 Let q(i) be the second derivative of 0 + 0*i**4 - 1/3*i**3 - 1/21*i**7 + z*i**5 + 0*i**6 + 0*i**2 - i. Factor q(v).
-2*v*(v - 1)**2*(v + 1)**2
Let b(q) be the first derivative of -q**7/315 - 13*q**6/540 - 8*q**5/135 - q**4/27 - 11*q**2/2 - 1. Let g(v) be the second derivative of b(v). Factor g(u).
-2*u*(u + 2)**2*(3*u + 1)/9
Let -37/3*h**2 + 0 - 4/3*h**3 + 40/3*h + 1/3*h**4 = 0. What is h?
-5, 0, 1, 8
Let k(p) be the first derivative of -p**5/4 + 5*p**4 + 45*p**3/2 + 35*p**2 + 95*p/4 + 26. Factor k(a).
-5*(a - 19)*(a + 1)**3/4
Let i be ((-84)/(-98))/(261/812). Suppose 16 - i*z - 20/9*z**2 - 2/9*z**3 = 0. Calculate z.
-6, 2
Suppose -98*z + 91*z + 84 = 0. Factor 585*t**2 - 587*t**2 - z*t + 36*t - 72.
-2*(t - 6)**2
Let r(t) be the second derivative of t**7/42 - 7*t**6/30 + 3*t**5/20 + 23*t**4/12 - 16*t**3/3 + 6*t**2 + 5*t - 10. Factor r(i).
(i - 6)*(i - 1)**3*(i + 2)
Let o(j) = 7*j + 16. Let i be o(-2). Factor -f**2 - 11*f**4 - i*f**3 + 8*f**4 + 2*f**4.
-f**2*(f + 1)**2
Let o be -1 + ((-16)/(-4) - -1). Solve -25*y**3 - y**2 - o*y**2 + y - 15*y**4 + 4*y = 0 for y.
-1, 0, 1/3
Let o(x) be the second derivative of -125*x**7/63 + 10*x**6/9 + 2*x**5 + 7*x**4/9 + x**3/9 - 96*x. Solve o(t) = 0.
-1/5, 0, 1
Let l be 13/(1053/180) + -2*1. Let b(h) be the first derivative of -2/45*h**5 - 8/9*h - 2 + 4/9*h**2 - 1/9*h**4 + l*h**3. Determine v so that b(v) = 0.
-2, 1
Suppose 10 = 3*t - w, 12 = -4*t - 5*w - 0. Factor 20*l - 483 + 465 - l**t - l**2.
-2*(l - 9)*(l - 1)
Let t(x) be the third derivative of -x**7/105 - x**6/12 + 11*x**5/30 + 11*x**4/4 + 6*x**3 - 629*x**2 - x. Let t(b) = 0. Calculate b.
-6, -1, 3
Let h(f) = -7*f**4 - 23*f**3 - 21*f**2 + 23*f + 20. Let n(d) = 10*d**4 + 24*d**3 + 22*d**2 - 24*d - 20. Let z(m) = -3*h(m) - 2*n(m). Let z(g) = 0. Calculate g.
-20, -1, 1
Let k(t) be the second derivative of 3*t**5/20 - 2*t**3 - 144*t. Factor k(d).
3*d*(d - 2)*(d + 2)
Let d be 4/((-4)/5)*-1. Let u = -3 + d. Solve -4*q**4 - 4*q - 4*q**5 - 12*q**4 - 8*q**2 - 3*q**2 - 5*q**u - 24*q**3 = 0.
-1, 0
Let x(s) be the second derivative of -s**6/360 + 2*s**5/15 - 8*s**4/3 + 2*s**3/3 + 21*s. Let b(f) be the second derivative of x(f). Factor b(k).
-(k - 8)**2
Let p = -162 - -165. What is v in 15/2*v**2 - 2 - 2*v**p - 6*v = 0?
-1/4, 2
Let c = 6979 + -34892/5. Factor 3/5*j**2 - 18/5 - c*j.
3*(j - 3)*(j + 2)/5
Let u(k) = -8*k**2 - 345*k - 43. Let y be u(-43). Let o(j) be the first derivative of 0*j + y*j**2 - 4/3*j**3 - 9. Factor o(c).
-4*c**2
Let t(m) be the second derivative of -m**7/840 + m**6/120 + 3*m**5/40 + 3*m**4/4 - 26*m. Let g(j) be the third derivative of t(j). Factor g(c).
-3*(c - 3)*(c + 1)
Let h be 1/7*(384/(-16) + 26). Factor 6/7*y**4 + 0*y - h*y**5 - 8/7*y**2 + 0*y**3 + 0.
