. Let w(x) = 2*x**3 - 4*x**2 + 2*x - 8. Let s(a) = -w(a) + 8*z(a). Factor s(t).
-2*t*(t + 1)**2
Let r(f) be the third derivative of -5*f**8/504 + 4*f**7/105 - f**6/45 - 33*f**2. What is i in r(i) = 0?
0, 2/5, 2
Let a = -19 - -21. Let i(d) be the first derivative of -1/4*d**4 - 1 + 1/6*d**a - 2/9*d**3 + 0*d. Factor i(x).
-x*(x + 1)*(3*x - 1)/3
Let p be 70/6 + (-3)/(-9). Factor -2 - p*r**2 + 1 + 15*r**2 - 2.
3*(r - 1)*(r + 1)
Let w(u) be the third derivative of u**6/24 - u**5/20 - 3*u**4/4 - 5*u**3/3 + 6*u**2. Let m(k) = -k - 1. Let n(i) = -6*m(i) + w(i). Factor n(v).
(v - 2)*(v + 1)*(5*v + 2)
Suppose c = 5*c - 20. Find v, given that 0*v + 3*v**3 - 9*v**4 - 12/5 + 9*v**2 - 27/5*v**c = 0.
-1, 2/3
Let r = 0 + 2. Suppose -4*z - 4 - r = -v, -z - 9 = -4*v. Let -l**4 - 2 + 0*l**3 + 1 + v*l**2 + 0*l**3 = 0. What is l?
-1, 1
What is b in -35*b + 41*b - 4*b**3 + 2*b**3 + 4*b**2 = 0?
-1, 0, 3
Let y(v) = -3*v - 10. Let c be y(-4). Factor 0 + f**c + 0*f**3 - 2/3*f - 1/3*f**4.
-f*(f - 1)**2*(f + 2)/3
Let s = -1649/168 + 69/7. Let d(r) be the third derivative of 2*r**2 + 0 - 3/20*r**5 - 2/15*r**3 - s*r**6 + 0*r - 1/5*r**4. Suppose d(o) = 0. Calculate o.
-1, -2/5
Suppose 0 = 3*j + 5*r + 17, -13 = 2*j + j + 4*r. Factor 0*w**2 - j + 4*w - 2*w**2 - 1.
-2*(w - 1)**2
Let v be (-2)/10 - (-4)/20. Factor 14/3*w**3 + 8*w**2 + v - 8/3*w.
2*w*(w + 2)*(7*w - 2)/3
Let w = -10 - -15. Let c be (-11)/(-55) - (-1)/w. Determine k so that 8/5 - 8/5*k + c*k**2 = 0.
2
Let l(w) = w**2 + w - 1. Let j be l(-2). Suppose j + 8 = 3*s. What is c in s*c**5 - c + 7*c**4 - 4*c**2 - 3*c**4 - c**5 - c = 0?
-1, 0, 1
Let p be -1 + -2 + (-86)/(-10) - 4. Factor -8/5*u**3 - 8/5 + 2/5*u**4 + 6/5*u**2 + p*u.
2*(u - 2)**2*(u - 1)*(u + 1)/5
Let j = 10 - 6. Let h(c) = -17*c**3 + 7*c**2 - 18*c - 5. Let d(s) = 6*s**3 - 2*s**2 + 6*s + 2. Let x(z) = j*h(z) + 11*d(z). Factor x(p).
-2*(p - 1)**3
Suppose -5 = 4*i - 13. Suppose 4*m + 13 = -4*x + 1, m - 12 = i*x. Factor -1/5*b**3 + 1/5 - 1/5*b**m + 1/5*b.
-(b - 1)*(b + 1)**2/5
Let i be 102/24 + 2/(-8). Let t be i/14 - (-48)/28. Factor -2 - u**5 + u**4 + t.
-u**4*(u - 1)
Suppose -2/15*g + 2/15*g**3 - 2/15 + 2/15*g**2 = 0. Calculate g.
-1, 1
Let p(c) be the third derivative of 1/120*c**6 + 1/60*c**5 - 1/6*c**3 - 1/24*c**4 + 0 + 0*c + 7*c**2. Let p(a) = 0. Calculate a.
-1, 1
Solve 14*a + 9*a + a**3 + 4*a**2 - 18*a + 2 = 0 for a.
-2, -1
Let r(c) = -2*c**4 + 1 + c**4 + c**2 + c + 0*c**2. Let o(a) = 4*a**4 + 2*a**3 - 6*a**2 - 5*a - 5. Let k(q) = o(q) + 5*r(q). Factor k(j).
-j**2*(j - 1)**2
Let b(w) = w**3 + 9*w**2 - w - 7. Let g be b(-9). Let u(n) be the second derivative of 1/27*n**3 + 0 + n + 1/9*n**g - 1/54*n**4 - 1/90*n**5. Factor u(z).
