2. Factor s**2 - s**2 + 2*s**3 - m*s + 0*s**2.
2*s*(s - 1)*(s + 1)
Let i(p) = -p**2 - 5*p + 8. Let s = 2 + -8. Let g be i(s). Suppose 2/5*v**3 - 2/5*v + 2/5*v**4 - 2/5*v**g + 0 = 0. Calculate v.
-1, 0, 1
Let r(o) be the second derivative of -o**4/3 + 16*o**3/3 - 25*o. Factor r(f).
-4*f*(f - 8)
Let u(l) = l - 10. Let r be u(12). Factor 0*d - 3*d**r + d**5 + d**2 - 3*d**3 + 0*d.
d**2*(d - 2)*(d + 1)**2
Let i(h) be the third derivative of 0*h + 0 - 2*h**2 + 1/2*h**6 + 5/3*h**4 + 4/3*h**3 + 37/30*h**5 + 3/35*h**7. Let i(c) = 0. What is c?
-1, -2/3
Let x be 0*-8*1/(-24). Factor 2/3 + 4/3*v - 4/3*v**3 - 2/3*v**4 + x*v**2.
-2*(v - 1)*(v + 1)**3/3
Suppose -9*g**2 - 7*g**4 + 2*g - 2*g + 4*g**4 - 3*g - 9*g**3 = 0. Calculate g.
-1, 0
Let w(q) be the third derivative of 0*q + 0*q**3 + 0 + 0*q**4 - 1/45*q**5 - 10*q**2 - 1/180*q**6. Suppose w(u) = 0. Calculate u.
-2, 0
Suppose -3*s - 1 = -5*n, 8*n = 3*s + 5*n - 3. Let m(q) = -4*q**2 - 4*q + 4. Let c(x) = x**2 + 1 - 5*x + 3 - 6*x**2. Let w(h) = s*m(h) - 2*c(h). Factor w(j).
-2*(j - 1)*(j + 2)
Let u(n) be the second derivative of n**5/20 - 5*n**4/12 + 4*n**3/3 - 2*n**2 + 5*n. Factor u(x).
(x - 2)**2*(x - 1)
Suppose -5*a = -0*a. Factor -2*v**3 - 1 + v + 0*v**2 + a*v**2 + v**5 - 2*v**2 + v**4 + 2.
(v - 1)**2*(v + 1)**3
Let n(i) = -i**3 + 10*i**2 - 7*i - 9. Let j be n(9). Factor -5*a**2 + 5*a**4 + 4 + 2*a - j*a**3 + 7*a**5 - 4.
a*(a - 1)*(a + 1)**2*(7*a - 2)
Find t such that 0*t**2 + 0 - 2/7*t**4 - 8/7*t + 6/7*t**3 = 0.
-1, 0, 2
Let b(k) be the third derivative of 2*k**2 + 1/420*k**6 + 1/420*k**5 - 1/84*k**4 + 0*k + 0 - 1/42*k**3. Factor b(u).
(u - 1)*(u + 1)*(2*u + 1)/7
Factor 17328*a**3 - 6936*a**2 + 4241*a**3 + 816*a - 32 - 1917*a**3.
4*(17*a - 2)**3
Let f = 1/94 - -363/1222. Factor 2/13*o**2 - 2/13*o - f.
2*(o - 2)*(o + 1)/13
Let h(b) = 9*b**3 + 29*b**2 - 33*b + 8. Let n(l) = -4*l**3 - 14*l**2 + 16*l - 4. Let o(x) = 6*h(x) + 13*n(x). Let o(r) = 0. What is r?
1, 2
Let m(d) be the third derivative of d**8/26880 - d**7/3360 + d**5/30 - 3*d**2. Let o(v) be the third derivative of m(v). Find x, given that o(x) = 0.
0, 2
Let q(k) = -k**2 + 4*k - 2. Let y be q(2). Find a such that a - 3*a - 2*a**2 + y + 2 = 0.
-2, 1
Let b(y) = -5*y**2 - 4. Let a(k) = 2*k**2 + 1. Let h(p) = -8*a(p) - 3*b(p). Suppose h(s) = 0. Calculate s.
-2, 2
Let g(f) be the first derivative of 0*f**2 - 2 + 2/15*f**3 - 1/10*f**4 + 0*f. Factor g(a).
-2*a**2*(a - 1)/5
Let m(v) be the second derivative of 1/60*v**5 + 1/45*v**6 + 1/126*v**7 + 0*v**3 + 0*v**4 + 0 + 0*v**2 + 3*v. What is q in m(q) = 0?
-1, 0
Let z(n) be the third derivative of n**6/420 + n**5/42 + n**4/12 + n**3/7 - 6*n**2. Solve z(r) = 0 for r.
-3, -1
Suppose -2*u + 2 + 1/2*u**2 = 0. Calculate u.
