t**q. Factor v(b).
-2*(b + 1)*(4*b + 1)**2/9
Let t = -21 - -21. Factor 0 + t*y + 2/7*y**3 - 2/7*y**2.
2*y**2*(y - 1)/7
Let p = -520 + 1055/2. Factor 3 + 6*m**2 + p*m + 3/2*m**3.
3*(m + 1)**2*(m + 2)/2
Let u = 11 + -7. Factor 52*a**3 + u*a**5 - 28*a**4 + 16*a - 48*a**2 + 2*a**4 + 2*a**4.
4*a*(a - 2)**2*(a - 1)**2
Let k = -4 - -6. Solve 2*t**2 - k + 0 + 0 = 0 for t.
-1, 1
Let z = -8 + 13. Factor -1 + 5 - 3*c**2 + 3*c**2 + 8*c + z*c**2 + c**3.
(c + 1)*(c + 2)**2
Let 3*k**3 + 12*k + 18*k**3 - 9*k**4 - 66*k**2 - k**5 - 5*k**5 + 24*k**4 + 24 = 0. Calculate k.
-2, -1/2, 1, 2
Let s be 0/(-1 - -4 - 4). Let a(q) be the third derivative of -2/21*q**3 + s - 1/28*q**4 + 0*q - 1/210*q**5 + 3*q**2. Factor a(r).
-2*(r + 1)*(r + 2)/7
Let o(s) be the third derivative of 4*s**2 + 0*s**4 + 0 - 3/70*s**7 - 1/60*s**5 + 0*s + 1/20*s**6 + 0*s**3. Factor o(q).
-q**2*(3*q - 1)**2
Let l be 4/(-34) + 319/1122. Factor 0*a + 0*a**2 + 0*a**4 + l*a**3 + 0 - 1/6*a**5.
-a**3*(a - 1)*(a + 1)/6
Let o(p) = p**3 - 20*p**2 + 90*p + 17. Let m be o(13). What is x in -16/3*x - 8*x**2 - 4*x**3 - 2/3*x**m + 0 = 0?
-2, 0
Let f be (-21)/(-180) - (-1)/12. Determine g so that 2/5*g**2 + 0 + 1/5*g + f*g**3 = 0.
-1, 0
Let o(y) be the second derivative of -y**6/150 - y**5/20 - 3*y**4/20 - 7*y**3/30 - y**2/5 + 11*y. Suppose o(q) = 0. What is q?
-2, -1
Let f(l) = -3*l + 3. Let k(v) = v**3 - v**2 + 8*v - 8. Let p(x) = 8*f(x) + 3*k(x). Factor p(d).
3*d**2*(d - 1)
Let k be 8 + -5 - (-14)/(-6). Let r(q) be the first derivative of -k*q + 2 - 2/9*q**3 + 2/3*q**2. Let r(o) = 0. What is o?
1
Suppose 2*q + 5*c = -0*q + 1, -3*c = -3. Let m be 3/q*(-1 - 1). Let 3*v**4 + 2*v**5 + 3*v**4 + 3*v**m + 5*v**5 - 4*v**5 = 0. What is v?
-1, 0
Let n = -492 - -12302/25. Let m(h) be the first derivative of -n*h**5 + 0*h + 1/5*h**2 + 2/15*h**3 + 2 - 1/10*h**4. Factor m(a).
-2*a*(a - 1)*(a + 1)**2/5
Factor 4/5*k - 8/5*k**2 + 8/5 - 4/5*k**3.
-4*(k - 1)*(k + 1)*(k + 2)/5
Let x = -3/43 + 135/86. Let x*v**4 + 3/2*v**3 - 3/2*v - 3/2*v**2 + 0 = 0. What is v?
-1, 0, 1
Let t be 4/(1 + -4 + 2). Let q be (10 + t)/(15/2). Let 0*b**2 + 2/5*b**5 - q*b**3 + 0 + 0*b**4 + 2/5*b = 0. What is b?
-1, 0, 1
Let o(d) be the first derivative of 0*d + 1 - 1/2*d**3 - 1/8*d**4 - 1/2*d**2. Factor o(t).
-t*(t + 1)*(t + 2)/2
Factor -4*j - 11*j**3 - j**4 - 4*j**2 + 4*j**3 + 10*j + j**3 + 5.
-(j - 1)*(j + 1)**2*(j + 5)
Factor -4*x**4 + 25 - 33 + 2*x**4 - 24*x - 12*x**3 - 26*x**2.
-2*(x + 1)**2*(x + 2)**2
Let v(n) be the second derivative of n**4/36 + n**3/9 - n**2/2 - 22*n. Factor v(j).
(j - 1)*(j + 3)/3
Let w(j) = -j**2 + 7*j - 6. Let v be w(6). Factor 2*c**3 + v*c + 4*c**2 + 5*c - 2*c - c.
