
Let g(q) = -q + 1. Let z(p) = -2*p**3 - 8*p**2 + 2*p - 10. Let r(f) = -10*g(f) - z(f). Factor r(b).
2*b*(b + 2)**2
Determine q, given that 1/2*q + 3/4*q**2 + 0 + 1/4*q**3 = 0.
-2, -1, 0
Let n be (-16 + 17)/((-1)/19). Let o be ((-1)/11)/(n/266). Find t, given that 30/11*t**2 + 8/11*t**4 + 26/11*t**3 + 2/11 + o*t = 0.
-1, -1/4
Suppose 3*r = -2*r. Let x(w) be the third derivative of 1/180*w**5 + 0 + 0*w**4 - 1/630*w**7 + 0*w - w**2 + r*w**3 + 0*w**6. Factor x(m).
-m**2*(m - 1)*(m + 1)/3
Let c(b) = -5*b**2 - 119*b - 834. Let u(v) = v**2 + 24*v + 167. Let k(q) = -2*c(q) - 11*u(q). Suppose k(o) = 0. Calculate o.
-13
Let c(j) be the second derivative of j**4/4 + j**3 + 3*j**2/2 + 6*j. Factor c(l).
3*(l + 1)**2
Let q(i) be the first derivative of i**6/30 - i**5/5 + i**4/20 + 13*i**3/15 - i**2/5 - 8*i/5 + 13. Suppose q(g) = 0. Calculate g.
-1, 1, 2, 4
Let a(q) be the third derivative of -q**6/120 - q**5/30 + q**4/6 + 4*q**3/3 + 15*q**2. Solve a(z) = 0.
-2, 2
Let c(l) be the second derivative of l**7/56 + l**6/40 + l. Factor c(d).
3*d**4*(d + 1)/4
Let o(w) be the third derivative of 5*w**8/336 - w**7/14 + w**6/12 + w**5/6 - 5*w**4/8 + 5*w**3/6 + 6*w**2. What is u in o(u) = 0?
-1, 1
Let v = -528 + 531. Factor 2/15*x**v + 0*x - 2/15*x**2 + 0.
2*x**2*(x - 1)/15
Let s(o) be the third derivative of o**7/840 - o**6/120 + o**5/60 - o**3/3 + 4*o**2. Let u(q) be the first derivative of s(q). Factor u(y).
y*(y - 2)*(y - 1)
Let r(f) be the second derivative of -2*f**2 - 1/3*f**4 + 4/3*f**3 - 5*f + 0. Determine l so that r(l) = 0.
1
Let p(w) be the second derivative of w**5/30 + 4*w**4/9 + 17*w**3/9 + 10*w**2/3 - 72*w. Determine o so that p(o) = 0.
-5, -2, -1
Let v(p) = -10*p**5 + 2*p**4 + 7*p**2 + 10*p + 9. Let s(z) = -z**5 + z**2 + z + 1. Let b(j) = 18*s(j) - 2*v(j). Factor b(f).
2*f*(f - 1)**3*(f + 1)
Let u = 20/9 + -8/9. Factor 0 + 8/3*i**2 - 4*i**3 + u*i**4 + 0*i.
4*i**2*(i - 2)*(i - 1)/3
Let w = -1490/77 + 216/11. Suppose 0 + w*l - 5/7*l**2 = 0. Calculate l.
0, 2/5
Let p = 323 - 321. Factor 1/3*s**5 + 0*s - s**p - 1/3*s**3 + 0 + s**4.
s**2*(s - 1)*(s + 1)*(s + 3)/3
Suppose 8*f + 2 = 18. What is n in 0 - 21/2*n**3 + 90*n**5 + 33/2*n**f - 3*n - 66*n**4 = 0?
-1/2, 0, 1/3, 2/5, 1/2
Let o(c) be the third derivative of -c**8/26880 + c**7/2520 - c**6/720 + c**4/24 + c**2. Let t(y) be the second derivative of o(y). Factor t(i).
-i*(i - 2)**2/4
Let r = -901 - -2704/3. What is m in 1/3 - 1/3*m**2 + 1/3*m**3 - r*m = 0?
-1, 1
Let d(a) be the second derivative of -4*a - 1/35*a**5 + 0 + 0*a**4 + 1/105*a**6 + 0*a**2 + 0*a**3. Find t such that d(t) = 0.
0, 2
Let f(c) be the second derivative of -c**5/10 - c**4/6 + 5*c**3/3 - 3*c**2 + 6*c + 3. Suppose f(v) = 0. Calculate v.
-3, 1
Factor 38/3*f**2 - 14*f + 4/3.
