econd derivative of 2*k**7/21 - 4*k**6/15 - 4*k**5/5 + 2*k**4/3 + 2*k**3 + 76*k. Factor q(j).
4*j*(j - 3)*(j - 1)*(j + 1)**2
Let l be (8/(-20) - 228/(-270)) + 0. Factor -1/9*i**2 - 4/9 - l*i.
-(i + 2)**2/9
Suppose 2*d - 5*r = 26, -3*d + 7*d - r = 16. Let 4*n**2 - 2*n - 6*n - 2*n**d + 6*n = 0. What is n?
0, 1
Factor -89/2*o**2 + 5/4*o**3 + 162 + 387*o.
(o - 18)**2*(5*o + 2)/4
Let p be (3/4 + -3)*-8. Suppose 0 = 6*w - p - 6. Solve 8*i**4 - 5*i**w - 9*i**2 - 4*i - 2*i = 0.
-1, 0, 2
Let q be (3 - (2 + -3)) + (0 - -1). Suppose q - 7*b**2 + 0*b**2 + 1 + 4*b**2 - 3*b = 0. What is b?
-2, 1
Let d(w) be the second derivative of w**5/140 - w**4/4 + 7*w**3/2 + 17*w**2 - 17*w. Let l(v) be the first derivative of d(v). Determine t so that l(t) = 0.
7
Let x(d) be the first derivative of -d**5/180 + d**4/72 + d**3/9 - 3*d**2 + 6. Let q(n) be the second derivative of x(n). Suppose q(k) = 0. What is k?
-1, 2
Suppose -j + 1 = 0, 21*t - 17 = 18*t - 2*j. Let f(a) be the first derivative of 0*a + 8 + 28/5*a**t + a**2 + 17/3*a**3 + 43/4*a**4. Factor f(r).
r*(r + 1)*(4*r + 1)*(7*r + 2)
Let m(r) be the first derivative of r**3/3 - 12*r**2 - 25*r - 213. Determine k, given that m(k) = 0.
-1, 25
Let t(a) = -a + 6. Let b be t(0). Solve -15*u**3 + u**2 + u**4 + 4*u + b*u**3 - u - 2 + 6*u**3 = 0.
-1, 1, 2
Suppose -10 + 30 = 2*w. Let j = -7 + w. Solve -k**3 - 2*k - 2*k**2 + 2 - k**3 + 6*k**j - 2*k**3 = 0.
-1, 1
Let x(k) = 53 - 2*k**2 - 51 + 3*k + 4*k - 2*k. Let a be x(0). Factor 2*j - 2/3*j**a - 4/3.
-2*(j - 2)*(j - 1)/3
Suppose 0*b = -2*b + 6. Suppose b*k = q + 5, 3*k - q = 6*k - 7. Factor -4*f**5 - 2*f**3 - k*f**5 - 4*f**4 + 4*f**5.
-2*f**3*(f + 1)**2
Let k(m) = 23*m**3 - 3*m - 1. Let u be k(2). Let j be (-3 - (-40)/12) + u/36. Suppose -j*t**4 - 3/4*t - 45/4*t**2 + 3/2 - 57/4*t**3 = 0. Calculate t.
-1, 2/7
Let i(q) be the first derivative of 6 + 1/3*q**3 + q - q**2. Factor i(y).
(y - 1)**2
Suppose 4*o + 9 = 7*o. Suppose -5*p + 5*r + 25 = 0, 3*r + 21 = 6*p - p. What is a in 2*a**o + a**2 + 0*a**3 + a**2 - 3*a**p = 0?
0, 2
Let v = 14864/3 - 4954. What is y in -1/6*y**2 - 1/2*y**4 - 4/3*y**3 + v + 4/3*y = 0?
-2, -1, -2/3, 1
Let n be ((-102)/272 - 61/8)/(-1). Let t(f) be the first derivative of -21*f**4 + 6*f**2 - n - 80/3*f**3 + 8*f. Let t(i) = 0. Calculate i.
-1, -2/7, 1/3
Let m be 5 + (7 - 10) + 1. Let l(j) be the second derivative of 10/3*j**m + 14*j - 4/3*j**4 + 1/5*j**5 - 4*j**2 + 0. Factor l(k).
4*(k - 2)*(k - 1)**2
Let y(c) be the second derivative of c**5/20 + 5*c**4/6 + 29*c**3/6 + 10*c**2 + c - 263. Factor y(r).
(r + 1)*(r + 4)*(r + 5)
Let x(f) = -10*f**3 - 80*f**2 + 85*f - 5. Let a(o) = 11*o**3 + 80*o**2 - 85*o + 6. Let k(i) = -5*a(i) - 6*x(i). Factor k(s).
