tive of 8/3*y**5 - 65/6*y**4 - 10/3*y - 46 + 35/3*y**3 - 5/6*y**2. What is j in k(j) = 0?
-1/4, 1/2, 1, 2
Let o = -304969/5 + 60994. Let -o*j**3 + 0 + 0*j - 2/5*j**4 + 1/5*j**2 = 0. Calculate j.
-1, 0, 1/2
Factor 0 + 5/3*n**2 + 5/3*n.
5*n*(n + 1)/3
Let i = -18811 + 18814. Factor 0*z + 0*z**2 + 4/3*z**5 + 0 - 4/3*z**4 + 0*z**i.
4*z**4*(z - 1)/3
Let s(w) be the first derivative of -4*w + 9 - 16/3*w**3 - 10*w**2. Factor s(o).
-4*(o + 1)*(4*o + 1)
Let q(g) be the third derivative of -5*g**5/24 + 10*g**4/3 - 5*g**3 - 21*g**2. Factor q(d).
-5*(d - 6)*(5*d - 2)/2
Let b(l) be the first derivative of 0*l**3 + 5 + 0*l + 1/10*l**5 + 1/8*l**4 + 1/40*l**6 - l**2. Let w(r) be the second derivative of b(r). Factor w(v).
3*v*(v + 1)**2
Let o(d) = 2*d**4 + 3*d**3 - 2*d**2 + 3*d + 3. Let f(w) = -w**3 - w - 1. Suppose 0 = -21*c + 24*c - 9. Let i(u) = c*f(u) + o(u). Factor i(t).
2*t**2*(t - 1)*(t + 1)
Let q = 854 + -68319/80. Let z(f) be the second derivative of 0 - 1/2*f**3 - q*f**5 - 1/8*f**4 - f**2 - f. Factor z(w).
-(w + 2)**3/4
Suppose -4*d - 55 = -15*d. Let c(r) be the first derivative of -2/27*r**3 + 2/9*r**2 + 0*r + d. Solve c(t) = 0.
0, 2
Let x(u) = -20*u**3 + 8*u**2 + 20*u - 20. Let y(b) = 8*b**3 - 3*b**2 - 8*b + 8. Let m be 0 + 0 + (0 - 5). Let s(p) = m*x(p) - 12*y(p). Factor s(f).
4*(f - 1)**2*(f + 1)
Factor 3*x + 4 - 5 - 1 - x**2.
-(x - 2)*(x - 1)
Suppose 7*j - 10 = 2*j. Factor 18/7*l - 27/7 - 3/7*l**j.
-3*(l - 3)**2/7
Suppose -7/8*n**4 + 15/4*n - 1/8*n**2 + 1 - 15/4*n**3 = 0. Calculate n.
-4, -1, -2/7, 1
Factor -h**3 - 7*h**2 + 110 - 10*h - 110.
-h*(h + 2)*(h + 5)
Let l(a) = a**3 - 11*a**2 + 57*a - 75. Let x(i) = -i**3 + 12*i**2 - 58*i + 74. Let w(k) = 2*l(k) + 3*x(k). Factor w(p).
-(p - 6)**2*(p - 2)
Let o(v) be the third derivative of -v**8/168 + v**7/105 + v**6/30 + 93*v**2. Factor o(f).
-2*f**3*(f - 2)*(f + 1)
Let r(g) be the second derivative of -10*g - g**3 + 0 + 1/3*g**4 + g**2. Factor r(x).
2*(x - 1)*(2*x - 1)
Let y be (5 - 3) + (5 - 1). Factor y - j**2 - 3 - j + 7*j**3 - 2 - 6*j**3.
(j - 1)**2*(j + 1)
Let b(t) = -5*t**2 + 29*t. Let c(j) = 6*j**2 - 30*j. Let n(u) = -3*b(u) - 2*c(u). What is l in n(l) = 0?
0, 9
Let p(j) be the third derivative of 1/30*j**6 - 6*j**2 + 0*j + 0 + 16/3*j**3 - 2/15*j**5 - 2/3*j**4. Factor p(x).
4*(x - 2)**2*(x + 2)
Suppose 20 = 2*k - 4*m, 10*m - 12 = -2*k + 12*m. Let -4/5 - k*c + 4/5*c**2 + 2*c**3 = 0. What is c?
-1, -2/5, 1
Let x be -1*((-3)/5 - 0). Suppose 0 = -o + 4*c - 4, 5 = -o - c + 6*c. Let o + 3/5*p - x*p**2 = 0. What is p?
0, 1
Let q(c) be the third derivative of -c**7/140 + 7*c**6/40 - 5*c**5/8 + 3*c**4/4 + 81*c**2. Factor q(f).
-3*f*(f - 12)*(f - 1)**2/2
Let h(w) = 21*w + 23. Let m be h(-1). Factor 1/2 + 1/2*u**3 - 1/2*u - 1/2*u**m.