-2*y**2*(y - 2)**2*(y + 1)/7
Let o = 5117/360 + -113/8. Let r(m) be the first derivative of -1/15*m**6 - o*m**3 + 7/30*m**4 + 0*m - 4/75*m**5 + 0*m**2 - 6. Solve r(a) = 0.
-2, 0, 1/3, 1
Suppose 5*w - 595 = -45. Let v be ((-1)/(w/(-8)))/(16/40). Solve -2/11*u**3 - 4/11*u**2 + v*u + 4/11 = 0 for u.
-2, -1, 1
Factor 64/3 + 436/3*g + 130/3*g**2.
2*(5*g + 16)*(13*g + 2)/3
Let m(s) be the second derivative of -s**5/10 + 10*s**4 - 400*s**3 + 8000*s**2 - s + 50. What is v in m(v) = 0?
20
Suppose -2*d - 7 = j, -j = -2*d - 8 - 5. Let t be 20/(-56)*(95/(-25) + j). What is y in -t*y**2 + 0 - 2/7*y**4 + 0*y - 4/7*y**3 = 0?
-1, 0
Let l(j) be the first derivative of 18*j**5/5 + 3*j**4/2 - 10*j**3/3 + j**2 + 92. Factor l(f).
2*f*(f + 1)*(3*f - 1)**2
Factor 1/6*m**2 + 73/3*m + 5329/6.
(m + 73)**2/6
Let m(y) = -3*y**3 - y**2 + 1. Let s(x) = 7*x**3 + 4*x**2 + x - 2. Let n(d) = 6*m(d) + 3*s(d). Factor n(l).
3*l*(l + 1)**2
Let o be (8/(-128))/((-3)/(-306)). Let k = -25/4 - o. Determine n, given that -1/8*n**2 + k*n + 0 = 0.
0, 1
Let f be -4 + (-240)/50 + 9. Factor -f*s**3 - 3/5*s**2 + 2/5 + 1/5*s + 1/5*s**4.
(s - 2)*(s - 1)*(s + 1)**2/5
Let t(c) be the third derivative of c**6/40 - 9*c**5/20 + 3*c**4 - 8*c**3 + 6*c**2 + 4. Find h, given that t(h) = 0.
1, 4
Let a(l) be the first derivative of 3*l**4/8 + 7*l**3/2 + 33*l**2/4 + 15*l/2 - 215. Determine r, given that a(r) = 0.
-5, -1
Suppose 0 = -0*y - 17*y. Let f(n) be the third derivative of 0*n + 1/70*n**5 + y - n**2 + 1/280*n**6 - 1/56*n**4 - 1/7*n**3. Factor f(w).
3*(w - 1)*(w + 1)*(w + 2)/7
Let g(j) be the first derivative of -4*j**6/5 + 204*j**5/25 - 207*j**4/10 + 23*j**3 - 129*j**2/10 + 18*j/5 + 349. Determine o, given that g(o) = 0.
1/2, 1, 6
Let d(m) be the first derivative of m**8/5040 + m**7/630 + m**6/360 - m**3/3 + 13. Let g(c) be the third derivative of d(c). Factor g(y).
y**2*(y + 1)*(y + 3)/3
Let a be (-6*4/240*8)/((-2)/4). Find u, given that 11/5*u**4 + 4/5 - 3*u**2 + u**3 + 3/5*u**5 - a*u = 0.
-2, -1, 1/3, 1
Let i(t) be the first derivative of t**4/36 + 11*t**3/27 + 13*t**2/9 + 16*t/9 - 688. Suppose i(n) = 0. What is n?
-8, -2, -1
Let a(b) be the second derivative of 15*b**3 - 11/2*b**6 - 5/6*b**7 - 20*b**2 + 0 + 205/12*b**4 - 11/4*b**5 - 9*b. Suppose a(m) = 0. Calculate m.
-4, -1, 2/7, 1
Let y(q) be the second derivative of q**7/273 - q**6/65 + q**5/65 + q**4/39 - q**3/13 + q**2/13 - 2*q + 44. Factor y(d).
2*(d - 1)**4*(d + 1)/13
Let d be (-4)/(-26)*(-1144)/(-616). What is o in -2/7*o**2 - 6/7*o**3 + 6/7*o - d*o**4 + 4/7 = 0?
-2, -1, 1
Suppose -a + 4*z = -9, 3*z = -0*a - 2*a + 7. Suppose -a*i = -14 - 26. Solve -12 - 6 + 18 - 44*g**2 - i*g = 0.
-2/11, 0
Let q(k) be the second derivative of k**8/2520 - k**6/540 + k**3/2 + 10*k. Let d(z) be the second derivative of q(z). Factor d(o).
