 1. Let z(w) = 4*i(w) - y(w). Factor z(h).
-3*(h - 2)*(h - 1)**2
Let o(m) be the third derivative of m**7/15120 - m**5/180 - m**4/6 + 2*m**2. Let p(s) be the second derivative of o(s). Factor p(f).
(f - 2)*(f + 2)/6
Let b(t) be the first derivative of -2*t**5/25 + t**4/20 + t**3/3 + t**2/5 + 8. Factor b(w).
-w*(w - 2)*(w + 1)*(2*w + 1)/5
Suppose -z + 4*z - 6 = 0. Suppose 0 = 4*s - 4*y + 9 - 1, -12 = -2*s - z*y. Suppose s*l**4 + 10/3*l**3 - 4/3 - 2/3*l**2 - 10/3*l = 0. Calculate l.
-1, -2/3, 1
Let m(c) be the first derivative of 2*c**5 - 17*c**4/2 + 14*c**3 - 11*c**2 + 4*c - 4. Find o such that m(o) = 0.
2/5, 1
Suppose 0 = 4*r - 0*r - 3*u - 1, -u = 2*r + 7. Let o be (r/18)/(6/(-27)). Suppose 1/4*s + o - 1/4*s**2 = 0. Calculate s.
-1, 2
Suppose c = 2*c - 3. Let -o**4 + 9*o**3 + 3*o**2 + 4*o**4 - c*o**3 = 0. Calculate o.
-1, 0
Let 0*z**2 + 3/4*z**3 + 0 - 3/4*z = 0. What is z?
-1, 0, 1
Let w(l) be the third derivative of l**5/75 - 2*l**4/15 - 10*l**2. Factor w(c).
4*c*(c - 4)/5
Suppose -v + 14 = 3*a, 4*v + a - 16 = -a. Let h be (-35)/(-21) - v/(-6). Factor -1/3*w + 1/3*w**h - 2/3.
(w - 2)*(w + 1)/3
Let d(y) be the third derivative of y**7/4200 - y**6/600 - y**3 + 8*y**2. Let x(r) be the first derivative of d(r). What is n in x(n) = 0?
0, 3
Let d = -142/9 - -746/45. Factor -2/5*x**2 - 2/5 - d*x.
-2*(x + 1)**2/5
Let a be (-15)/(-7) - 3/21. Let o = a - 2. Factor o*j + 0 + 1/2*j**3 - 1/2*j**2.
j**2*(j - 1)/2
Let v(w) = -6*w**5 - 14*w**4 - 16*w**3 - 2*w + 2. Let c(h) = 7*h**5 + 13*h**4 + 16*h**3 + 3*h - 3. Let d(p) = 2*c(p) + 3*v(p). Find t, given that d(t) = 0.
-2, 0
Let s(p) be the third derivative of p**10/302400 - p**8/40320 + p**5/20 - p**2. Let n(f) be the third derivative of s(f). Find q such that n(q) = 0.
-1, 0, 1
Let z(m) be the first derivative of 1/14*m**4 - 8/7*m - 10 + 0*m**2 + 2/7*m**3. Factor z(u).
2*(u - 1)*(u + 2)**2/7
Let t(d) be the third derivative of d**5/30 + d**4/24 + 3*d**2. Let f be t(-3). Factor -f*p - 5*p**2 - 1 + 17*p + 4*p**2.
-(p - 1)**2
Let o(g) be the first derivative of 3*g**5/5 + 9*g**4/2 + 9*g**3 - 6. Factor o(u).
3*u**2*(u + 3)**2
Let w be ((-1)/2)/(4 + -6 + -238). Let m(l) be the third derivative of 0*l**3 + w*l**6 + 1/240*l**5 - 1/96*l**4 - 3*l**2 - 1/840*l**7 + 0*l + 0. Factor m(a).
-a*(a - 1)**2*(a + 1)/4
Let l be 3 - 6/(-4)*(2 + -4). Let v(s) be the third derivative of 2/75*s**5 + 1/525*s**7 + 2*s**2 + 0 + 0*s**3 + l*s**4 + 0*s + 1/75*s**6. Factor v(z).
2*z**2*(z + 2)**2/5
Let z(o) be the first derivative of -5*o**4/8 + 5*o**3/4 - 5*o**2/8 - 2. Factor z(m).
-5*m*(m - 1)*(2*m - 1)/4
Let c = 568/1345 + -6/269. Determine h so that -c*h**3 + 0*h**2 + 0 + 0*h = 0.
0
Let b = 22/7 + -37/14. Find k, given that 0 + 1/4*k**4 + b*k**3 - 1/2*k - 1/4*k**2 = 0.
