the third derivative of -j**6/540 - 7*j**5/270 + 2*j**4/27 + 66*j**2 - 2. Let b(p) = 0. What is p?
-8, 0, 1
Let k = -1000 - -1002. Find j, given that -3/2 - 9/2*j**k - 3/2*j**3 - 9/2*j = 0.
-1
Let y(c) = -c**3 - 4*c**2 - 4*c + 5. Let r(s) = -1. Suppose -3*k + 5*m + 45 = 0, 0*k - 4*m = -k + 22. Let j(h) = k*r(h) + 2*y(h). Factor j(f).
-2*f*(f + 2)**2
Suppose -2*x = -13 + 7. Factor 3*m**3 - 7*m + 5*m**3 + 2*m**2 + 4 + 0*m**3 - 7*m**x.
(m - 1)**2*(m + 4)
Let y(i) be the first derivative of -i**6/180 - i**5/60 + i**4/72 + i**3/18 - 22*i + 12. Let j(z) be the first derivative of y(z). Factor j(n).
-n*(n - 1)*(n + 1)*(n + 2)/6
Factor -5*m**4 + m**4 - 429*m**2 + m**4 + 35*m**3 - 110*m**3 + 507*m.
-3*m*(m - 1)*(m + 13)**2
Let t(j) be the second derivative of j**4/12 + 5*j**3/2 - 8*j**2 + 4*j - 32. Factor t(c).
(c - 1)*(c + 16)
Let t(c) be the first derivative of -6*c**2 - 28 + 0*c + 1/2*c**3. Let t(l) = 0. Calculate l.
0, 8
Let r be (2/(-56))/(140/(-490)). Let j(h) be the third derivative of 1/40*h**6 + 8*h**2 + 1/20*h**5 + 0 - 1/2*h**3 + 0*h - r*h**4. What is g in j(g) = 0?
-1, 1
Factor 6*d**2 + 0 - 4/3*d - 14/3*d**3.
-2*d*(d - 1)*(7*d - 2)/3
Let y = 22 + 6. Factor 58*w**3 - 22*w**3 + 0 + 0 - 8*w**2 - y*w**4.
-4*w**2*(w - 1)*(7*w - 2)
Let g(x) be the third derivative of -169*x**5/100 - 13*x**4/10 - 2*x**3/5 + x**2 - 2. Factor g(c).
-3*(13*c + 2)**2/5
Let x = -61 + 64. Determine u so that u**3 + 3*u**4 + u**4 + 4*u**3 - u**x = 0.
-1, 0
Factor 2/7*a**3 + 0*a**4 - 1/7*a - 1/7*a**5 + 0 + 0*a**2.
-a*(a - 1)**2*(a + 1)**2/7
Let p(d) be the third derivative of -d**5/150 + d**4/30 + 8*d**3/5 + 301*d**2. Suppose p(w) = 0. Calculate w.
-4, 6
Suppose 6*v - 2*v = k + 17, -3*k = -4*v + 11. Let n(u) be the first derivative of -3/4*u**4 + 6 - 4*u**k - 6*u - 15/2*u**2. Find d such that n(d) = 0.
-2, -1
Suppose 2*f - 374 = 2*y, -109 = 4*f - 3*y - 859. Let p be 9/(f/12)*(0 + 1). Factor p*r - 4/7*r**2 + 0.
-4*r*(r - 1)/7
Let k(x) = -190*x**2 + 3*x + 4. Let v(j) = -3*j**2 - j - 1. Let i(a) = -3*k(a) - 12*v(a). Suppose i(u) = 0. What is u?
-1/202, 0
Let k = 977 - 969. Let q(w) be the third derivative of 0 - 1/180*w**5 - k*w**2 + 0*w - 1/18*w**3 + 1/36*w**4. Factor q(x).
-(x - 1)**2/3
Let -27/5*f**3 - 57/5*f - 18/5 - 63/5*f**2 - 3/5*f**4 = 0. Calculate f.
-6, -1
Let m be 1330/285*(-3)/(-49). Factor -12/7*u**2 + 12/7 - 2/7*u + m*u**3.
2*(u - 6)*(u - 1)*(u + 1)/7
Solve -32 + 1/2*r**4 - 8*r + 63/2*r**2 + 8*r**3 = 0 for r.
-8, -1, 1
Solve -2/11*q**2 + 16/11*q - 14/11 = 0 for q.
1, 7
Let q be (1*-1 + 0)/((-81)/243). Let z(k) be the second derivative of 5*k + 0*k**2 - k**4 + 3/5*k**5 + 0 - 1/10*k**6 + 0*k**q. What is n in z(n) = 0?
0, 2
Let a(l) be the first derivative of -l**3/3 - 20*l**2 - 76*l - 204. Factor a(x).