5*s*(s - 1)*(s + 17)
Let q be 151/(-369)*1916/12. Let p = -5/1107 - q. Factor 112/3*a + 16/3 + p*a**2.
4*(7*a + 2)**2/3
Let z(o) be the third derivative of -o**5/60 - 5*o**4/8 - 22*o**3/3 + 523*o**2. Factor z(a).
-(a + 4)*(a + 11)
Let t(u) be the second derivative of u**6/2340 + u**5/780 + 3*u**3/2 + 6*u. Let o(j) be the second derivative of t(j). Solve o(a) = 0 for a.
-1, 0
Determine o, given that -8/5 - 4/5*o + 4/5*o**2 = 0.
-1, 2
Let l(f) be the second derivative of 3*f**5/80 + 5*f**4/16 + f**3 + 3*f**2/2 + 68*f. Factor l(b).
3*(b + 1)*(b + 2)**2/4
Let c(j) be the third derivative of -j**6/540 - 7*j**5/135 - 17*j**4/36 - 2*j**3 - 2*j**2 - 17*j. Solve c(z) = 0.
-9, -3, -2
Find m, given that -60/13*m - 2/13*m**2 - 58/13 = 0.
-29, -1
Let q(l) be the third derivative of 1/10*l**5 + 1/315*l**7 - 8*l**2 + 0 - 1/36*l**6 + 0*l - 7/36*l**4 + 2/9*l**3. Factor q(d).
2*(d - 2)*(d - 1)**3/3
Let n(l) be the third derivative of 0*l + 3*l**2 - 1/18*l**4 + 0 + 1/1080*l**6 - 1/3*l**3 + 0*l**5. Let u(y) be the first derivative of n(y). Solve u(b) = 0.
-2, 2
Factor 14/3*y + 0 - 11*y**2 - 5/3*y**3.
-y*(y + 7)*(5*y - 2)/3
Let i(y) = -16*y**2 + 53*y - 113. Let l(t) = 2*t**2 - t - 1. Let n(u) = 2*i(u) + 14*l(u). Factor n(r).
-4*(r - 20)*(r - 3)
Let w(g) be the second derivative of -3/4*g**5 + 0*g**2 - 6*g + 5/42*g**7 + 1/6*g**6 - 5/12*g**4 + 5/3*g**3 + 0. What is j in w(j) = 0?
-2, -1, 0, 1
Let i(z) be the second derivative of -2*z**7/147 + 2*z**6/35 + z**5/35 - z**4/7 + 10*z. Determine w so that i(w) = 0.
-1, 0, 1, 3
Let p(q) be the second derivative of q**6/330 - 2*q**5/55 + 5*q**4/33 - 8*q**3/33 - 3*q - 49. Factor p(c).
c*(c - 4)*(c - 2)**2/11
Let l(u) be the first derivative of -u**5/20 + 3*u**4/8 - u**3 + u**2 - 102. Let l(p) = 0. Calculate p.
0, 2
Let h(g) be the first derivative of -5*g**4/4 - 50*g**3/3 - 30*g**2 + 360*g - 27. Factor h(r).
-5*(r - 2)*(r + 6)**2
Factor 5*s**4 + s**3 - 415*s**2 + 822*s**2 - 412*s**2 + 4*s**3 - 5*s.
5*s*(s - 1)*(s + 1)**2
Let u(q) be the second derivative of -3/2*q**2 - 1/120*q**6 + 0*q**3 + 1/24*q**4 + 0*q**5 + 0 + 2*q. Let h(w) be the first derivative of u(w). Factor h(n).
-n*(n - 1)*(n + 1)
Let s be (22/2 - 11)/2. Factor s*z + 0*z**3 + 2/15*z**2 - 2/15*z**4 + 0.
-2*z**2*(z - 1)*(z + 1)/15
Factor 10*s**2 + 8 - 3/2*s**3 - 18*s.
-(s - 4)*(s - 2)*(3*s - 2)/2
Let o(r) be the third derivative of -1/80*r**5 - 1/480*r**6 + 0*r + 0 + 36*r**2 + 0*r**3 + 0*r**4. Solve o(u) = 0.
-3, 0
Suppose 89*o - 92*o = -6. Let z(j) be the first derivative of 4*j - 3*j**o - 4/3*j**3 + 10 + 3/2*j**4. Factor z(k).
2*(k - 1)*(k + 1)*(3*k - 2)
Suppose -3*k + 5*o = 0, 77*k + 5*o = 73*k + 35. Find u such that -1/3*u**4 + 4/3*u**2 + 3*u**3 + 0 - 4/3*u - 2/3*u**k = 0.
-2, -1, 0, 1/2, 2
Suppose -40 = -17*q - 39*q + 36*q. Suppose -3/5*k + 0 - 1/5*k**3 - 4/5*k**q = 0. Calculate k.