-2, -1, 0, 1
Suppose -4*a = -a - 0*a. Factor -1/3*x**4 + 0 + 1/3*x**2 + a*x**3 + 0*x.
-x**2*(x - 1)*(x + 1)/3
Let s be (-8)/(-5) - (132/30)/(-11). Find j such that -j**3 + 5/4*j**s - 1/2 + 7/4*j = 0.
-1, 1/4, 2
Suppose 2/13*x**4 - 2/13*x**2 - 2/13*x**3 + 2/13*x + 0 = 0. What is x?
-1, 0, 1
Suppose -y = -0 + 2. Let s(v) = -4*v**3 - v**2 - 4*v. Let j(u) = -3*u**3 - 3*u. Let k(l) = y*s(l) + 3*j(l). Find x, given that k(x) = 0.
0, 1
Let w(b) be the first derivative of -1/24*b**3 + 2 + 0*b**2 - 1/16*b**4 + 1/20*b**5 - 2*b. Let j(z) be the first derivative of w(z). Let j(g) = 0. What is g?
-1/4, 0, 1
Let o(v) be the second derivative of 0 - 7/360*v**6 + 0*v**4 - 1/3*v**3 + 0*v**2 + 2*v + 1/60*v**5. Let t(r) be the second derivative of o(r). Factor t(k).
-k*(7*k - 2)
Let a be (-2)/23 - 212/(-322). Let -10/7*l**2 - 6/7*l**3 + a*l + 0 = 0. What is l?
-2, 0, 1/3
Suppose -16 = -2*r + 3*d, r - 2*d - 10 = -0*r. Factor 4*j**5 + 2*j**4 - j**2 - 2*j**3 + 2*j**2 - j**r.
2*j**3*(j + 1)*(2*j - 1)
Let y be (-7)/(-11)*-3 + 2. Let j = 41/33 + y. Suppose 2/3*g - 2/3*g**5 + 0 + 4/3*g**2 - j*g**4 + 0*g**3 = 0. What is g?
-1, 0, 1
Let q be (-624)/(-21) - 4/(-14). Let a be (-4)/(-8) + q/4. Suppose 5 - 10*l + 1 - a*l**4 - 4 + 6*l**2 + 10*l**3 = 0. What is l?
-1, 1/4, 1
Let h = -94 - -97. Determine r so that -1/4*r**h - 1/4*r - 1/2*r**2 + 0 = 0.
-1, 0
Factor 5/2*x**3 + 0 + 2*x + 8*x**2 - 25/2*x**4.
-x*(x - 1)*(5*x + 2)**2/2
Let y(r) be the third derivative of -r**5/15 - r**4/3 - 5*r**2. Suppose y(j) = 0. Calculate j.
-2, 0
Let z(i) = i**2 - 18*i + 65. Let a be z(13). What is u in a + 0*u - 1/3*u**4 - 2/3*u**2 - u**3 = 0?
-2, -1, 0
Let z be 1 + 75/(-10) + 7. Find o such that 2*o + z*o**2 + 2 = 0.
-2
Let f(b) = b**2 - 5*b - 3. Let h be f(7). Let c = h + -7. Factor 0 + 2*y**4 + 1 - 5 + 6 - c*y**2.
2*(y - 1)**2*(y + 1)**2
Let z(g) be the third derivative of g**6/20 + g**5/20 - g**4 - 2*g**3 + 8*g**2. Solve z(j) = 0 for j.
-2, -1/2, 2
Let u(q) be the second derivative of -2*q**6/15 - 3*q**5 - 74*q**4/3 - 88*q**3 - 144*q**2 + 3*q - 4. Factor u(x).
-4*(x + 1)*(x + 2)*(x + 6)**2
Let z be -2 + -3*155/(-225). Let w(a) be the second derivative of -a + 4/3*a**3 + 2/5*a**5 + z*a**6 + a**2 + a**4 + 0. Let w(q) = 0. Calculate q.
-1
Let l(m) be the first derivative of 4*m**3 - 27/2*m**2 + 5 + 6*m. Find f, given that l(f) = 0.
1/4, 2
Let d(n) be the first derivative of 1/5*n**5 - n + 1/2*n**4 + 0*n**3 - n**2 + 2. Find b, given that d(b) = 0.
-1, 1
Let b(q) be the third derivative of 0*q**4 - 1/525*q**7 + 0 + 0*q**3 - q**2 + 0*q + 1/300*q**6 + 0*q**5. What is z in b(z) = 0?
0, 1
Let f(w) = -9*w**3 - 15*w**2 + 9*w + 15. Let z(t) = 8*t**3 + 14*t**2 - 8*t - 14. Let v(o) = -6*f(o) - 7*z(o). Factor v(r).