2
Let l(x) be the first derivative of 4*x**3/27 + 4*x**2/9 + 4*x/9 + 3. Factor l(v).
4*(v + 1)**2/9
Suppose 2 = 2*r - 6*r + 5*f, 2*r + 3*f - 10 = 0. Solve -2/3*x - 4/3 + 16/3*x**r - 10/3*x**3 = 0.
-2/5, 1
Let h(t) = t**2 - 27*t + 50. Let b be h(25). Factor 0*z**4 + 2/5*z**5 + b*z + 0 + 0*z**3 + 0*z**2.
2*z**5/5
Let c(z) be the third derivative of z**6/40 + 4*z**5/45 + 5*z**4/72 - z**3/9 + 5*z**2. Suppose c(p) = 0. What is p?
-1, 2/9
Let g(k) be the third derivative of -k**7/945 - k**6/270 + k**5/270 + k**4/54 + 17*k**2. Factor g(a).
-2*a*(a - 1)*(a + 1)*(a + 2)/9
Suppose 16*h = 20*h. Let p(u) be the third derivative of -1/560*u**8 - 1/50*u**6 + 0 + 3*u**2 + h*u**3 - 1/120*u**4 - 1/105*u**7 + 0*u - 1/50*u**5. Factor p(w).
-w*(w + 1)**3*(3*w + 1)/5
Let c(m) = m**5 - 7*m**4 + 16*m**3 - 8*m**2 - 11*m + 21. Let b(z) = -z**5 + 7*z**4 - 16*z**3 + 8*z**2 + 10*z - 22. Let o(w) = 5*b(w) + 6*c(w). Factor o(h).
(h - 2)**4*(h + 1)
Let k(m) be the second derivative of 0 - 1/3*m**4 + 2*m + 0*m**2 + 1/7*m**7 - 8/15*m**6 + 7/10*m**5 + 0*m**3. Factor k(c).
2*c**2*(c - 1)**2*(3*c - 2)
Let m(u) be the third derivative of -u**7/1890 + u**6/1080 + u**5/270 - 4*u**2. Suppose m(d) = 0. Calculate d.
-1, 0, 2
Let w be 2 + 6/(-3) + 1. Let v be 0/(-1) + w - -1. Let -2/3 - 2/3*s**v - 4/3*s = 0. What is s?
-1
Let w = -824/7 - -118. Determine g so that 2/7*g**3 + 4/7*g**2 - 4/7 - w*g = 0.
-2, -1, 1
Let s(z) be the first derivative of -3*z**5/25 + 3*z**4/10 - z**3/5 - 4. Factor s(q).
-3*q**2*(q - 1)**2/5
Let g be -1 + (4 - 12/5). Solve 0*r + 3/5*r**5 + 3/5*r**4 - 3/5*r**2 - g*r**3 + 0 = 0.
-1, 0, 1
Let w(j) be the third derivative of -j**8/1008 + j**7/630 + j**6/120 - j**5/180 - j**4/36 + 3*j**2. Determine c so that w(c) = 0.
-1, 0, 1, 2
Let c be 0/(-1) - (-4 - -1). Let w(y) be the first derivative of -2/5*y**5 + 1 - 2/3*y**c + 0*y**2 - y**4 + 0*y. Determine s so that w(s) = 0.
-1, 0
Let t(y) = -y + 2. Let k be t(-6). Let -8*q - 4*q**4 + 0*q + 6 + k*q**3 - 2 = 0. Calculate q.
-1, 1
Let v(h) = h**2. Let m(x) = 8*x**2 + 8*x. Let n(c) = m(c) - 12*v(c). Suppose n(i) = 0. Calculate i.
0, 2
Let v be (-3)/12 + (-14)/(-56). Find f, given that -6*f + v - 18*f**4 + 51/2*f**3 + 12*f**2 - 27/2*f**5 = 0.
-2, -2/3, 0, 1/3, 1
Let s be -4*4/(-8)*2. Let w(b) be the second derivative of 7/30*b**6 - b + 0 - 4/5*b**5 - 1/3*b**3 + 0*b**2 + 11/12*b**s. Factor w(p).
p*(p - 1)**2*(7*p - 2)
Let l(k) = -k**3 - k**2 + k - 1. Let s(x) = 2*x**3 + 3*x**2 - 2*x - 1. Let v(j) = 4*l(j) + s(j). Let g(a) = -a**2 - 1. Let r(o) = 3*g(o) - v(o). Factor r(d).
2*(d - 1)**2*(d + 1)
Let o(c) be the second derivative of c**6/50 + 3*c**5/100 - c**4/10 + 5*c. Factor o(p).
3*p**2*(p - 1)*(p + 2)/5
Let z = -6 - -11. Suppose -8 = -4*p + z*k - k, -4*p = 4*k - 16. Solve -2*j**p - 3*j**3 + 4*j**3 = 0 for j.
