**4 - 51*l + 0. Find t, given that c(t) = 0.
-2, -1/2
Determine y so that -38/21*y**2 + 40/7 + 2/21*y**4 - 4/21*y**3 + 16/21*y = 0.
-3, -2, 2, 5
Let p(z) = 52*z**2 - 485*z - 988. Let w(b) = -21*b**2 + 243*b + 494. Let y(s) = -6*p(s) - 15*w(s). Factor y(c).
3*(c - 247)*(c + 2)
What is r in 3*r**3 + 449*r**2 - 579*r**2 - 8*r**3 - 26*r + 306*r + 0*r**3 = 0?
-28, 0, 2
Suppose 0 = -3*s - 10 + 25. Suppose -s*h = z - 25, 0 = -3*z + z + 3*h - 2. Solve 25*x**3 + 21*x**2 + 8*x**z + 20*x**4 - 3*x**5 - 11*x**2 = 0.
-2, -1, 0
Suppose -169 = -7*u - 50. Factor -6*l + 15*l**3 - 54*l**3 + 24*l**3 + u*l**3 + 4.
2*(l - 1)**2*(l + 2)
Solve 425/2*f**3 - 90525*f - 45369 - 1/4*f**4 - 179773/4*f**2 = 0.
-1, 426
Solve 74683*j**5 - 74650*j**5 - 178*j**3 + 48 + 12*j**2 - 60*j**4 + 276*j - 131*j**3 = 0.
-2, -1, -2/11, 1, 4
Let r(u) be the third derivative of -1/105*u**6 - 59/105*u**5 + 10/7*u**4 + 102*u**2 + 0*u + 600/7*u**3 + 0 + 2/735*u**7. Factor r(h).
4*(h - 6)**2*(h + 5)**2/7
Let l(a) = -5*a**2 + 11*a - 3. Let r = -57 + 59. Let u(i) = 122*i - 18*i**2 - 32 - 22*i**r - 16*i**2. Let j(m) = 68*l(m) - 6*u(m). Factor j(o).
-4*(o - 3)*(o - 1)
Su