*s + 3. Factor -3/2*k**d + 1/2*k - 1/2*k**4 + 0 + 3/2*k**3.
-k*(k - 1)**3/2
Suppose -4*u + 2 = -6. Factor -2/9*p**3 + 2/9*p**4 + 2/9*p + 0 - 2/9*p**u.
2*p*(p - 1)**2*(p + 1)/9
Let y(h) be the third derivative of 2*h**2 + 0*h + 0*h**5 + 0 + 0*h**3 + 1/60*h**6 - 1/12*h**4. Factor y(a).
2*a*(a - 1)*(a + 1)
Let l be (2/(-2) + -1)*-1. Let y(g) = g**2 - 11*g + 12. Let w be y(10). Factor -l*n**w + 2*n**4 + 2*n**2 - 2*n**2.
2*n**2*(n - 1)*(n + 1)
Let p = 10 + -8. Let z = 5 + -3. Let 4*k + 0*k**3 - 2*k**2 + 2*k**2 - 4*k**3 - p*k**z + 2 = 0. Calculate k.
-1, -1/2, 1
Let u = -183 + 185. Let r(m) be the third derivative of 0 + 1/36*m**5 + 1/12*m**4 + 0*m + 1/18*m**3 + m**u. Factor r(s).
(s + 1)*(5*s + 1)/3
Factor 7*m + 2*m + 3*m**2 + 3*m - 3*m + 6.
3*(m + 1)*(m + 2)
Let f be (-445)/(-356)*(-2)/(-15). Factor -1/6 + f*c**2 + 1/6*c**3 - 1/6*c.
(c - 1)*(c + 1)**2/6
Suppose 3*f + 15 = 4*f + 3*b, 4 = b. Factor -3*i**4 + 4*i**4 + f*i**4 - 8*i**2 + 4*i**2.
4*i**2*(i - 1)*(i + 1)
Suppose -5*y - 10 = 0, 4*b - 3*b + 5*y + 7 = 0. Let l(j) be the second derivative of 0 - 1/18*j**b + 0*j**2 - j - 1/36*j**4. Factor l(i).
-i*(i + 1)/3
Find v such that 4/7*v**3 - 1/7*v**4 - 6/7*v**2 - 1/7 + 4/7*v = 0.
1
Factor 1/9*q - 1/3*q**2 + 0.
-q*(3*q - 1)/9
Suppose 4 = -21*h + 23*h. Determine k, given that -1/7*k**h - 4/7 - 4/7*k = 0.
-2
Let d(c) = 2 - 19*c + 0*c**2 + 4*c**2 + 6. Let i(y) = -2*y**2 + 10*y - 4. Let a(p) = -4*d(p) - 7*i(p). Factor a(l).
-2*(l - 2)*(l - 1)
Let v(j) be the second derivative of -j**6/120 - j**5/20 - j**4/8 - j**3/6 - j**2/8 + 7*j. Factor v(r).
-(r + 1)**4/4
Let k(w) be the third derivative of w**7/1260 + w**6/180 + w**4/12 + 2*w**2. Let j(x) be the second derivative of k(x). Factor j(r).
2*r*(r + 2)
Let g(k) = -k**2 - 7*k - 4. Let s be g(-6). Let r(p) be the second derivative of 0*p**s + 1/80*p**5 - p + 0 + 0*p**3 - 1/48*p**4. Solve r(c) = 0.
0, 1
Factor 4/5*t**3 + 0*t + 0*t**2 - 6/5*t**4 + 0 + 2/5*t**5.
2*t**3*(t - 2)*(t - 1)/5
Factor -1/2*z**2 + 0 + z.
-z*(z - 2)/2
Let b(o) be the second derivative of -o**4/24 + 5*o**3/12 - o**2 + 3*o + 7. Suppose b(n) = 0. Calculate n.
1, 4
Let z(k) be the third derivative of -k**8/84 + 2*k**7/35 - k**6/30 - k**5/5 + k**4/3 + 15*k**2. Find c such that z(c) = 0.
-1, 0, 1, 2
Suppose 0 = -2*s - 2, 0*n - n - 5*s - 7 = 0. Let l = 0 - n. Solve -l*i**4 + 4*i - 2 + 1 + 4*i**3 + i**4 - 6*i**2 + 0*i**4 = 0 for i.
1
Find b, given that -14/9*b + 8/9*b**2 + 28/9*b**3 - 4/9*b**4 - 4/9 - 14/9*b**5 = 0.
-1, -2/7, 1
Let q(a) = -1435*a**3 + 665*a**2 + 755*a + 85. Let x(g) = 239*g**3 - 111*g**2 - 126*g - 14. Let r(b) = 6*q(b) + 35*x(b). Factor r(j).
