 of 3*c**4/2 + c**3 - 12*c**2 - 12*c - 13. Factor s(p).
3*(p - 2)*(p + 2)*(2*p + 1)
Let y(s) be the second derivative of -s**5/20 - s**4/4 + 2*s**2 + 36*s. What is i in y(i) = 0?
-2, 1
Factor -4/21*z - 8/21*z**3 + 0 - 10/21*z**2 - 2/21*z**4.
-2*z*(z + 1)**2*(z + 2)/21
Let v(a) be the first derivative of a**6/51 - 4*a**5/17 + 15*a**4/17 - 80*a**3/51 + 25*a**2/17 - 12*a/17 + 35. Suppose v(k) = 0. What is k?
1, 6
Let o = -4/77 - -10/11. Let v = 248/133 - 30/19. Factor -o*h**4 + 4/7*h**2 - 6/7*h + 2/7*h**5 + v + 4/7*h**3.
2*(h - 1)**4*(h + 1)/7
Let r(f) be the third derivative of -1/60*f**4 + 1/525*f**7 + 0*f + 1/50*f**5 - 1/100*f**6 + 0 + 0*f**3 - f**2. Factor r(c).
2*c*(c - 1)**3/5
Let j be (9/(-12))/(18/(-16)). Factor 0 - j*b + 2/3*b**2 - 2/3*b**4 + 2/3*b**3.
-2*b*(b - 1)**2*(b + 1)/3
Let p(o) = -o**2 - 3*o + 2. Let t be p(-3). Factor 2*v**5 - v - 2*v**3 - v**5 + 2*v - v**4 + 0*v**3 + t*v**2 - 1.
(v - 1)**3*(v + 1)**2
What is v in 0 - 84 - 32*v**2 + 4*v**4 + 148 = 0?
-2, 2
Suppose 4*g - 3*q + 9 = 0, 3*q = 2*q + 3. Let w = 0 + 2/3. Factor 0 + g*x - 2/3*x**3 - w*x**4 + 0*x**2.
-2*x**3*(x + 1)/3
Let v(k) be the second derivative of 0 + 3*k - 1/126*k**7 + 0*k**5 - 1/30*k**6 + 0*k**3 + 1/9*k**4 + 0*k**2. Factor v(z).
-z**2*(z - 1)*(z + 2)**2/3
What is v in -4 - 5 - 136*v**2 - 1 - 15*v + 131*v**2 = 0?
-2, -1
Let f(u) be the first derivative of 1/3*u**3 - 5 + u**2 + u. Solve f(c) = 0 for c.
-1
Let r(k) = k**4 + 3*k**3 - 3*k**2 + 3*k + 2. Let f(j) = j**5 - j**4 + j**3 + j + 1. Let x(l) = 2*f(l) - r(l). Determine n so that x(n) = 0.
-1, 0, 1/2, 1
Let s(v) be the second derivative of 0*v**2 - 1/36*v**3 + 2*v - 1/120*v**5 - 1/36*v**4 + 0. Factor s(y).
-y*(y + 1)**2/6
Suppose 0*x + 3*x - 6 = 0. Let j(v) be the second derivative of 0 - 1/18*v**4 + 0*v**x + 1/30*v**5 + 0*v**3 - v. Factor j(s).
2*s**2*(s - 1)/3
Let p(l) = l - 7. Let k be p(7). Suppose b + 0*b = k. Let -6*i - 8*i**4 - 4*i**2 + 14*i**3 + 0*i**2 + 4*i + b*i**2 = 0. Calculate i.
-1/4, 0, 1
Let a = 7301/50 + -146. Let u(y) be the second derivative of 2*y + 0 - a*y**5 + 0*y**4 + 1/75*y**6 + 0*y**2 + 0*y**3. Factor u(h).
2*h**3*(h - 1)/5
Let f = 15 - 9. Let r(z) be the third derivative of 1/420*z**f + 5/84*z**4 + 2/105*z**5 + 0*z + 0 + 4*z**2 + 2/21*z**3. Factor r(y).
2*(y + 1)**2*(y + 2)/7
Let j(r) be the second derivative of -r**4/138 + r**3/23 - 2*r**2/23 + 3*r. Factor j(o).
-2*(o - 2)*(o - 1)/23
Factor 25/3*f**2 - 5/3*f + 0 - 20/3*f**3.
-5*f*(f - 1)*(4*f - 1)/3
Suppose 3*a - 7 = 8. Solve 6*b**2 - 6*b**4 + 3*b**2 + 3*b**a - 5*b**2 + 2*b**2 - 3*b = 0 for b.
-1, 0, 1
Factor -1/8*x**2 + 1/4 + 1/8*x.
-(x - 2)*(x + 1)/8
Let c(k) be the third derivative of -k**8/672 - k**7/140 + k**6/240 + k**5/40 + 16*k**2. Solve c(i) = 0 for i.