(u - 1)**2*(u + 1)/2
Suppose -192*d + 0 - 99/4*d**3 + 216*d**2 + 3/4*d**4 = 0. What is d?
0, 1, 16
Find b, given that -2733*b + 10*b**3 + 5 + 45*b**4 - 25*b**5 - 50*b**2 + 0 + 2748*b = 0.
-1, -1/5, 1
Let i(j) be the first derivative of -2*j**3/3 - 9*j**2 - 40*j + 36. What is g in i(g) = 0?
-5, -4
Let v(j) be the first derivative of -3*j - 3/4*j**3 + 9/2*j**2 - 15/16*j**4 + 7. Factor v(s).
-3*(s - 1)*(s + 2)*(5*s - 2)/4
Suppose -3*z = -5*t - 0*z + 9, t - 5*z = 15. Suppose t = 4*n, 3*o = 4*o + 5*n - 2. Factor -12*s**2 - 3*s**o - 12 - 6*s**2 + 60*s - 27*s**3.
-3*(s - 1)*(s + 2)*(9*s - 2)
Let l(q) be the first derivative of q**4/6 - 8*q**3/3 + 11*q**2/3 + 23. Factor l(s).
2*s*(s - 11)*(s - 1)/3
Factor 21 + 19 - 40*u**2 - 62*u**3 + 8*u**2 - 8 + 44*u + 18*u**3.
-4*(u - 1)*(u + 1)*(11*u + 8)
Let r(z) = 59*z**2 + 8*z + 3 - 35*z**2 - 25*z**2. Let o be r(0). Factor 2/5*u - 2/5*u**o + 2/5 - 2/5*u**2.
-2*(u - 1)*(u + 1)**2/5
Let p(f) = -14*f**3 + 4*f**2 + 4*f - 6. Let o(d) = 14*d**3 - 5*d**2 - 4*d + 5. Let t = -55 - -38. Let x = t - -22. Let k(i) = x*p(i) + 6*o(i). Factor k(h).
2*h*(h - 1)*(7*h + 2)
Let w be 15/(30/(-16)) + (-10 - -20). Factor 0 - 2*l**3 - 2/3*l + 8/3*l**w.
-2*l*(l - 1)*(3*l - 1)/3
Let l(s) be the first derivative of -4*s**7/189 - s**6/15 - s**5/15 - s**4/54 + 21*s - 22. Let h(t) be the first derivative of l(t). Factor h(k).
-2*k**2*(k + 1)**2*(4*k + 1)/9
Factor 96 - 32 - 12*x - 46 + 2*x**2.
2*(x - 3)**2
Let v(j) = -j**2 + 3 + 6*j**2 + 3*j**2. Let l(p) = 17*p - 16 - 19 - 17*p - 95*p**2. Let w(c) = 3*l(c) + 35*v(c). Determine u so that w(u) = 0.
0
Let l(u) be the second derivative of u**4/24 + 38*u**3/3 + 1444*u**2 + 270*u. Factor l(n).
(n + 76)**2/2
Let f(c) be the third derivative of c**6/180 - 11*c**5/90 + 7*c**4/18 + 80*c**3/9 - 431*c**2. Let f(z) = 0. Calculate z.
-2, 5, 8
Let w = 207 + -205. Let c(q) be the first derivative of 1/7*q**4 - 6 - 1/7*q**w - 2/7*q - 1/21*q**6 - 2/35*q**5 + 4/21*q**3. Find l, given that c(l) = 0.
-1, 1
What is q in -8/7*q**5 + 0 + 8/7*q**3 - 6/7*q**2 + 0*q + 6/7*q**4 = 0?
-1, 0, 3/4, 1
Factor 2 - 17 + 354*i**3 + i + 15*i**2 - 355*i**3.
-(i - 15)*(i - 1)*(i + 1)
Factor -10/11*m**3 - 10/11*m**2 - 5/11*m - 5/11*m**4 - 1/11 - 1/11*m**5.
-(m + 1)**5/11
Let b(r) = -r**4 + r**3 + 3*r**2 + 1. Let p(q) = 12*q**4 - 9*q**3 - 33*q**2 - 2*q - 12. Let t(k) = 33*b(k) + 3*p(k). Determine j, given that t(j) = 0.
-1, 1
Let b(d) be the first derivative of 4*d**3/21 + 65*d**2/7 + 64*d/7 - 670. Factor b(s).
2*(s + 32)*(2*s + 1)/7
Let b(k) be the first derivative of -k**3/3 - k**2 + 8*k - 364. Factor b(j).
-(j - 2)*(j + 4)
Let r(q) be the third derivative of q**7/15120 - q**6/4320 - q**5/120 + q**4/4 - q**3/2 + 22*q**2. Let w(k) be the second derivative of r(k). Factor w(i).