2*c*(c + 1)**2
Let x(v) be the third derivative of v**8/252 + 2*v**7/105 + v**6/45 - 2*v**5/45 - v**4/6 - 2*v**3/9 + 5*v**2. Determine i, given that x(i) = 0.
-1, 1
Let d be (2 + (-742)/297)*-6. Let y = d + -28/11. Factor -2/3*f**3 + y - 8/9*f**2 + 2/9*f.
-2*(f + 1)**2*(3*f - 2)/9
Factor 18*f**2 + 8/5 - 56/5*f.
2*(5*f - 2)*(9*f - 2)/5
Let g(r) be the first derivative of r**6/9 - 8*r**5/45 + r**4/18 + 17. Factor g(s).
2*s**3*(s - 1)*(3*s - 1)/9
Let u(p) be the first derivative of 1/2*p**2 - 2/3*p**3 + 2 - 1/4*p**4 + 2*p. Solve u(h) = 0 for h.
-2, -1, 1
Let x(u) be the first derivative of -u**6/2 + 3*u**5/5 - 1. Factor x(c).
-3*c**4*(c - 1)
Let s(k) be the third derivative of -5*k**6/48 + 11*k**5/24 + 7*k**4/6 + k**3 - 5*k**2. Factor s(z).
-(z - 3)*(5*z + 2)**2/2
Let b(w) be the third derivative of 0*w - 1/60*w**6 + 0*w**7 + 1/336*w**8 + 0*w**3 + 1/24*w**4 + 0 + 3*w**2 + 0*w**5. Factor b(n).
n*(n - 1)**2*(n + 1)**2
Let x(t) be the second derivative of t**4/6 + 2*t**3 + 9*t**2 + 6*t. Solve x(g) = 0.
-3
Suppose -82/7*f**4 + 0 + 8/7*f**3 + 8/7*f**2 - 6*f**5 + 0*f = 0. What is f?
-2, -2/7, 0, 1/3
Let i(y) be the second derivative of -1/48*y**4 + 0 + 1/42*y**7 + 0*y**2 + 1/16*y**5 + 3*y - 1/15*y**6 + 0*y**3. Let i(b) = 0. Calculate b.
0, 1/2, 1
Suppose 5*l + 4*x = 25, -5*l + 27 - 2 = 3*x. Let u(j) = 4*j**2 + 4*j - 3. Let q(w) = w**3 + 8*w**2 + 7*w - 5. Let o(t) = l*u(t) - 3*q(t). Factor o(b).
-b*(b + 1)*(3*b + 1)
Let c(p) be the first derivative of p**4/30 - p**2/5 + 5*p + 1. Let r(y) be the first derivative of c(y). Let r(f) = 0. What is f?
-1, 1
Let r(q) = 3*q**3 + 3*q**5 + 4*q**4 + 0*q + 3*q**2 + 5*q**4 + 3*q. Let m(t) = -t**4 - t**2 - t. Let k = 5 + -4. Let n(l) = k*r(l) + 3*m(l). Factor n(a).
3*a**3*(a + 1)**2
Factor -3*h**3 - 99*h**2 + 197*h**2 - 99*h**2 + 3*h - h**4 + 2.
-(h - 1)*(h + 1)**2*(h + 2)
Let o(q) be the second derivative of 0 + 0*q**2 + 1/18*q**4 + 2*q - 1/60*q**5 - 1/18*q**3. Find z such that o(z) = 0.
0, 1
Suppose 0*x - 4*i - 15 = -x, 6 = -x - 3*i. Factor -9*p**2 + x - 6*p - p - p + 2*p.
-3*(p + 1)*(3*p - 1)
Suppose -c = -3*c + 4. Find t, given that -t - c*t + t**4 - t**2 + 4*t + 0*t**2 - t**3 = 0.
-1, 0, 1
Let z(p) = 5*p**2 - 5*p + 9. Let s(d) = 9*d**2 - 11*d + 18. Let k(n) = 4*s(n) - 7*z(n). Let f(l) = l**2 - 8*l + 9. Let r(c) = -3*f(c) + 2*k(c). Factor r(j).
-(j - 3)**2
Let k = -46 + 51. Let s be 7 + (-4)/(20/k). Let 8/7*m + s*m**3 + 48/7*m**2 + 0 - 14*m**4 = 0. Calculate m.
-2/7, 0, 1
Let s(a) be the second derivative of -7/120*a**6 + 0*a**2 - a + 0 - 1/84*a**7 - 9/80*a**5 - 1/24*a**3 - 5/48*a**4. Factor s(c).
-c*(c + 1)**3*(2*c + 1)/4
Let x(o) = 3*o**3 - 6*o**2 + 9*o - 2. Let j be (5/2)/(5/10). Let d(c) = -6*c**3 + 11*c**2 - 19*c + 4. Let f(t) = j*x(t) + 2*d(t). Let f(g) = 0. What is g?