-5*(j - 1)*(7*j + 2)**2
Suppose -4 = 2*s + 3*h, 5*s - s = -4*h. Let f(c) be the third derivative of -1/12*c**3 + 0*c - 1/96*c**s + 0 + 1/240*c**5 + c**2. Factor f(t).
(t - 2)*(t + 1)/4
Let v(u) = -u**3 + 4*u**2 - 2*u. Let f be v(3). Determine c so that -7*c**4 - 25*c**5 - 4*c**f - 4*c**2 + 32*c**4 + 8*c**3 = 0.
-2/5, 0, 2/5, 1
Let l be (-4020)/(-42) - (-2)/7. Let y = l - 668/7. Factor 32/7*j**2 + 2*j**3 + 22/7*j + y.
2*(j + 1)**2*(7*j + 2)/7
Suppose 0*f = f - 3*h + 12, -2*f + 31 = 5*h. Let p(s) be the first derivative of 4*s - 2 + 5*s**2 - 14/3*s**f. Factor p(n).
-2*(n - 1)*(7*n + 2)
Let t(i) = -i**2 - 9*i - 5. Let a be t(-7). Let f be (30/9)/(6/a). What is h in 1/4*h + 0 + 0*h**3 - 1/4*h**f - 1/2*h**4 + 1/2*h**2 = 0?
-1, 0, 1
Let r(i) be the third derivative of i**7/1050 - i**6/600 - i**5/300 + i**4/120 + i**2. Factor r(o).
o*(o - 1)**2*(o + 1)/5
Let c(p) be the first derivative of -2/21*p**3 + 0*p**2 + 1/21*p**6 + 0*p + 3 - 1/14*p**4 + 2/35*p**5. Factor c(o).
2*o**2*(o - 1)*(o + 1)**2/7
Let t(y) be the third derivative of -y**5/20 - 3*y**4 - 72*y**3 + 9*y**2 + 2. Suppose t(g) = 0. What is g?
-12
Suppose -1 = -q, 3*q = -2*y + 3 + 4. Let x(r) be the third derivative of -1/270*r**5 + 0*r**3 - 1/108*r**4 + 0*r - y*r**2 + 0. Factor x(m).
-2*m*(m + 1)/9
Let a = -13/9 + 35/18. Let f(w) be the first derivative of 7/4*w**2 - 23/8*w**4 + 4/3*w**6 - 4 - 7/6*w**3 + 4/5*w**5 - a*w. Solve f(j) = 0.
-1, 1/4, 1
Let q = 22 - 18. Let r(u) be the second derivative of 1/3*u**2 - 1/18*u**3 + u + 0 - 1/36*u**q. Factor r(z).
-(z - 1)*(z + 2)/3
Let f(t) be the first derivative of 2*t**3/15 + 4*t**2/5 + 8*t/5 - 59. Factor f(k).
2*(k + 2)**2/5
Let k(b) be the third derivative of 1/90*b**5 + 0*b**3 + 0*b**4 + 0 - 2*b**2 + 1/504*b**8 + 1/105*b**7 + 1/60*b**6 + 0*b. Let k(g) = 0. Calculate g.
-1, 0
Let k(v) be the first derivative of v**4/4 - 20*v**3/3 - 14*v**2 - 17*v + 3. Let q(g) = g**3 - 30*g**2 - 42*g - 25. Let b(i) = 7*k(i) - 5*q(i). Factor b(s).
2*(s + 1)**2*(s + 3)
Let u(o) = -4*o**3 - 3*o - 2. Let f be u(-1). Determine r so that -18*r + 3 + 42*r - 17*r + f*r**2 + r**3 = 0.
-3, -1
Let u(j) be the first derivative of 5 + 1/10*j**4 + 0*j**2 + 0*j + 2/15*j**3. What is v in u(v) = 0?
-1, 0
Let w(k) = 5*k**3 + 3*k**2 - k - 3. Let l(r) be the third derivative of -r**6/120 - r**5/60 + r**3/6 - r**2. Let p(i) = -4*l(i) - w(i). Factor p(m).
-(m - 1)**2*(m + 1)
Let o(j) be the second derivative of j**5/90 + j**4/18 + 2*j**3/27 - 27*j. Factor o(u).
2*u*(u + 1)*(u + 2)/9
Let x(z) be the first derivative of -7*z**6/3 + 242*z**5/5 - 332*z**4 + 624*z**3 + 1296*z**2 - 864*z - 7. Suppose x(i) = 0. Calculate i.
-1, 2/7, 6
Suppose 8 = 4*j - 0*j. Let a be -2*((-15)/3 - -4). Solve 7*l - 3*l**a + j*l - 7*l**3 + 6*l**4 - 2*l**3 + 1 - 4 = 0 for l.
-1, 1/2, 1
Let -4/9*j - 2/9*j**2 + 2/9*j**3 + 0 = 0. What is j?