-3, -1, 0
Suppose -5*q - 7 = -32. Suppose q = -5*s, k - 3*s = 2*s + 7. Determine j, given that 3*j**k + 3/2*j + 0*j**3 + 0 - 3/2*j**5 - 3*j**4 = 0.
-1, 0, 1
Let i(x) be the third derivative of -x**7/70 + 3*x**5/20 + x**4/4 + 217*x**2. Factor i(r).
-3*r*(r - 2)*(r + 1)**2
Let s = 57982/16891 - 10/2413. What is g in s - 32/7*g + 2*g**2 - 2/7*g**3 = 0?
2, 3
Let t(m) be the first derivative of m**7/2520 + m**6/1080 - m**5/360 - m**4/72 + 5*m**3/3 + 9. Let c(v) be the third derivative of t(v). Factor c(y).
(y - 1)*(y + 1)**2/3
Factor -3/4*h**2 - 75/4*h - 69/2.
-3*(h + 2)*(h + 23)/4
Let p(o) = 5*o**4 + 10*o**3 - 29*o**2 + 17*o. Let g(d) = 10*d**4 + 20*d**3 - 56*d**2 + 33*d. Let f(t) = 3*g(t) - 7*p(t). Find q, given that f(q) = 0.
-4, 0, 1
Determine z, given that 419*z**2 - 208*z**2 + 260*z - 210*z**2 + 24*z + 20164 = 0.
-142
Let i(y) be the third derivative of y**5/80 + 29*y**4/16 + 841*y**3/8 - 67*y**2. Determine b so that i(b) = 0.
-29
Let z(i) be the third derivative of -1/60*i**4 - 1/300*i**6 - 1/75*i**5 + 0*i + 0 + 10*i**2 + 0*i**3. Solve z(y) = 0 for y.
-1, 0
Let a(o) = -5*o**5 + 6*o**4 + 19*o**3 + 12*o**2 + 10*o. Let u(b) = 4*b**5 - 6*b**4 - 18*b**3 - 12*b**2 - 9*b. Let t(n) = 5*a(n) + 6*u(n). Factor t(p).
-p*(p + 1)**2*(p + 2)**2
Let r = 38 - 23. Factor 5*z**2 + z + 3*z + 5*z - r + z.
5*(z - 1)*(z + 3)
Suppose -4014*v - 154 = -4091*v. Factor 0 + 5/4*u**v + 1/2*u.
u*(5*u + 2)/4
Let m(h) = 5*h**2 + 90*h - 92. Let g(x) = -5*x**2 - 90*x + 93. Let s(d) = 3*g(d) + 2*m(d). Factor s(a).
-5*(a - 1)*(a + 19)
Let o(f) be the third derivative of -f**5/120 - 61*f**4/24 - 3721*f**3/12 - 13*f**2 + f. Suppose o(z) = 0. What is z?
-61
Let n(y) be the second derivative of y**6/10 - 33*y**5/20 - 18*y**4 - 62*y**3 - 96*y**2 - 43*y. What is k in n(k) = 0?
-2, -1, 16
Let v(p) = -p**2 + p. Let z(j) = -j**3 - 3*j**2 + 6*j - 2. Let y(u) = -20*v(u) + 4*z(u). Factor y(o).
-4*(o - 2)*(o - 1)*(o + 1)
Let k(j) be the third derivative of j**11/83160 - j**9/7560 + j**7/1260 - j**5/6 + 13*j**2. Let f(l) be the third derivative of k(l). Factor f(x).
4*x*(x - 1)**2*(x + 1)**2
Let t(k) be the third derivative of -k**7/1680 + k**6/480 + 3*k**5/40 + k**4/3 + 4*k**2. Let p(a) be the second derivative of t(a). Factor p(b).
-3*(b - 3)*(b + 2)/2
Suppose 0 = 2*t - 5*q + 9, -28*t = -30*t + 2*q. Factor 2/7*j**t - 6/7*j**2 + 8/7 + 0*j.
2*(j - 2)**2*(j + 1)/7
Suppose 2 = 8*f - 14. Let v(s) be the first derivative of 1/14*s**4 + 3/7*s**f + 5 + 18/7*s - 10/21*s**3. Factor v(r).
2*(r - 3)**2*(r + 1)/7
Let k(v) = -5*v**3 - 50*v**2 - 70*v + 130. Let m(z) = -z**2 + 2. Let b(s) = -k(s) + 5*m(s). Factor b(r).
5*(r - 1)*(r + 4)*(r + 6)
Factor 2/11*l**3 + 0 + 0*l + 0*l**2.
2*l**3/11
Factor 0 + 24/13*l