2*(f - 1)*(19*f - 2)/3
Let z(b) = 3*b**2 - b. Let y be z(1). Let 2*w**4 + 4*w**2 + 0*w**y + 8*w**3 + 2*w**4 = 0. Calculate w.
-1, 0
Let x(z) be the first derivative of -3*z**4/14 + 2*z**3/3 - 8*z/7 - 5. Suppose x(r) = 0. Calculate r.
-2/3, 1, 2
Let p(s) = s**2 + s + 1. Let b(m) = 7*m**2 + 15*m - 7. Let a(r) = b(r) - 5*p(r). Solve a(n) = 0.
-6, 1
Let d(y) be the third derivative of y**8/112 + y**7/98 - 9*y**6/280 - y**5/28 + y**4/28 + 4*y**2 + 8. What is b in d(b) = 0?
-1, 0, 2/7, 1
Let p(w) be the second derivative of w**8/560 + w**7/280 - w**6/120 - w**5/40 - w**3/3 + 4*w. Let m(o) be the second derivative of p(o). Factor m(v).
3*v*(v - 1)*(v + 1)**2
Let l(q) = -q - 5. Suppose -3*d + 3 = 27. Let y be l(d). Find o, given that -y*o**2 - 1/2*o**4 + 2*o - 1/2 + 2*o**3 = 0.
1
Let i(o) = -o**3 - 11*o**2 - 3*o - 9. Let y be i(-11). Let b = 28 - y. Factor 0*u**3 - 4/5*u**2 + 2/5 + 0*u + 2/5*u**b.
2*(u - 1)**2*(u + 1)**2/5
Let p(h) be the third derivative of -1/300*h**6 - 2/525*h**7 + 0*h**3 + 0*h**5 + 3*h**2 + 0*h**4 + 0*h + 0 - 1/840*h**8. Find n such that p(n) = 0.
-1, 0
Let i = -835/3 + 279. Suppose -2/3*o**2 + 0*o - i*o**3 + 0 = 0. Calculate o.
-1, 0
Factor 2*c - 2/5*c**2 + 12/5.
-2*(c - 6)*(c + 1)/5
Let h(c) be the second derivative of c**4/42 - c. Factor h(r).
2*r**2/7
Let z(y) be the first derivative of y**9/756 + y**8/560 - y**7/168 - y**6/120 + y**5/120 - y**3 - 3. Let g(j) be the third derivative of z(j). Factor g(w).
w*(w - 1)*(w + 1)**2*(4*w - 1)
Let y be 8/(-14) - -2*85/175. Let b(o) be the first derivative of -2/5*o - 1 - 2/15*o**3 + y*o**2. Determine z, given that b(z) = 0.
1
Let 0 - 3/2*w**3 + 3/2*w + 9/4*w**4 - 9/4*w**2 = 0. What is w?
-1, 0, 2/3, 1
Let v(p) = -33*p**2 - 69*p - 11. Let f(s) = 26*s + 3 + 2 + 17*s**2 + 9*s. Let w(m) = 5*f(m) + 3*v(m). Suppose w(b) = 0. Calculate b.
-2, -2/7
Let s = -4 + 8. Factor 8*b**s - 32*b**3 - 4*b**5 - 17*b**4 - 11*b**4 - 16*b**2.
-4*b**2*(b + 1)*(b + 2)**2
Suppose n - 7 = -4. Factor -4*z**4 + 16*z**5 + n*z**5 - 5*z**5.
2*z**4*(7*z - 2)
Factor 1/10*a**2 + 18/5 + 6/5*a.
(a + 6)**2/10
Let m(s) be the first derivative of -3 - 3/2*s**3 + 3/10*s**5 + 3/2*s**2 + 0*s + 0*s**4. Solve m(f) = 0 for f.
-2, 0, 1
Let u(o) be the second derivative of o**6/120 - o**5/30 + o**4/24 - 3*o**2/2 + 4*o. Let l(y) be the first derivative of u(y). Factor l(s).
s*(s - 1)**2
Let c(f) = -4*f**4 + 40*f**3 - 192*f**2 + 248*f + 8. Let u(o) = -o**3 - o + 1. Let t(m) = -c(m) + 8*u(m). Factor t(n).
4*n*(n - 4)**3
Let y(t) be the third derivative of t**6/1260 + t**5/420 - t**3/3 + 4*t**2. Let u(s) be the first derivative of y(s). Factor u(p).
2*p*(p + 1)/7
Let q(b) be the second derivative of -b**4/132 - b**3/66 + b**2/11 + 24*b. Factor q(a).