2/3, 1
Let o(a) be the third derivative of -a**9/7560 - a**8/3360 + a**7/1260 + a**6/360 - 7*a**4/24 - 6*a**2. Let v(u) be the second derivative of o(u). Factor v(n).
-2*n*(n - 1)*(n + 1)**2
Let q(t) be the second derivative of -t**2 + 2*t - 4/9*t**3 + 1/9*t**4 + 0 + 2/15*t**5 + 1/45*t**6. Factor q(j).
2*(j - 1)*(j + 1)**2*(j + 3)/3
Let r(q) be the second derivative of 5*q**6/3 - 3*q**5/2 - 3*q**4/2 - q**3/3 + 12*q. Factor r(b).
2*b*(b - 1)*(5*b + 1)**2
Factor -4/3*v**4 + 0 + 2/3*v + 4/3*v**2 + 0*v**3 - 2/3*v**5.
-2*v*(v - 1)*(v + 1)**3/3
Let r(a) be the second derivative of 3*a**5/20 + a**4/4 - a**3/2 - 3*a**2/2 + a. Suppose r(z) = 0. Calculate z.
-1, 1
Let k(a) = -a**2 - 7*a - 5. Let l be k(-5). Factor -3*c**3 - l*c + 4*c + 2*c**3 + 3*c**2 - c.
-c*(c - 2)*(c - 1)
Let l(u) = 13*u**2 - 6*u. Let m(y) = -66*y**2 + 30*y. Let q(v) = -16*l(v) - 3*m(v). Factor q(o).
-2*o*(5*o - 3)
Let u(h) = -h**3 - 5*h**2 + 6*h + 3. Let a be u(-6). Suppose a = y - 0. Factor -p - p + p + p**y.
p*(p - 1)*(p + 1)
Suppose -15 = 3*b + 4*j, 2*b - 2 = b + j. Let p be 3 + (-3)/(2 - b). What is q in 4*q**4 - 6*q**4 - 3*q**2 + 2*q**3 + 7*q**p = 0?
-1, 0, 2
Let p be (3*2/(-9))/(-2). Factor -1/3*k - p*k**2 + 2/3.
-(k - 1)*(k + 2)/3
Let r(t) be the first derivative of -t**5 - 15*t**4/4 - 5*t**3 - 5*t**2/2 - 64. Determine o, given that r(o) = 0.
-1, 0
Factor -4/5*i**3 + 2/5*i**4 + 0 + 4/5*i - 2/5*i**2.
2*i*(i - 2)*(i - 1)*(i + 1)/5
Let t be (3268/(-1084) + 3)/2. Let m = t - -1098/1897. Let m*l**3 - 2/7 + 6/7*l**4 - 6/7*l + 2/7*l**5 - 4/7*l**2 = 0. What is l?
-1, 1
Let 72/11*v - 16/11 + 28/11*v**2 - 54/11*v**4 - 114/11*v**3 = 0. Calculate v.
-2, -1, 2/9, 2/3
Let m(a) be the third derivative of -a**6/480 - a**5/80 - a**4/48 + a**2 + 14. Factor m(p).
-p*(p + 1)*(p + 2)/4
Let h(s) be the first derivative of -4/3*s**3 + 5 + 8*s**2 - 12*s. Find u such that h(u) = 0.
1, 3
Let z(g) be the first derivative of 1/9*g**2 - 2/9*g**3 + 0*g + 2. Factor z(t).
-2*t*(3*t - 1)/9
Let v(a) = a**5 - a**3 + a**2 - a + 1. Let b(p) = 5*p**5 - p**4 - p**3 + 11*p**2 - 10*p + 2. Let u(d) = -b(d) + 6*v(d). Solve u(r) = 0 for r.
-2, -1, 1, 2
Let l = 2155665/6549319 + 2/40679. Let r = l - 1/23. Factor r*h**3 - 2/7*h**2 + 0 - 2/7*h + 2/7*h**4.
2*h*(h - 1)*(h + 1)**2/7
Suppose 5*s + 2 = 3*d, -4*s + 3*s + 2*d - 6 = 0. Determine r so that -6*r**s - 2*r**4 - 2*r**3 + 10*r + 4 + 11*r**2 + r**2 = 0.
-1, 2
Let v(m) be the first derivative of -m**4/14 - 2*m**3/7 - 2*m**2/7 + 1. Suppose v(l) = 0. Calculate l.
-2, -1, 0
Let v(w) be the second derivative of -w**7/126 + w**6/30 - w**5/60 - w**4/12 + w**3/9 - 11*w. Find n such that v(n) = 0.
-1, 0, 1, 2
Let k(n) be the first derivative of 5*n**4 + 0*n**4 + 4*n + 12*n**2 - 4*n**4 + 4*n + 6*n**3 - 1. Factor k(a).
2*(a + 2)**2*(2*a + 1)
Let g(f) be the second derivative of 3*f**5/20 - 3*f**