2*o**2*(o - 1)*(o + 1)/3
Let a(h) = 4*h**2 + 7*h. Let d(w) = -w**2. Let l(t) = -a(t) - 5*d(t). Let c be l(7). Factor c - 1/4*z**5 + 1/4*z**4 + 0*z**2 + 0*z + 0*z**3.
-z**4*(z - 1)/4
Let l(o) be the second derivative of 0 + 1/4*o**2 - o - 1/24*o**4 + 1/8*o**3. Factor l(p).
-(p - 2)*(2*p + 1)/4
Let k be (-4959)/(-4872) + 1/8. Factor 0 - k*y**3 - 4/7*y**2 + 0*y.
-4*y**2*(2*y + 1)/7
Let u(v) be the second derivative of v**4/48 + 35*v**3/24 + v + 240. Factor u(g).
g*(g + 35)/4
Let s(z) be the second derivative of -7*z**5/36 + 5*z**4/6 + 10*z**3/9 + 21*z**2/2 + 17*z. Let j(l) be the first derivative of s(l). Find d such that j(d) = 0.
-2/7, 2
Let f(y) = y - 1. Let a(z) = -3*z**2 + 9*z - 6. Let c(p) = a(p) - 6*f(p). Factor c(w).
-3*w*(w - 1)
Let y be (4/(-5))/((-2)/15). Factor -687*n**2 - y*n - 2*n**3 - 4*n + 699*n**2.
-2*n*(n - 5)*(n - 1)
Let k(i) = i**4 - 6*i**3 + 8*i**2 - 2*i - 5. Let d(g) = -3*g**4 + 15*g**3 - 23*g**2 + 7*g + 15. Let b(l) = 4*d(l) + 11*k(l). Suppose b(n) = 0. What is n?
-5, -1, 1
Let k(p) = p**4 - 8*p**3 + 4. Suppose -14 = 9*a + 13. Let c(o) = o**4 - 7*o**3 + o**2 + 3. Let l(w) = a*k(w) + 4*c(w). Determine u so that l(u) = 0.
0, 2
Factor 27/8*h**2 + 0 + 3/4*h.
3*h*(9*h + 2)/8
Factor -3*q**2 + 38 - 40 - 56 - 50 + 36*q.
-3*(q - 6)**2
Let i be -2 + -1 + (-1 - -8) + 4. Let p be -19 + 27 - 1/(2/i). Let 0 - 2*v**2 - 1/3*v - 3*v**3 - 4/3*v**p = 0. What is v?
-1, -1/4, 0
Let m = 35 + -27. Factor -4*u**5 + m*u**2 - 2*u**3 + 6*u**5 + 0*u**2 - 2*u**4 - 6*u**2.
2*u**2*(u - 1)**2*(u + 1)
Let b be (15106/35 - 16) + 12/(-2). Factor -1/5*n**4 - 32/5*n**3 - 384/5*n**2 - b*n - 4096/5.
-(n + 8)**4/5
Let f(r) = 22*r - 110. Let y be f(5). Let l(q) be the third derivative of 8*q**2 + 0*q**3 + 0 + y*q - 3/40*q**6 + 1/6*q**4 + 4/15*q**5. Factor l(d).
-d*(d - 2)*(9*d + 2)
Let t = -664 + 4650/7. Let x(i) be the first derivative of 0*i - 1/7*i**4 - t*i**2 + 1 - 8/21*i**3. Factor x(c).
-4*c*(c + 1)**2/7
Let s(m) be the second derivative of 0 + 1/12*m**4 - 1/12*m**3 - 1/40*m**5 + 0*m**2 - 13*m. Factor s(h).
-h*(h - 1)**2/2
Let q(d) be the first derivative of -d**3/3 + 4*d**2 - 7*d + 52. Suppose q(x) = 0. Calculate x.
1, 7
Let p(s) be the second derivative of 1/180*s**5 + 1/6*s**3 - 1/360*s**6 + 3*s + 3*s**2 + 0 + 5/72*s**4. Let t(v) be the first derivative of p(v). Factor t(a).
-(a - 3)*(a + 1)**2/3
Let i(a) be the first derivative of 4*a**3/3 + 174*a**2 - 352*a - 140. Suppose i(u) = 0. What is u?
-88, 1
What is z in 2/7*z**5 - 102/7*z**3 + 0 + 48/7*z**4 + 0*z + 52/7*z**2 = 0?
-26, 0, 1
What is y in -4*y**3 + y**4 + 279*y**2 - 22*y**3 - 512*y + 2*y**3 - 87*y**2 = 0?
0, 8
Let u(f) be the third derivative of -f**6/120 - f**5/30 + f**4/8 - f**2 + 93. Find x such that u(x) = 0.
-3, 