-(a - 1)*(a + 2)/11
Let x(c) = -5*c**5 - 6*c**4 + 20*c**3 - 16*c**2 - 21*c + 16. Let n(w) = w**4 + w**2 + w - 1. Let o(f) = -6*n(f) - x(f). Determine h, given that o(h) = 0.
-2, -1, 1
Let f(t) be the first derivative of -t**6/1260 - t**5/210 - t**4/84 - t**3/3 - 2. Let q(i) be the third derivative of f(i). Determine d so that q(d) = 0.
-1
Let x(g) = -g**2 - 9*g + 12. Let k be x(-10). Find w such that -k*w + 2*w + 2*w**2 + 2 - 4*w = 0.
1
Let b be ((-2)/(-15))/((-4 - -10)/36). Find w, given that 0 - 2/5*w + b*w**2 = 0.
0, 1/2
Find m such that 103*m - 10*m**5 - 23*m - 137*m**3 - 85*m**4 + 6*m**3 - 64*m**3 - 40*m**2 = 0.
-4, -1, 0, 1/2
Let 1/3*q**3 - 16/3 - 4/3*q + 4/3*q**2 = 0. Calculate q.
-4, -2, 2
Let z(o) be the first derivative of 0*o - 9/10*o**4 + 2/15*o**3 + 2/5*o**2 + 4 - 26/25*o**5 - 1/3*o**6. Factor z(b).
-2*b*(b + 1)**3*(5*b - 2)/5
Let g = -3 + 3. Let y be ((-6)/21 + g)/(-1). Factor -2/7*u**2 + 4/7 + y*u.
-2*(u - 2)*(u + 1)/7
Determine a, given that -29*a**3 + 14*a**3 + 2*a**2 + 18 + 64*a**2 - 69*a = 0.
2/5, 1, 3
Suppose -8*r = -3*r - 15. Suppose 3*z = -r*z. Let z - k**4 + 0*k - 1/3*k**5 - 1/3*k**2 - k**3 = 0. What is k?
-1, 0
Let a(y) be the second derivative of -y**6/360 - y**5/15 - 2*y**4/3 + y**3/6 + 6*y. Let u(i) be the second derivative of a(i). Find o, given that u(o) = 0.
-4
Let w(a) = -3*a**2 - 5 - a + a**2 + 3*a + 5*a**2. Let m(i) = 3*i**2 + i - 4. Let z(y) = 5*m(y) - 4*w(y). Factor z(t).
3*t*(t - 1)
Let y(m) be the first derivative of 1/4*m**6 - 3/4*m**2 + 2 + m**3 + 0*m**4 - 3/5*m**5 + 0*m. Factor y(b).
3*b*(b - 1)**3*(b + 1)/2
Suppose -2 = 4*u - 10. Let r(p) be the second derivative of -4*p - 1/2*p**4 + 0*p**3 + 0*p**u + 3/20*p**5 + 0. Find g, given that r(g) = 0.
0, 2
Let j = 3 + 0. Suppose -8 = 2*z + 4*p, -2*p = 3*p + 10. Factor -1/3*y**j - 2/3*y**2 + 0 + z*y.
-y**2*(y + 2)/3
Let q(k) be the third derivative of k**6/240 - k**5/40 + k**4/16 - k**3/12 - k**2 + 33. Factor q(g).
(g - 1)**3/2
Let s be (-15)/(-4) - 3/4. Let -v - 30*v**3 + 2*v + v**5 + 28*v**s = 0. What is v?
-1, 0, 1
Let d(o) be the third derivative of -o**8/60480 - o**7/7560 - o**6/2160 + o**5/15 + 4*o**2. Let k(a) be the third derivative of d(a). Solve k(j) = 0 for j.
-1
Factor -1/3 + 2/3*y - 1/3*y**2.
-(y - 1)**2/3
Let w be (1 - 7) + -4 + (-64)/(-6). Factor 1/3*b**4 + 2/3*b - 1/3*b**2 + 0 - w*b**3.
b*(b - 2)*(b - 1)*(b + 1)/3
Let h = 47 - 24. Determine y, given that y**2 + 21*y + y**2 - h*y = 0.
0, 1
Let z(o) be the second derivative of o**6/30 + o**5/10 + o**4/12 + 17*o. Factor z(n).
n**2*(n + 1)**2
Let k(v) be the first derivative of 12*v**2 - 2 + 8*v + 10/3*v**3. Solve k(l) = 0.
-2, -2/5
Suppose 9/4 - 3/2*f + 1/4*f**2 = 0. What is f?
3
Let f(o) = 0*o - 4*o**2 + 0*o**2 + 3*o + 3*o. Let c(r) = 9*r**2 - 13*r - 1. Let s(w) = 2*