-2*(r - 1)*(r + 1)*(r + 4)
Let r(f) be the third derivative of 0 - 1/30*f**4 + 0*f**3 - f**2 + 0*f - 1/50*f**5. Factor r(i).
-2*i*(3*i + 2)/5
Factor 1/5*b + 1 - b**2 - 1/5*b**3.
-(b - 1)*(b + 1)*(b + 5)/5
Let a(b) be the second derivative of -b**7/2100 + b**6/900 - b**3/2 + 2*b. Let h(c) be the second derivative of a(c). Factor h(n).
-2*n**2*(n - 1)/5
Let s(l) be the first derivative of -2*l**3/27 - 4*l**2/9 - 2*l/3 - 2. Factor s(i).
-2*(i + 1)*(i + 3)/9
Let j(i) be the third derivative of i**6/720 + i**5/120 + i**4/48 + i**3/36 - 13*i**2. Factor j(u).
(u + 1)**3/6
Factor 12/7*d**3 + 0 + 15/7*d**5 + 0*d + 0*d**2 + 36/7*d**4.
3*d**3*(d + 2)*(5*d + 2)/7
Factor -2*k**2 - 1 - 5/2*k - 1/2*k**3.
-(k + 1)**2*(k + 2)/2
Let v(h) = 3*h**4 - 3. Let r(k) = 6*k**4 + k**3 - k**2 - k - 5. Let d(c) = -3*r(c) + 5*v(c). Determine s so that d(s) = 0.
-1, 0, 1
Suppose 0 = -4*d + 7*d. Suppose 4*j**2 + d*j**2 - 5*j**2 + 12*j - 12 - 2*j**2 = 0. Calculate j.
2
Let n(r) be the third derivative of -r**6/360 + r**5/180 + r**4/72 - r**3/18 + 5*r**2. Find k such that n(k) = 0.
-1, 1
Let o be ((-2)/(-18))/(16/24). Let a(h) be the first derivative of -1/4*h**2 + 1/2*h - o*h**3 + 1/8*h**4 - 2. Factor a(v).
(v - 1)**2*(v + 1)/2
Suppose -4*u + 6*u = 6. Let x(r) be the second derivative of 7/30*r**4 + r + 0 + 4/5*r**u - 4/5*r**2. Factor x(y).
2*(y + 2)*(7*y - 2)/5
Let c be 2 + -3 + 2 + 3. Let m be (-3)/c*8/(-12). Factor 0 + 1/2*i + m*i**3 + i**2.
i*(i + 1)**2/2
Let v = -331892 - -99899671/301. Let p = v - 1/43. Factor 4/7*w**3 - p*w - 2/7*w**4 + 2/7 + 0*w**2.
-2*(w - 1)**3*(w + 1)/7
Let h(c) be the first derivative of -2/3*c**3 + 4*c + 3 - c**2. Factor h(l).
-2*(l - 1)*(l + 2)
Let r = -362 + 2538/7. Find h, given that -r*h - 6/7*h**2 + 6/7*h**4 + 4/7*h**3 + 0 = 0.
-1, -2/3, 0, 1
Let o(x) be the third derivative of -x**8/84 + 2*x**7/105 + x**6/15 - 2*x**5/15 - x**4/6 + 2*x**3/3 - 13*x**2. Factor o(r).
-4*(r - 1)**3*(r + 1)**2
Let q(l) be the second derivative of l**10/15120 - l**9/3780 + l**7/630 - l**6/360 - l**4/12 - 2*l. Let u(g) be the third derivative of q(g). Solve u(t) = 0.
-1, 0, 1
Let o(k) = 3*k**2 + 9*k + 3. Let s be o(-3). Factor -3/2*l**4 - 1/2*l**5 - l**s + l**2 + 1/2 + 3/2*l.
-(l - 1)*(l + 1)**4/2
Let m(s) be the first derivative of -25*s**6/6 - 4*s**5 + 21*s**4/4 + 20*s**3/3 + 2*s**2 - 11. Find l, given that m(l) = 0.
-1, -2/5, 0, 1
Let f(j) be the third derivative of 0*j**3 - 1/12*j**4 + 0*j - 3/20*j**5 - 4*j**2 - 7/120*j**6 + 0. Factor f(r).
-r*(r + 1)*(7*r + 2)
Factor -2*w + 2*w**2 + 0*w**2 - 2*w**2 + 4 - 2*w**2.
-2*(w - 1)*(w + 2)
Suppose -3*i**4 + 85*i**2 - 30*i**3 + 6*i**4 - 10*i**2 = 0. What is i?
0, 5
Let w(m) be the third derivative of -m**7/525 + m**6/75 - m**5/25 + m**4/15 - m**3/15 - 29*m**2. Factor w(i).
-2*(i - 1)**4/5
D