-2*(z - 1)*(z + 1)**2/9
Let y(g) be the third derivative of g**10/90720 - g**9/45360 - g**4/8 - 3*g**2. Let q(i) be the second derivative of y(i). Factor q(p).
p**4*(p - 1)/3
Determine k so that -413 - 3*k**2 + 407 - 30*k**3 + 15*k + 6*k = 0.
-1, 2/5, 1/2
Let a(l) be the first derivative of -2*l**6/9 + 4*l**5/5 + l**4/3 - 44*l**3/9 + 8*l**2 - 16*l/3 - 13. Solve a(n) = 0 for n.
-2, 1, 2
Let x(n) be the second derivative of n**6/5 + 3*n**5/4 + n**4/4 - n**3 - 11*n. Find a, given that x(a) = 0.
-2, -1, 0, 1/2
Let v(s) = -15*s**4 - 48*s**3 - 61*s**2 - 22*s - 4. Let l(g) = -29*g**4 - 95*g**3 - 122*g**2 - 45*g - 8. Let i(y) = -6*l(y) + 11*v(y). Factor i(n).
(n + 2)**2*(3*n + 1)**2
Suppose -y + 10 = -4*i - 10, 4*y - 36 = 5*i. Factor 5*a**y + 2*a**3 - 2*a**2 - 3*a**4 + 0*a**2 - 2*a.
2*a*(a - 1)*(a + 1)**2
Let q(z) be the first derivative of -z**4/24 - 4*z**3/9 - 7*z**2/12 - 46. Find i, given that q(i) = 0.
-7, -1, 0
Let s(h) be the second derivative of 3*h**5/20 - h**4/4 - 5*h. Factor s(n).
3*n**2*(n - 1)
Let v be ((-7197)/(-900) + -8)/(1/(-2)). Let r(o) be the second derivative of 0*o**3 - o + 0*o**2 + 0 + v*o**6 + 0*o**5 + 0*o**4. Factor r(b).
b**4/5
Let n(p) = 10*p**3 + 87*p**2 + 153*p. Let q(m) = 5*m**3 + 44*m**2 + 76*m. Let b(w) = 4*n(w) - 7*q(w). Factor b(u).
5*u*(u + 4)**2
Let f be ((-6)/(-20))/((-396)/(-11)). Let h(j) be the third derivative of 0*j**3 - 1/48*j**4 + f*j**5 + 0 + 0*j - 2*j**2. Solve h(k) = 0.
0, 1
Suppose -t - 7*t + 16 = 0. Let v(d) be the first derivative of -78/25*d**5 - 6/5*d**2 + 6/5*d**6 + 4/5*d**3 + 2*d**4 + 2/5*d + t. Solve v(b) = 0 for b.
-1/2, 1/3, 1
Let k(q) = q**2. Let h(b) = -7*b**2 - 3*b - 2. Let v(l) = -h(l) - 6*k(l). Let u be v(-3). Solve 0*a + 1/4*a**u - 1/4 = 0 for a.
-1, 1
Let y be ((-9)/12)/((-1)/(-16)*-6). Factor 1/3*z**y - 4/3*z + 4/3.
(z - 2)**2/3
Determine n, given that 12/7*n**2 - 3/7*n**3 - 12/7*n + 0 = 0.
0, 2
Let r(w) be the third derivative of -2*w**10/315 - w**9/105 - 3*w**8/560 - w**7/840 + w**4/8 - 6*w**2. Let i(q) be the second derivative of r(q). Factor i(y).
-3*y**2*(4*y + 1)**3
Let f(c) be the second derivative of -c**8/30240 - c**7/11340 - c**4/3 + c. Let x(w) be the third derivative of f(w). Factor x(l).
-2*l**2*(l + 1)/9
Suppose -5*n - 6 + 26 = 0. Factor -4*o**3 + 3*o**3 - 4*o**2 - 3*o**4 + o + o**2 + 4*o**n + 2.
(o - 2)*(o - 1)*(o + 1)**2
Let j be 9/(-6)*2*3/(-18). Let q(m) be the first derivative of 0*m - 4 + j*m**3 + 1/2*m**4 - 1/4*m**2. Suppose q(h) = 0. Calculate h.
-1, 0, 1/4
Let i(r) = -r**5 + r**3 + r**2 + 1. Let d(h) = 16*h**5 + 6*h**4 - 12*h**3 - 20*h**2 - 4*h - 14. Let w(p) = 2*d(p) + 28*i(p). Solve w(z) = 0.
-2, -1, 0, 1
Let w(m) be the first derivative of 2*m**4 + 14*m**3/13 + 2*m**2/13 + 9. Find y such that w(y) = 0.
