 l(g) be the first derivative of -g**8/1344 + g**7/840 + g**6/480 - g**5/240 + 7*g**2 + 9. Let n(h) be the second derivative of l(h). Factor n(p).
-p**2*(p - 1)**2*(p + 1)/4
Let w(r) = r**3 + 3*r**2 - 21*r + 9. Let s be w(-9). Let b be (-12)/s*6*(13 - -1). Suppose b*n - 1 - 3/2*n**2 = 0. Calculate n.
1/3, 2
Let p(d) be the second derivative of -d**5/20 - 3*d**4/16 + 5*d**3/4 + d**2 + 3*d + 1. Factor p(u).
-(u - 2)*(u + 4)*(4*u + 1)/4
Let m(g) = g**3 + 2*g**2 - g + 3. Let j(v) = 4*v**3 + 92*v**2 - 80*v - 138. Let i(x) = -j(x) + 6*m(x). Factor i(u).
2*(u - 39)*(u - 2)*(u + 1)
Let w(m) = m**3 + 6*m**2 + 2*m - 12. Let c be w(-5). Let k(x) be the second derivative of 1/3*x**3 + 0*x**2 + 1/12*x**4 + 0 - c*x. What is i in k(i) = 0?
-2, 0
Let b be (-5)/3 + 14 + 185/(-15). Factor b - 2/3*f - 2/9*f**2.
-2*f*(f + 3)/9
Let r(p) be the first derivative of p**3/4 + 297*p**2/2 + 29403*p - 514. Factor r(c).
3*(c + 198)**2/4
Let r(p) = p**3 - 4. Let z be r(2). Suppose -4*h = -5*f + 20, 3*h = -2*h + f - z. Factor 0*a + 2/5*a**3 + h + 2/5*a**2.
2*a**2*(a + 1)/5
Let v(l) = -l + 6. Let i be v(6). Let h be (2 - -6)*41/492. Find f such that 2*f**3 + 0*f**4 + 0 - 8/3*f**5 + i*f + h*f**2 = 0.
-1/2, 0, 1
Let n be (-544)/(-306) - 2/(-18)*2. Let d = 94 - 844/9. Factor 0 - d*p**n + 0*p.
-2*p**2/9
Let a(j) be the first derivative of -j**6/75 + 3*j**5/50 - 4*j**3/15 - 27*j - 8. Let w(n) be the first derivative of a(n). Factor w(m).
-2*m*(m - 2)**2*(m + 1)/5
Let q(m) = 2*m**3 - 2*m**2. Let k(g) = 10*g**3 - 11*g**2 + 7*g. Let d(z) = -z**3 + z**2 - z. Let u(a) = 6*d(a) + k(a). Let t(p) = 5*q(p) - 2*u(p). Factor t(s).
2*s*(s - 1)*(s + 1)
Suppose -2*f + 2*n + 1 = -7, 2*f - 13 = 3*n. Let k be 1 + (5 - 2 - 5) - f. Factor -3*x**2 + 0 + 3/2*x**5 - 3/2*x + 3*x**4 + k*x**3.
3*x*(x - 1)*(x + 1)**3/2
Let h(n) = n + 13. Let a be h(-12). Let m be ((-2)/2 - -10)*a. What is l in -m*l + 2*l**2 + l**2 - l**2 + 6 + l**2 = 0?
1, 2
Let u(s) be the first derivative of 4*s**3/3 - 24*s**2 - 52*s - 102. Determine c so that u(c) = 0.
-1, 13
Let y(t) be the second derivative of -5*t**7/21 - 11*t**6/5 + 109*t**5/10 - t**4/2 - 104*t**3/3 + 36*t**2 + 312*t. Determine x, given that y(x) = 0.
-9, -1, 2/5, 1, 2
Let n be (-4)/8 - (-5 - (-3 - 0)). Let i = 55/2 + -27. Factor n*d**2 + i*d**3 - 1/2*d - 1 - 1/2*d**4.
-(d - 2)*(d - 1)*(d + 1)**2/2
Suppose -3 = 12*b - 11*b - 3*i, -24 = -5*b + 2*i. Let n(k) = k**3 + 13. Let o be n(0). Determine u so that 4*u**2 - 8*u + 2*u**3 + 9 + b*u**3 - o = 0.
-1, -1/2, 1
Let d(v) = -v**3 - 2*v**2 + 5*v + 6. Let g(k) = -k**2 + 1. Suppose 4*t - 10 = 2*t - 3*l, -21 = 5*t - 4*l. Let o(i) = t*d(i) + 3*g(i). Factor o(b).
(b - 3)*(b + 1)**2
Let m(w) be the second derivative of w**7/3780 + w**6/1620 - w**5/540 - w**4/108 + 2*w**3/3 - 2*w. Let o(x) be the second derivative of m(x). Factor o(u).