-(x + 2)*(x + 38)
Factor 3*k**4 + 6*k**4 - k**4 - 22*k**3 - 6*k**4 - 4*k**2 + 20*k**3.
2*k**2*(k - 2)*(k + 1)
Suppose -71*t = -77*t + 1008. Let y be (-48)/t - (9/(-7) + -1). Determine d, given that -1/3*d**y + 4/3*d - 4/3 = 0.
2
Let n(l) be the second derivative of -40*l - 1/112*l**7 + 0*l**3 + 1/80*l**6 + 0*l**2 + 0 - 1/32*l**4 + 3/160*l**5. Find w such that n(w) = 0.
-1, 0, 1
Let g(z) be the third derivative of -z**7/560 - 21*z**6/320 - z**5/8 - 76*z**2. Factor g(r).
-3*r**2*(r + 1)*(r + 20)/8
Let d(i) be the third derivative of -i**8/56 - 2*i**7/15 - 61*i**6/180 - 14*i**5/45 - i**4/9 - 69*i**2. Factor d(o).
-2*o*(o + 2)**2*(3*o + 1)**2/3
Let a(p) be the third derivative of p**9/3780 + p**8/560 + p**7/315 + 5*p**4/12 - 19*p**2. Let j(b) be the second derivative of a(b). Factor j(u).
4*u**2*(u + 1)*(u + 2)
Let v be (4 - 0)/(-4) - -3. Let n(l) = -l**3 + 8*l**2 + 10*l - 9. Let p be n(9). Suppose p - 2/9*d**v - 4/9*d = 0. Calculate d.
-2, 0
Let j be 11/5*2080/2860. Solve 0*w**4 - 8/5 - 4/5*w**5 + j*w**2 - 12/5*w + 16/5*w**3 = 0 for w.
-1, 1, 2
Suppose -3/2*s**2 + 3/4 - 3/8*s - 3/8*s**5 + 3/4*s**3 + 3/4*s**4 = 0. Calculate s.
-1, 1, 2
Let l = 1465 + -1461. Let n(j) be the second derivative of 0*j**l + 0*j**2 - 5*j + 0*j**5 + 0 + 1/30*j**6 + 0*j**3. Factor n(i).
i**4
Factor -233/3*v + 22 + 7/3*v**2.
(v - 33)*(7*v - 2)/3
Let x be 7 - (3 + 4) - (4 - (-224)/(-49)). Suppose -6/7*k**4 + 2/7*k**5 + x*k**3 + 0 + 0*k**2 + 0*k = 0. What is k?
0, 1, 2
Let w(d) = 9*d**2 - 8*d - 163. Let o(u) = -3*u**2 + 3*u + 54. Let b(q) = 17*o(q) + 6*w(q). Factor b(n).
3*(n - 4)*(n + 5)
Suppose -5*y = -v + 30, -2*y - 9 = 3*v + 3. Factor v*n - n**4 + 0 + 2/5*n**2 - 3/5*n**3.
-n**2*(n + 1)*(5*n - 2)/5
Let s(f) = -f**2 - f. Let w(b) = b**4 + b. Let a(x) = 14 - 4 - 13*x + 12*x. Let j be a(9). Let h(z) = j*s(z) + w(z). Solve h(i) = 0 for i.
-1, 0, 1
Let k(q) be the second derivative of -q**6/18 + q**5/20 + 7*q**4/36 - q**3/6 - q**2/3 + 2*q - 118. Find p, given that k(p) = 0.
-1, -2/5, 1
Let w(d) = 4*d**2 - 164*d + 169. Let f(k) = k**2 + 2. Let y(a) = -6*f(a) + 2*w(a). Determine m, given that y(m) = 0.
1, 163
Let c = 67 + -67. Let h be 7/21 + (-10)/(-6). Solve -2/9*o**h - 2/9*o + c = 0 for o.
-1, 0
Factor -92*u**2 - 119*u**3 - 124*u - 45 + 5 + 111*u**3.
-4*(u + 1)*(u + 10)*(2*u + 1)
Suppose 0 = -u - 5*c + 300 + 18, 4*u = 5*c + 1247. Let o = u + -3441/11. Factor 4/11*n**4 + 2/11*n + 0 - o*n**5 + 0*n**3 - 4/11*n**2.
-2*n*(n - 1)**3*(n + 1)/11
Let r(m) = 3*m**2 - 40*m - 71. Let q be r(15). Find j such that -4/9*j**4 + 20/9*j**3 - 2/9*j**5 - 22/3*j + 16/9*j**2 + q = 0.
-3, 1, 2
Let r(x) be the third derivative of x**6/180 - x**5/10 + 3*x**4/4 + 19*x**3/6 + 8*x**2. Let h(n) be the first derivative of r(n). What is o in h(o) = 0?