-3, -1, 0, 1
Let o(m) be the third derivative of 0 - 3/160*m**5 + 1/48*m**4 + 0*m + 1/360*m**6 - 1/6*m**3 - m**2. Let b(r) be the first derivative of o(r). Factor b(v).
(v - 2)*(4*v - 1)/4
Suppose 0 = 7*l + 2*l - 18. Let z(c) be the first derivative of -3/2*c**4 - 2 + 0*c - 6/5*c**5 - 2/3*c**3 + 0*c**l - 1/3*c**6. Factor z(m).
-2*m**2*(m + 1)**3
Suppose -6/11*j - 8/11 + 2/11*j**2 = 0. What is j?
-1, 4
Let a(b) = 5 + 2*b**4 - 2*b**4 + b**5 - 6. Let o(d) = -8*d**5 - 3*d**4 + 6*d**3 + 5. Let f(u) = -5*a(u) - o(u). Factor f(r).
3*r**3*(r - 1)*(r + 2)
Determine y, given that 1/3*y**2 + 1/3 + 2/3*y = 0.
-1
Let q(k) be the third derivative of k**7/1050 - k**6/600 - k**5/75 + k**4/30 + 15*k**2. Suppose q(d) = 0. What is d?
-2, 0, 1, 2
Determine s so that -9*s + 5 + 28*s**3 - 2 - 16*s**3 = 0.
-1, 1/2
Let k(a) = -2*a**3 - 10 + 3 + 12*a**3 + 7*a**2 - 7*a. Let g(p) = -7*p**3 - 5*p**2 + 5*p + 5. Let u(l) = 7*g(l) + 5*k(l). Factor u(f).
f**3
Let m = 41728/3 - 14391. Let k = 487 + m. Factor 8/3 - k*x - 10/3*x**2.
-2*(x + 2)*(5*x - 2)/3
Suppose -5*o = 2*u - 49, 0 = 4*o - 5*u - 20 - 6. Suppose 0 = 4*w - w - o. Factor 0*j + 4/5*j**2 - 2/5*j**4 + 0*j**w - 2/5.
-2*(j - 1)**2*(j + 1)**2/5
Suppose 32 = 3*x + x + 4*v, 2*x - 1 = 3*v. Let h = 11 + -8. Find p such that 4 - p**2 - p**x - 4 + p**4 - 2*p**h + 3*p**3 = 0.
-1, 0, 1
Factor 4 - c**4 - 5 - 24*c**2 + c + 14*c**2 + 12*c**2 + c**5 - 2*c**3.
(c - 1)**3*(c + 1)**2
Let x = 59 - 175/3. Let 0 + 1/3*j**2 + 1/3*j**3 - x*j = 0. Calculate j.
-2, 0, 1
Let t = 179 - 179. Factor 0 + 8/5*h**4 + t*h + 0*h**2 - 2/5*h**5 - 8/5*h**3.
-2*h**3*(h - 2)**2/5
Let u(i) be the first derivative of -i**6/6 - 2*i**5/5 - i**4/4 - 1. Factor u(x).
-x**3*(x + 1)**2
Let n(i) be the first derivative of -3/2*i**2 - 4 + i**3 + 3/4*i**4 - 3/5*i**5 + 0*i. Factor n(j).
-3*j*(j - 1)**2*(j + 1)
Suppose 90*v - 97*v + 14 = 0. Factor -z**v - 5/2*z**3 + 0*z + 0 - 1/2*z**5 - 2*z**4.
-z**2*(z + 1)**2*(z + 2)/2
Let u(g) be the second derivative of -g**5/10 + g**4/2 - g**3 + g**2 - 2*g. Solve u(v) = 0.
1
Let k(w) be the second derivative of w**6/180 - w**5/30 + w**4/12 + w**3/2 - 2*w. Let t(h) be the second derivative of k(h). Factor t(r).
2*(r - 1)**2
Let k(v) be the second derivative of -v**7/168 - v**6/120 + v**5/80 + v**4/48 - 6*v. Factor k(p).
-p**2*(p - 1)*(p + 1)**2/4
Suppose 2/7*b**2 + 0 - 6/7*b = 0. What is b?
0, 3
Factor 1/4*r**4 + 0*r - 1/4*r**2 + 0*r**3 + 0.
r**2*(r - 1)*(r + 1)/4
Let t(y) be the first derivative of y**7/1260 - 4*y**3/3 + 4. Let q(i) be the third derivative of t(i). Factor q(h).
2*h**3/3
Suppose -j**4 + 3*j**4 - 11*j**2 + j**4 + 8*j**2 = 0. Calculate j.
-1, 0, 1
Let p = 6 + -4. Factor -4*o**3 + 1 - o**3 + p*o**3 + 2*o**3 - o**2 + o.