2*(u - 1)*(u + 1)**2/9
Let y(m) be the second derivative of -3*m**5/20 + 5*m**4/3 + 61*m**3/6 + 9*m**2 - 366*m. Factor y(w).
-(w - 9)*(w + 2)*(3*w + 1)
Let m(x) be the second derivative of -1/330*x**6 + 0*x**5 + 0 - 27*x + 0*x**2 + 0*x**3 + 1/132*x**4. Determine f, given that m(f) = 0.
-1, 0, 1
Let p(y) be the first derivative of 120/11*y**2 + 200/11*y - 19 + 1/22*y**4 + 14/11*y**3. Find i, given that p(i) = 0.
-10, -1
Let r(o) be the first derivative of -o**4/46 + 6*o**3/23 - 27*o**2/23 + 54*o/23 + 122. Factor r(t).
-2*(t - 3)**3/23
Let u = 5311/58230 - 3/1294. Let h(f) be the second derivative of -u*f**3 + 0 - 4*f - 4/15*f**2 - 1/90*f**4. Determine n so that h(n) = 0.
-2
Let n(c) = -4*c**3 - 124*c**2 - 236*c - 106. Let q(t) = 20*t**3 + 620*t**2 + 1180*t + 525. Let g(s) = -11*n(s) - 2*q(s). Factor g(a).
4*(a + 1)**2*(a + 29)
Let x = -2859/65 - -577/13. Factor x*c**3 - 2/5*c - 4/5*c**2 + 4/5.
2*(c - 2)*(c - 1)*(c + 1)/5
Let g(b) be the first derivative of -5/4*b**4 + 5/3*b**3 + 46 - 5*b + 5/2*b**2. Factor g(q).
-5*(q - 1)**2*(q + 1)
Let y = -1393 - -1396. Let f(s) be the third derivative of 0 - 2/3*s**y + 0*s - 27/20*s**5 + 5*s**2 - 3/2*s**4. Factor f(i).
-(9*i + 2)**2
Let t(o) be the first derivative of 2*o**5/15 - 13*o**4/3 + 94*o**3/3 + 364*o**2/3 + 392*o/3 - 467. Find d such that t(d) = 0.
-1, 14
Let o(v) be the first derivative of -v**6 + 38*v**5/5 - 31*v**4/2 - 2*v**3 + 18*v**2 - 154. Let o(h) = 0. Calculate h.
-2/3, 0, 1, 3
Let p(z) = -z**2 - 11*z - 13. Let i be p(-9). Let 10/3*d + 5*d**2 - 5*d**4 - 5/3*d**3 + 0 - 5/3*d**i = 0. What is d?
-2, -1, 0, 1
Suppose 29 = -3*a - 4*c + 28, -4*a - 2*c = -12. Factor 0*f**2 + 3/4*f**a + 3/4*f**3 - 3/2*f**4 + 0 + 0*f.
3*f**3*(f - 1)**2/4
Let a = 93 + -88. Suppose a*k + 3*d = 7*k + 3, 4*d - 4 = 5*k. What is n in k - n**4 + n**2 - 1/2*n + 1/2*n**5 + 0*n**3 = 0?
-1, 0, 1
Let l = 25 - 23. Factor 5 + o**3 + 113*o**2 - 116*o**2 - l - o.
(o - 3)*(o - 1)*(o + 1)
Let x be (1/(-1))/(1/(-8)). Let i = -49 - -52. Let -8*f**3 + i*f - 7*f - x*f**2 + 4*f**3 = 0. Calculate f.
-1, 0
Let w be (-1)/(-4) - 7/(-36). Let p be 15/95 + 9205/4997. Factor -10/9*r**p - w - 14/9*r.
-2*(r + 1)*(5*r + 2)/9
Let i = 26558/3 + -8852. Let 4/3 - i*x**2 + 7/3*x = 0. Calculate x.
-1/2, 4
Let n(r) = -12*r**3 + 32*r**2 + 476*r - 496. Let u(i) = i**3 - 3*i**2 - 43*i + 45. Let v(g) = -3*n(g) - 32*u(g). Suppose v(j) = 0. What is j?
-4, 1, 3
Suppose 10 = -4*l + 26. Let g be l/18 + (-64)/(-36). Solve 0*n - 2*n**3 + 10*n**5 - n**4 - 1 - 9*n**5 + n + g*n**2 = 0 for n.
-1, 1
Factor -93*d + 140*d**2 + 178*d**2 - 18 - 285*d**2.
3*(d - 3)*(11*d + 2)
Let x be (-28)/(-14) + (1 - -2). Suppose -4*g + 4*f = -20, x*g + 0*g + 5*f - 5 = 0. Solve -27/2 - 3/2*j**4 - 33*j**2 - 12*j**g - 36*j = 0 for j.
