q**5/20 + 2*q**3 - 31*q. Factor f(b).
-3*b*(b - 1)*(b + 2)**2
Let q = -5 - -9. Suppose q*z - 1 = 11. Suppose 0*d**4 + 0*d**4 - 3*d**z + 3*d**2 - d + d**4 = 0. What is d?
0, 1
Let y(i) = -11*i**5 - 36*i**4 - 19*i**3 + i**2 - 5. Let m(r) = -17*r**5 - 54*r**4 - 29*r**3 + r**2 - 7. Let u(n) = -5*m(n) + 7*y(n). Factor u(s).
2*s**2*(s + 1)**2*(4*s + 1)
Let h(r) be the second derivative of r**5/140 + r**4/42 - r**3/14 - 2*r. Factor h(q).
q*(q - 1)*(q + 3)/7
Suppose 0 = 3*a + 3*n - 6, -3*a + 0*n + 12 = -3*n. Determine u, given that 1/2*u**a + 0*u + 0*u**2 + 1/2*u**4 + 0 = 0.
-1, 0
Suppose 0*h + h + 2*w = 7, 4*h - 15 = 5*w. Factor 6*s**4 + 2*s**2 - 8*s**2 + 5*s**h - 2*s**5 - 3*s.
3*s*(s - 1)*(s + 1)**3
Let t(r) = -r + 7. Let v be t(4). Factor -3*y**3 - 1 - 2*y**v - 2*y**2 - y + 3 + 6*y**3.
(y - 2)*(y - 1)*(y + 1)
Let a(u) = u + 1. Let c be a(1). Suppose 3*z**2 + 3 - 5 + c*z - 3*z = 0. What is z?
-2/3, 1
Let t(p) be the second derivative of p**9/7560 + p**8/1120 + p**7/420 + p**6/360 - p**4/3 + p. Let z(r) be the third derivative of t(r). Factor z(l).
2*l*(l + 1)**3
Let a(z) = 8*z**2 - 8*z + 2. Let m(l) = 7*l**2 - 8*l + 3. Let o(f) = 5*a(f) - 6*m(f). Factor o(c).
-2*(c - 2)**2
Let s(q) be the first derivative of q**4/32 - q**3/8 - q**2/16 + 3*q/8 + 5. Factor s(k).
(k - 3)*(k - 1)*(k + 1)/8
Let s(b) be the second derivative of -16*b**7/51 - 8*b**6/85 + 13*b**5/34 - 7*b**4/34 + 2*b**3/51 - 2*b. Determine d so that s(d) = 0.
-1, 0, 1/4, 2/7
Let m(r) = r**2 + 5*r - 3. Let u be m(-6). Factor -4*o - u*o**4 - 3*o**3 + 3*o**2 + 12*o - 5*o.
-3*o*(o - 1)*(o + 1)**2
Let a be (-25)/15 + -2 + 2 + 2. Determine q so that -a*q**5 - 2/3*q**2 + 1/3*q**3 + 0 + 2/3*q**4 + 0*q = 0.
-1, 0, 1, 2
Suppose 7*x = 10*x - 63. Suppose -x = -14*z + 7*z. Determine f so that 0*f - 2/9*f**z + 0 + 0*f**2 = 0.
0
Let g(y) = y**3 - 7*y**2 + 6*y - 3. Let o be g(6). Let x = -1 - o. Factor -3*m**4 - 6*m**x + 3*m**3 + 12*m - 3*m**3 + 8 - 11*m**3.
-(m - 1)*(m + 2)**2*(3*m + 2)
Solve -16*j + 1/3*j**4 + 0 - 11/3*j**3 + 40/3*j**2 = 0 for j.
0, 3, 4
Suppose -5*d = 5*g + 1010, -3*d - 196 = -2*d - 5*g. Let x = d + 1008/5. Let x*f**2 + 0 + 6/5*f = 0. What is f?
-2, 0
Suppose -4 = -v - 3*y + 10, 5*v = 4*y - 6. Suppose -s - 3*n - 12 = 0, -2*s = 3*n + 1 + 8. Let m**s - 3/2*m**v + 2*m**4 + 3/4*m**5 - 1/2 - 7/4*m = 0. What is m?
-1, -2/3, 1
Let c(n) be the second derivative of -n**5/4 + 5*n**4/3 - 25*n**3/6 + 5*n**2 + 3*n. Factor c(h).
-5*(h - 2)*(h - 1)**2
Let v = 6 + 4. Let g be v/45 + (-56)/(-18). Factor -g*i**2 + 2/3*i**3 - 8/3 + 16/3*i.
2*(i - 2)**2*(i - 1)/3
Let t(s) be the third derivative of s**7/1470 - s**5/140 + s**4/84 + 56*s**2. Suppose t(m) = 0. What is m?
-2, 0, 1
Let a be 2/(-10) + (-80)/(-25). Suppose 0 = z - a*z + 4. Factor -1/2*p - 1/2*p**z + 0.
-p*(p + 1)/2
Let m(i) be the first derivative of -i**6/9 + 4*i**5/5 - 13*i**4/6 + 8*i**3/3 - 4*i**2/3 + 25. Factor m(n).
-2*n*(n - 2)**2*(n - 1)**2/3
Let w(t) be the second derivative of t**2 - 1/2*t**3 + 2*t + 0 + 1/12*t**4. Let w(s) = 0. Calculate s.