-1, 0, 2
Let n(s) = -23*s**3 + 30*s**2 - 65*s + 41. Let o(c) = -4*c**3 + 5*c**2 - 11*c + 7. Let g(d) = -6*n(d) + 34*o(d). Factor g(j).
2*(j - 2)**2*(j - 1)
Let t be ((-135)/(-60))/((-6)/(-4)). Let s be -3*(-2 + (-4)/(-3)). Find q such that 3/2*q + 1/2 + t*q**s + 1/2*q**3 = 0.
-1
Let d(p) = -38*p**3 + 26*p**2 + 12*p. Let a(w) be the first derivative of -17/3*w**3 - 4*w**2 - 2 + 25/4*w**4 + 0*w. Let r(n) = -8*a(n) - 5*d(n). Factor r(x).
-2*x*(x - 1)*(5*x + 2)
Let w(c) be the third derivative of -c**5/180 + c**4/24 - c**3/9 - 7*c**2. Factor w(r).
-(r - 2)*(r - 1)/3
Let s(r) be the second derivative of -2*r + 1/60*r**5 + 0 + 0*r**3 - r**2 + 1/36*r**4. Let n(f) be the first derivative of s(f). Factor n(i).
i*(3*i + 2)/3
Let u(c) be the first derivative of c**6/11 + 6*c**5/11 + 27*c**4/22 + 14*c**3/11 + 6*c**2/11 - 37. Determine d so that u(d) = 0.
-2, -1, 0
Let h = -9699675 + 10747240739/1108. Let y = h + -2/277. Factor y*w**2 + 0*w - 3/4.
3*(w - 1)*(w + 1)/4
Let k = 9 + -6. Let x be (-16 - -19)*(-2)/(-3). Suppose -1/3*z**4 + 0*z - 1/3*z**k + 0 + 0*z**x = 0. What is z?
-1, 0
Solve -1/4*r + 0 + 3/8*r**2 - 9/2*r**4 + 35/8*r**3 = 0.
-1/4, 0, 2/9, 1
Let j = -15 - -27. Suppose 0 = -2*f + 6*f - j. Factor -3/4*a**f + 0 - 5/4*a**2 - 1/2*a.
-a*(a + 1)*(3*a + 2)/4
Let m be 3/(-4) - (-3)/(-12). Let l be m/(-5) + 9/(-45). Let 0*k + l + 2/7*k**2 = 0. Calculate k.
0
Factor 0 + 0*c - 4/9*c**3 + 2/9*c**2 + 2/9*c**4.
2*c**2*(c - 1)**2/9
Let q(b) be the third derivative of b**7/70 + b**6/40 - 3*b**5/20 - b**4/8 + b**3 + 9*b**2. Factor q(z).
3*(z - 1)**2*(z + 1)*(z + 2)
Let z(i) be the third derivative of -2*i**2 + 1/210*i**7 + 1/60*i**6 - 1/24*i**4 + 0*i + 0 - 1/30*i**5 + 1/6*i**3 - 1/336*i**8. Find x, given that z(x) = 0.
-1, 1
Let t(l) = 5*l**3 + 3*l**2 + l + 2. Let a be t(-2). Let d be ((-2)/(-5))/(a/(-20)). Factor d*o + 0 - 2/7*o**3 + 0*o**2.
-2*o*(o - 1)*(o + 1)/7
Let s(l) be the first derivative of l**3 - 6*l**2 + 12*l - 5. Factor s(d).
3*(d - 2)**2
Let n(m) = m**4 - 2*m**2 + 10*m + 2. Let x(g) = g**3 + g**2 + g + 1. Suppose 2 = -h + 3. Let f(o) = h*n(o) - 2*x(o). Let f(k) = 0. Calculate k.
-2, 0, 2
Let n be (24/(-20))/(6/(-20)). Suppose j - n = -j. Factor s**j + 4*s**4 - s**4 - 4*s**4.
-s**2*(s - 1)*(s + 1)
Let g(r) be the third derivative of -2*r**7/105 + r**6/30 + r**5/15 - r**4/6 - 21*r**2. Factor g(f).
-4*f*(f - 1)**2*(f + 1)
Let g(v) be the second derivative of v**5/15 - 5*v**4/9 + 2*v**3/3 + 6*v**2 - 12*v. Factor g(i).
4*(i - 3)**2*(i + 1)/3
Suppose v = 5 - 2. Factor a**4 + 3*a**2 + a**5 - 7*a**3 + a**3 + a**v + 0*a**5.
a**2*(a - 1)**2*(a + 3)
Let j(m) be the third derivative of m**7/1260 - m**5/180 + m**3/3 - 2*m**2. Let x(h) be the first derivative of j(h). Solve x(d) = 0.
-1, 0, 1
Let s = 1121 + -12323/11. Suppose 0 - 2/11*t**2 +