-3, -1
Let l(q) be the third derivative of q**8/336 - q**6/72 + q**3/2 + 14*q**2. Let i(g) be the first derivative of l(g). Factor i(o).
5*o**2*(o - 1)*(o + 1)
Let d = 1279 - 1274. Let x(a) be the third derivative of 0 + 1/14*a**4 - a**2 - 2/7*a**3 + 0*a - 1/140*a**d. Let x(b) = 0. Calculate b.
2
Let i(a) be the third derivative of -a**6/180 - 2*a**5/45 + a**4/12 + 2*a**3 - 90*a**2. Factor i(j).
-2*(j - 2)*(j + 3)**2/3
Let m be 0*(1 + (-3)/(-2))*(-444)/1110. Solve -5*l + 10/3 + 5/3*l**3 + m*l**2 = 0.
-2, 1
Let v be -3 - (-1 - 6)*1. Suppose 30*n**5 - 2*n**2 - 2 - 4*n**3 - 31*n**5 + 3*n**v + 5*n + n**4 = 0. Calculate n.
-1, 1, 2
Factor 4/9*j**3 + 8/3*j**2 - 80/9*j - 2/9*j**4 + 64/9.
-2*(j - 2)**3*(j + 4)/9
Suppose -4*d + 12 = -0*d. Factor -6 - 23*x**2 - x + 0*x + 27*x**2 - x**d.
-(x - 3)*(x - 2)*(x + 1)
Suppose 16/13*w + 18/13 - 2/13*w**2 = 0. What is w?
-1, 9
Suppose -5*q = -4*q - 2. Suppose q*i - 10 = 3*f + f, -2*i - f + 5 = 0. Determine b so that 26*b - 12 - 18*b**2 + 4*b**i - 3*b**3 + 3*b**3 = 0.
1, 3/2, 2
Let k(x) = -20*x + 24. Let l be k(-1). Suppose -24*j = -2*j - l. Factor -2/7 + 4/7*c - 2/7*c**j.
-2*(c - 1)**2/7
Determine m so that 0 - 3/8*m**2 + 21/8*m = 0.
0, 7
Let s(w) = 11*w - 22*w**2 + 18*w**2 - 5 + 9*w**2. Let k(a) = a**2 + 2*a - 1. Let f(b) = 22*k(b) - 4*s(b). Suppose f(h) = 0. What is h?
-1, 1
Let k(h) = h**3 + 10*h**2 + 3. Let z be k(-10). Let -6*b**3 - 5 - 9*b**z - 15*b - 15*b**2 + 10*b**3 = 0. Calculate b.
-1
Let x = -12549 + 12552. Factor -15/4*k**x + 9*k**2 - 9/2 + 33/4*k.
-3*(k - 3)*(k + 1)*(5*k - 2)/4
Let l(m) = m**2 - m + 1. Let k = 1 + 19. Let v(n) = 5*n**2 - 8*n + 4. Let f(s) = k*l(s) - 5*v(s). Factor f(t).
-5*t*(t - 4)
Let a(k) be the third derivative of -3*k**7/70 + 23*k**6/40 - 43*k**5/60 + 7*k**4/24 + k**2 - 32. Factor a(v).
-v*(v - 7)*(3*v - 1)**2
Let f(i) = -i**3 + 5*i + 5. Let j be f(-2). Determine n, given that 30*n**2 + 16 - 260*n**4 + 63*n**j + 112*n - 200*n**5 + 35*n**3 - 10*n**3 + 214*n**2 = 0.
-1, -1/2, -2/5, 1
Let g(o) be the second derivative of 4*o**6/15 + 11*o**5/10 + 5*o**4/6 - 2*o**3/3 + 5*o - 10. Factor g(c).
2*c*(c + 1)*(c + 2)*(4*c - 1)
Let b(w) be the second derivative of -1/36*w**3 + 5/12*w**2 + 1/120*w**5 - 5/72*w**4 + 0 + 22*w. Solve b(q) = 0 for q.
-1, 1, 5
Let c(p) be the first derivative of 6 + 2/3*p**3 - 16*p**2 + 128*p. Factor c(d).
2*(d - 8)**2
Let i(f) = -f**3 - 3*f**2 + 9*f - 2. Let o be i(-5). Factor 0*n**2 + o*n**2 - 6*n**2 + 122*n - 6 - 113*n.
-3*(n - 2)*(n - 1)
Let v(g) = -11*g + 51. Let o be v(4). Find t, given that -9*t**2 - o*t**2 + 18*t**4 + 56*t**3 + 10*t**5 - 62*t**4 = 0.
0, 2/5, 2
Let x(m) be the second derivative of m**7/63 + m**6/3 + 8*m**