(i - 3)*(i + 2)/6
Let s(a) be the second derivative of a**5/5 + 10*a**4/3 + 22*a**3 + 72*a**2 - 25*a. Factor s(z).
4*(z + 3)**2*(z + 4)
Let x(q) be the third derivative of q**6/180 - 2*q**5/135 - q**4/108 + 2*q**3/27 - 2*q**2 + 137*q. Factor x(r).
2*(r - 1)**2*(3*r + 2)/9
Suppose -j - 3 = -i, 0 = 4*j + 2*i + i - 23. Solve 13*p**2 + 3*p**2 - j*p**5 + 6*p**3 - 4*p**4 - 21*p + 29*p = 0 for p.
-2, -1, 0, 2
Solve 459*k**2 + 320 + 15*k**3 - 564*k - 44 - 780*k**2 = 0 for k.
-2, 2/5, 23
Let b(k) be the first derivative of 3/16*k**2 + 9/8*k**5 - 7/8*k**3 + 21/32*k**4 + 0*k - 17. Suppose b(t) = 0. Calculate t.
-1, 0, 1/5, 1/3
Let t(k) be the second derivative of -1/120*k**6 + 1/24*k**4 + 0*k**3 + 9*k + 0 + 0*k**2 - 1/80*k**5. Factor t(y).
-y**2*(y - 1)*(y + 2)/4
Let x = 1/29 - -49/261. Let s(f) be the second derivative of -4/63*f**7 - 1/36*f**4 - x*f**3 + 1/6*f**5 + 2/45*f**6 - 1/6*f**2 - f + 0. Factor s(n).
-(n - 1)**2*(2*n + 1)**3/3
Suppose 5*b - 5 = 40. Let g(p) = -p + 3. Let q be g(3). What is z in -z + 15*z**3 - b*z**2 - 5*z + q*z = 0?
-2/5, 0, 1
Factor -5*o**2 - 4*o + 4*o**4 + 7*o**3 + o**3 + o**2 - 4*o.
4*o*(o - 1)*(o + 1)*(o + 2)
Let 21/10*l**2 + 39/10*l + 1/10*l**3 + 19/10 = 0. What is l?
-19, -1
Suppose 68*j - 2*j - 132 = 0. Determine m, given that -4/9 - 2/3*m - 2/9*m**j = 0.
-2, -1
Let m be (-26)/(-40) + 6/(-15). Let s = 1111/2216 + -3/2216. Factor -s*d**2 + m*d**4 + 0*d**3 + 1/4 + 0*d.
(d - 1)**2*(d + 1)**2/4
Let t(f) be the second derivative of 0 - 8*f**2 - 49/3*f**4 + 5*f + 56/3*f**3. Factor t(c).
-4*(7*c - 2)**2
Let r(a) be the third derivative of -a**6/720 - 17*a**5/360 + a**4/8 + 541*a**2. Solve r(j) = 0 for j.
-18, 0, 1
Let i(z) be the third derivative of 5/12*z**4 + 0 + 0*z + 11*z**2 - 5/18*z**3 - 5/36*z**5. Suppose i(k) = 0. What is k?
1/5, 1
Let b(w) = -5*w**2 + w + 3. Let d(p) = -3*p**2 + 2. Let i(j) = 4*b(j) - 6*d(j). Factor i(u).
-2*u*(u - 2)
Let i(a) be the first derivative of -a**3/6 - a**2/2 + 170. Factor i(v).
-v*(v + 2)/2
Let k(j) = -7*j - 14. Let t be k(-4). Factor -3*o**2 - 9*o - 4 - o**2 + 3*o + t*o.
-4*(o - 1)**2
Factor o**2 + 1225 - 74*o + 70*o + 74*o.
(o + 35)**2
Suppose -12 = -m - m. Let c(h) = 2*h + 9. Let v be c(m). Factor -5*n - 3*n**5 + 5*n - 6*n - v*n**2 - 27*n**3 - 15*n**4.
-3*n*(n + 1)**3*(n + 2)
Let v(m) be the first derivative of -289*m**5/20 + 357*m**4/16 + 253*m**3/6 - 33*m**2/2 + 2*m - 131. Determine y so that v(y) = 0.
-1, 2/17, 2
Let i = 22951/135 - 170. Let f(c) be the third derivative of -1/540*c**6 + 0*c + 2/27*c**3 + 1/108*c**4 + 0 + 4*c**2 - i*c**5. Determine y so that f(y) = 0.
-2, -1, 1
Suppose 0 = -h - 0*h + 3. Let z be 1/(h + (-20)/8). Factor -n**4 + 0*n**2 - n**2 + 2*n - z*n**2 + 3*n**3 - n.
-n*(n - 1)**3
Let r = -20107 - -80429/4. Fa