-(o - 1)*(o + 1)**2
Let c(i) be the second derivative of i**4/36 + 2*i**3/3 + 6*i**2 - i. Factor c(b).
(b + 6)**2/3
Suppose 0 = 12*u - 15*u + 6. Suppose -d - 2 = -2*d, 4 = u*q + 2*d. Suppose -3/2*s**2 + q - 3*s = 0. Calculate s.
-2, 0
Let f(k) be the second derivative of -k**4/3 - 4*k**3/3 - 2*k**2 - 5*k. What is q in f(q) = 0?
-1
Let r be (12/8)/((-3)/(-8)). Suppose 7*z = d + 5*z - 10, 2*d - 24 = 5*z. What is v in 0*v + 0*v**3 + 0 - 1/4*v**5 + 0*v**d - 1/2*v**r = 0?
-2, 0
Let w(c) be the first derivative of -c**6/48 - c**5/40 + c**4/32 + c**3/24 + 5. Suppose w(p) = 0. Calculate p.
-1, 0, 1
Let u(d) be the first derivative of 2*d**5/25 + d**4/5 + 2*d**3/15 + 11. Factor u(k).
2*k**2*(k + 1)**2/5
Factor 2*x**2 + x - 3*x - 2*x + 2*x**2.
4*x*(x - 1)
Let v = -1 - 0. Let r be (8 - 2) + v + 3. Factor -r + 8*l**2 + 8 + 2*l.
2*l*(4*l + 1)
Let r = 5 - 1. Factor -21*h**5 + 0*h**r + h**4 - 7*h**4.
-3*h**4*(7*h + 2)
Let n(j) be the second derivative of -j**6/105 + j**4/42 + 6*j. Factor n(f).
-2*f**2*(f - 1)*(f + 1)/7
Let o(r) be the third derivative of r**5/12 - 24*r**2. Determine x so that o(x) = 0.
0
Suppose -4 = -4*x + 4. Let c be ((-12)/(-27))/(x/4). Solve -c*v - 2/9*v**2 - 8/9 = 0 for v.
-2
Let x = 112 - 107. Let w(g) be the second derivative of 1/60*g**x + 1/126*g**7 + 0*g**2 + 0*g**4 + 0*g**3 - 4*g - 1/45*g**6 + 0. Solve w(p) = 0.
0, 1
Let t(a) be the third derivative of 3*a**7/70 + 19*a**6/80 + 11*a**5/20 + 11*a**4/16 + a**3/2 - 27*a**2. Determine i so that t(i) = 0.
-1, -2/3, -1/2
Suppose -r + 4*w = -9, -4*r + 2*w + 13 + 9 = 0. Solve -3*o - r + 0 + 3 + 0 - o**2 = 0.
-2, -1
Let g = -6/11 + 40/33. Let 4/3 - g*j**2 - 2/3*j = 0. What is j?
-2, 1
Let o be -1 + (-10)/((-4)/(-2)). Let r(c) = 12*c**2 - 11*c**2 - 9*c - 2 - 5 + 8*c**2. Let l(j) = 5*j**2 - 5*j - 4. Let g(v) = o*r(v) + 11*l(v). Factor g(n).
(n - 2)*(n + 1)
Let m(w) be the first derivative of w**7/3780 + w**6/1620 + w**3/3 + 2. Let g(k) be the third derivative of m(k). Factor g(f).
2*f**2*(f + 1)/9
Factor 2/3*x**3 - 7/6*x**2 + 1/6 + 1/3*x.
(x - 1)**2*(4*x + 1)/6
Let b(h) = h**3 - 20*h**2 + 38*h - 26. Let s(r) = 6*r**3 - 141*r**2 + 267*r - 183. Let t(v) = -15*b(v) + 2*s(v). Solve t(p) = 0.
2
Factor 2*p**4 + 5*p**3 - 3*p**3 - 6*p**5 - 4*p**4 + 4*p**5 + 2*p**2.
-2*p**2*(p - 1)*(p + 1)**2
Let k be 10/4 - 8/(-16). Find f, given that -4*f - 2 - 2*f + k - 3*f**2 - 4 = 0.
-1
Let g be (-4)/(-4)*(-2)/1. Let k be (g + 2)/(1/(-1)). Determine h, given that k*h + 4/5*h**5 + 8/5*h**3 + 0 - 2*h**4 - 2/5*h**2 = 0.
0, 1/2, 1
Let j = 6 + -12. Let x = 7 + j. Factor 2*q**3 - x - 2*q + 4*q**2 - 2*q**2 - 1.
2*(q - 1)*(q + 1)**2
Let l(j) be the first derivative of 2/33*j**3 + 0*j + 1 + 0*j**2. Find o, given that l(o) = 0.
0
Let r(i) be the third derivative of -1/12*i**4 + 0 + 1/2*i**3 + 5*i**2 - 1/60*i**5