-1/4, -2/13, 0
Let a(z) be the first derivative of z**6/12 - 3*z**5/10 - z**4/8 + 7*z**3/6 - 2*z + 6. Find n, given that a(n) = 0.
-1, 1, 2
Suppose 0 = -3*s + 4*z + 7, -2*z = -3*s + 4 + 1. Factor -d**2 - 8/3*d + s.
-(d + 3)*(3*d - 1)/3
Factor 0 + 2/5*i**2 - 2/5*i**4 - 2/5*i**3 + 2/5*i.
-2*i*(i - 1)*(i + 1)**2/5
Let z(d) be the second derivative of 3*d**5/20 + d**4/4 - 5*d**3/2 + 9*d**2/2 - d + 6. Suppose z(i) = 0. What is i?
-3, 1
Let 3*j + 7*j - 10*j + j**2 + j = 0. Calculate j.
-1, 0
Let z(w) be the first derivative of -w**6/360 + w**5/60 - w**4/24 - 4*w**3/3 - 3. Let j(c) be the third derivative of z(c). Factor j(b).
-(b - 1)**2
Let r(d) be the first derivative of -33/4*d**4 + 25/2*d**6 + 0*d - 12*d**3 + 6*d**2 + 4 + 18*d**5. Solve r(g) = 0.
-1, 0, 2/5
Let u(z) be the third derivative of -1/32*z**4 + 0 + 1/24*z**3 + 1/160*z**6 + 0*z + 2*z**2 - 1/240*z**5. What is r in u(r) = 0?
-1, 1/3, 1
Let z(m) = -8*m**2 + 4*m - 9. Let n(i) = 7*i**2 - 3*i + 8. Suppose 6*f - 2*f = -28. Let g(q) = f*n(q) - 6*z(q). Factor g(k).
-(k + 1)*(k + 2)
Suppose 1 = -2*y + y - d, 5*d + 5 = y. Suppose s + 6 = 4*s. Factor 0 + y + s*q**3.
2*q**3
Suppose r = -2*r + 21. Let a = -7 + r. Factor 4/3*k**2 - 1/3*k + a.
k*(4*k - 1)/3
Let i(j) be the third derivative of -j**5/180 + 2*j**3/9 + 2*j**2. Factor i(u).
-(u - 2)*(u + 2)/3
Let n(r) be the third derivative of 1/27*r**3 + 0*r - r**2 - 1/540*r**6 + 1/90*r**5 - 1/36*r**4 + 0. Let n(i) = 0. Calculate i.
1
Let v be 546/84 - 6/4. Factor -b**3 + 0 + 1/2*b**v - 1/2*b**4 + 0*b + 0*b**2.
b**3*(b - 2)*(b + 1)/2
Let s(u) be the third derivative of -u**8/112 + u**7/70 + u**6/40 - u**5/20 + 13*u**2. Factor s(x).
-3*x**2*(x - 1)**2*(x + 1)
Let a(v) = 15*v**4 - 177*v**3 + 48*v**2 + 144*v - 96. Let c(b) = b**4 - 11*b**3 + 3*b**2 + 9*b - 6. Let y(u) = 2*a(u) - 33*c(u). Suppose y(f) = 0. What is f?
-1, 1, 2
Suppose 3*x + 5*t - 12 = 14, 0 = -5*t + 20. Suppose -10 = -x*j - 3*j. Factor z**3 - 2*z**2 + 5*z + j + z**2 + 5*z**2.
(z + 1)**2*(z + 2)
Let i be ((-44)/99)/((-28)/18). Suppose -2*z = -5*m - 4 + 24, -4*m + 4*z + 28 = 0. Suppose 4/7*q**m - i*q**3 - 2/7*q + 0 = 0. What is q?
0, 1
Let g(v) be the first derivative of -v**5 - 5*v**4/4 + 53. Let g(a) = 0. What is a?
-1, 0
Let q be ((-36)/4)/((-6)/10). Let l be (-3)/1 - (-54)/q. Suppose 0 + 0*o - 3/5*o**4 - 2/5*o**5 + 2/5*o**2 + l*o**3 = 0. What is o?
-2, -1/2, 0, 1
Let a = -1/25 + 28/75. Let n(h) be the second derivative of 1/12*h**4 - h + a*h**2 - 5/18*h**3 + 0. Factor n(k).
(k - 1)*(3*k - 2)/3
Let x(t) = -t**3 + 9*t**2 + 6*t. Let n(d) = -10*d**2 - 5*d. Let o(v) = 4*n(v) + 5*x(v). Find k, given that o(k) = 0.
-1, 0, 2
Let f(d) = 8*d**3 - 11*d**2 + 8*d - 1. Let a(b) = -9*b**3 + 11*b**2 - 8*b + 2. Let j(o) = 5*a(o) + 6*f(o). Suppose j(p) = 0. What is p?
-1/3, 2
Let o(h) be the third derivative of 