0
Factor -1/3*j**2 + 0*j + 0 + 1/3*j**3.
j**2*(j - 1)/3
Let u be (-33)/(-7) + 3/(-63)*-6. Suppose 2*g - 4 = g. Factor k + 4*k**3 - 2*k - 14*k**g + 2*k**2 + 8*k**u + k.
2*k**2*(k - 1)**2*(4*k + 1)
Factor 0 - 3/4*h**5 + 0*h - 1/2*h**4 + 0*h**2 + 1/4*h**3.
-h**3*(h + 1)*(3*h - 1)/4
Let s(n) be the third derivative of -n**5/270 + n**4/54 + 6*n**2. Factor s(a).
-2*a*(a - 2)/9
Let o(q) be the second derivative of q**7/3360 - q**6/960 - q**5/80 - 5*q**4/12 - 2*q. Let z(m) be the third derivative of o(m). Factor z(h).
3*(h - 2)*(h + 1)/4
Suppose -m = 4*r - 8, -4*m + 11 = -7*r + 2*r. Let f be 2*r + 4/(-2). Factor 0 + f*z**3 - 2*z**4 + 0*z + 1/2*z**2.
-z**2*(2*z - 1)*(2*z + 1)/2
Let d = 20 + -18. Suppose 1/2*u**d - 1/2 - 1/2*u**3 + 1/2*u = 0. What is u?
-1, 1
Factor -6/13*h + 2/13*h**2 + 0.
2*h*(h - 3)/13
Let w = 1 + 1. Suppose 0 = 5*s - 12 + w. Suppose 0*p**3 + 3*p**3 - s*p**3 = 0. Calculate p.
0
Let k = -18 - -3. Let g be k/(-2) + (-1)/(-2). Find m such that -g + 0 - 23*m**4 + 2*m**5 + 25*m**4 + 16*m - 10*m**3 - 2*m**2 = 0.
-2, 1
Let m = -4 - -8. Suppose 2*g**2 - 2*g**m - 3*g**2 - 1 + 5*g**2 - 2*g - 2*g**5 - 1 + 4*g**3 = 0. Calculate g.
-1, 1
Let p(f) be the first derivative of -2*f**6/15 + 24*f**5/25 - 12*f**4/5 + 32*f**3/15 - 24. Let p(n) = 0. Calculate n.
0, 2
Factor 0 + 5/4*d**2 + 1/4*d**3 + 0*d.
d**2*(d + 5)/4
Let q(l) be the first derivative of -2*l**6/27 + 2*l**5/9 - l**4/9 - 8*l**3/27 + 4*l**2/9 - 2*l/9 + 2. Determine w, given that q(w) = 0.
-1, 1/2, 1
Let z(h) = 3*h + 53. Let q be z(-17). Suppose 6/5*j**3 - 2*j**q + 8/5 - 8/5*j = 0. What is j?
-1, 2/3, 2
Suppose 2*v + 11 = 5*n, 18*v - n + 11 = 22*v. Factor 2/3 + 0*z**3 - 2/9*z**4 - 16/9*z + 4/3*z**v.
-2*(z - 1)**3*(z + 3)/9
Factor -3/5*i**3 + 3/5*i**2 + 0*i + 0.
-3*i**2*(i - 1)/5
Let 0 - 12/5*n**2 + 3/5*n = 0. Calculate n.
0, 1/4
Let q(v) = 4*v**2 + 5*v - 3. Let r(k) = 9*k**2 + 11*k - 7. Let c(w) = -7*q(w) + 3*r(w). Factor c(d).
-d*(d + 2)
Suppose -u - n = -40 + 4, 20 = -5*n. Suppose 5*d - d + w = 21, -5*d - 4*w + u = 0. Find x such that -2*x**4 + 3*x**d - 2*x**3 + x**3 = 0.
0, 1
Let j = 79/183 + -6/61. Find m such that -1/3*m**4 + 1/3*m + 2/3*m**2 + 1/3*m**5 - 2/3*m**3 - j = 0.
-1, 1
Suppose -5*g = 2*k - 31, 0 = k + 3*g - 21 + 3. Let j be 0/k*-1*1. Factor -2/7 + j*w + 2/7*w**2.
2*(w - 1)*(w + 1)/7
Let b = -6 - -4. Let h(n) = n**4 - n**2. Let m(w) = w**3 - 4*w**3 + 4*w**3 + 2*w**4 - w**2. Let q(p) = b*m(p) + 3*h(p). Factor q(c).
-c**2*(c + 1)**2
Let -37/4*h + 13/4*h**2 - 3/2 = 0. Calculate h.
-2/13, 3
Suppose 29 = 4*v + 4*q - q, 2*q = v + 1. Suppose 4*z = -3*t + 32, -v*z = 7*t - 3*t - 40. Suppose 2 - 2*a + 2*a**2 - z*a**2 - 2*a = 0. Calculate a.
-1, 1/3
Let z(v) be the third derivative of 8*v**7/735 + v**6/105 - v**