3
Let c(f) = -5*f**5 + 2*f**4 + 10*f**3 + 9*f**2. Let l(x) = -x**5 + x**2. Let s(i) = 2*c(i) - 6*l(i). Find h such that s(h) = 0.
-1, 0, 3
Let x(k) be the first derivative of 175*k**6/3 - 66*k**5 - 69*k**4/14 - 2*k**3/21 - 179. Find m such that x(m) = 0.
-1/35, 0, 1
Let m be ((-27)/(-108))/(50/24). Let p(s) be the second derivative of -6*s + m*s**5 - 2/5*s**3 - 1/20*s**4 + 0 + 3/10*s**2. Factor p(b).
3*(b - 1)*(b + 1)*(4*b - 1)/5
Let h(f) be the second derivative of f**7/14 - 9*f**6/10 + 27*f**5/10 + 27*f**4/2 - 243*f**3/2 + 729*f**2/2 - 101*f. Factor h(k).
3*(k - 3)**4*(k + 3)
Let u(s) be the first derivative of 33*s**7/280 - 7*s**6/40 + 23*s**5/240 - s**4/48 - s**2 + 36. Let x(b) be the second derivative of u(b). Factor x(l).
l*(3*l - 1)**2*(11*l - 2)/4
Suppose -4*x + 3*b - 5 = -24, 3*x + 2*b - 10 = 0. Let s(t) be the second derivative of 10*t**2 - 4/3*t**3 + 11*t + 0 + 1/15*t**x. Factor s(q).
4*(q - 5)**2/5
Let f = -195/1043 + 113/149. Let 0*q - f*q**3 - 1/7*q**2 + 0 = 0. What is q?
-1/4, 0
Suppose -282*n = -120*n. Find s, given that 0 + 1/8*s**5 + n*s - 1/8*s**3 - 1/4*s**2 + 1/4*s**4 = 0.
-2, -1, 0, 1
Suppose -2 = 30*a - 28*a. Let g be 8/(-12) - 1*a. Suppose 0*u - g*u**2 + 0 + 7/6*u**3 = 0. What is u?
0, 2/7
Let u(n) be the third derivative of -9*n**2 + 1/160*n**6 + 0 + 0*n - 1/20*n**5 + 0*n**4 + 0*n**3. Find p such that u(p) = 0.
0, 4
Let s(u) be the third derivative of u**6/120 - u**5/10 + 5*u**4/24 - 12*u**2 - 2*u. Determine j so that s(j) = 0.
0, 1, 5
Let m = -7827 + 39167/5. Factor m + 2/5*t**3 - 14/5*t**2 + 16/5*t.
2*(t - 4)**2*(t + 1)/5
Let w(q) be the second derivative of 1/5*q**5 - 1/45*q**6 + 10/9*q**3 - 2/3*q**4 + 0 + 6*q - q**2. Solve w(l) = 0.
1, 3
Solve 1242*v + 206*v**3 - 495*v**2 - 500 + 532*v + 1485*v**2 + 14*v**4 - 324*v = 0.
-5, 2/7
Let q(a) be the third derivative of -25/33*a**3 - 1/330*a**5 + 20*a**2 + 0 + 0*a + 5/66*a**4. Solve q(d) = 0 for d.
5
Let d be ((-291)/485)/((8/(-30))/2). Let z(x) be the second derivative of 3*x - d*x**2 + 1/4*x**4 + x**3 + 0. Factor z(f).
3*(f - 1)*(f + 3)
Let o(d) = -d**2 - 15*d - 21. Let p be o(-13). Suppose 0 = 3*h - 2*t, -4*h = -0*h + p*t. Suppose 2/7*m**4 + 0*m**3 + h + 0*m - 2/7*m**2 = 0. Calculate m.
-1, 0, 1
Let o(j) = 8*j**4 + 35*j**3 + 65*j**2 - 15*j - 90. Let b(l) = 23*l**4 + 105*l**3 + 195*l**2 - 45*l - 270. Let f(t) = 3*b(t) - 8*o(t). Factor f(u).
5*(u - 1)*(u + 2)*(u + 3)**2
Let p(a) = a**3 - 4*a**2 - 6*a + 6. Let r be p(5). Suppose 4*h = 11 + r. Factor -4*x + 7*x + 5*x**3 - 14*x**3 - h*x**4 + 9*x.
-3*x*(x - 1)*(x + 2)**2
Let c(k) be the first derivative of -5*k**3/3 - 55*k**2/2 - 59. Solve c(t) = 0 for t.
-11, 0
Let m(s) be the third derivative of 8*s**2 + 0*s**3 + 0*s + 0 + 0*s**5 + 1/30*s**6 + 0*s**4. Let m