1, 2
Let r(c) be the second derivative of 5*c**7/84 - 11*c**6/30 + 7*c**5/10 - c**4/3 + 7*c. Suppose r(u) = 0. What is u?
0, 2/5, 2
Let s = 0 + 0. Suppose 2*b - 4*l + 8 = 0, s = b - l + 3*l - 8. Factor o - o - o - o**b.
-o*(o + 1)
Let m = -11/2 + 116/21. Let a(y) be the second derivative of -y + m*y**4 + 0*y**2 + 0*y**3 + 0. Determine n so that a(n) = 0.
0
Let o be (-4)/(-6) - ((-200)/(-48) - 5). Solve 39/4*g - 33/2*g**4 - o - 24*g**2 + 57/2*g**3 + 15/4*g**5 = 0.
2/5, 1
Let j(o) be the third derivative of -o**6/210 - o**5/15 - 11*o**4/42 - 10*o**3/21 - 2*o**2. Let j(u) = 0. What is u?
-5, -1
Let o(z) = -z**3 - 12*z**2 - 6*z + 57. Let q be o(-11). Let 4/5 - 2/5*u - 2/5*u**q = 0. Calculate u.
-2, 1
Suppose 1/4*v**2 - 1/4*v**4 + 1/2*v + 1/4*v**5 - 3/4*v**3 + 0 = 0. What is v?
-1, 0, 1, 2
Suppose 0*n + 5*n = 0. Let z(o) be the third derivative of -1/360*o**6 - o**2 + 1/72*o**4 + 1/180*o**5 + n*o - 1/18*o**3 + 0. Factor z(r).
-(r - 1)**2*(r + 1)/3
Find u, given that 6/11*u**2 + 48/11*u + 96/11 = 0.
-4
Let j(p) = 6*p - 3 + 3*p**2 - 9 + 3. Let h(q) = -2*q**2 - 7*q + 9. Let l(m) = 6*h(m) + 5*j(m). Solve l(y) = 0.
1, 3
Let p(x) = x**2 - 1. Let q(v) = -3 + 0*v + 4*v**2 + 5*v - 3*v. Let h(l) = -6*p(l) + 2*q(l). Factor h(z).
2*z*(z + 2)
Let p be 2/(-10) - 22/(-10). Factor -2*j**p + 0*j**2 + j + 2*j**4 + j**3 - 2*j.
j*(j - 1)*(j + 1)*(2*j + 1)
Let u(r) be the third derivative of -r**8/14112 + r**7/5880 + r**6/1260 + r**5/30 + 2*r**2. Let t(h) be the third derivative of u(h). Factor t(s).
-2*(s - 1)*(5*s + 2)/7
Let d(u) = -u**2 + 0*u**2 - 12 - 10*u + 4 + u. Let r be d(-8). Factor -1/2*s**4 + r + 3/2*s**3 - 3/2*s**2 + 1/2*s.
-s*(s - 1)**3/2
Suppose j - 60 = 6*j. Let p = 14 + j. Solve 8/5 - 8/5*i + 2/5*i**p = 0.
2
Find w, given that -w**5 - 3*w**5 - 9*w**2 + 4*w**4 + 16*w**3 - 7*w**2 = 0.
-2, 0, 1, 2
Let w(f) be the third derivative of 0*f**5 + 0*f - 1/60*f**6 - 3*f**2 + 1/12*f**4 + 0*f**3 + 0. Solve w(z) = 0 for z.
-1, 0, 1
Let m(z) be the third derivative of -1/210*z**7 + 0*z**3 + 0*z**4 - 2*z**2 + 1/60*z**6 + 0 + 0*z - 1/60*z**5. Factor m(t).
-t**2*(t - 1)**2
Suppose -8*j + 9 = -5*j. Let y(s) be the first derivative of 0*s**j - 1 + 0*s + 0*s**4 + 0*s**2 + 2/5*s**5. Factor y(p).
2*p**4
Let w(i) be the third derivative of 0 - 1/84*i**4 + 0*i**3 + 1/210*i**5 + 0*i - i**2. Factor w(t).
2*t*(t - 1)/7
Solve 1/2*s**4 - 1/2*s**2 + 0 + 0*s**3 + 1/4*s**5 - 1/4*s = 0 for s.
-1, 0, 1
Let i(t) = t**2 + 10*t + 12. Let p be i(-9). Factor -4*o**2 + 5*o**2 + p*o**4 - 4*o**4.
-o**2*(o - 1)*(o + 1)
Suppose -3 = 2*s - 7. Suppose 4*g - 6 = s. Determine j, given that 0*j - 3/4 + 3/4*j**g = 0.
-1, 1
Factor -r**5 + r**3 + 2*r - 15*r**2 - 4*r + 3*r**4 + 2*r**5 + 12*r**2.
r*(r - 1)*(r + 1)**2*(r + 2)
Let o(c) = c**2 - c. Let p(a) = a**3 - 3*a**2 + 2*a. Let y(i) = -5*o(i) - 5*p(i). Factor y(j).
-5*j*(j - 1)**2
Factor -2/15*r**2 - 4/15 - 2/5*r.
-2*(r + 1)*(r + 2)/15
Let a be (9/(-90)*10)/(5/(-6)). Factor 0*s**2 + 9/5*s - 3/5*s**3 - a.
-3*(s - 1)**2*(s + 2)/5
Let x(b) be the second derivative of -1/7*b**4 + 0*b**2 + 0 - 3/7*b**3 + 9*b - 1/70*b**5. Factor x(c).
-2*c*(c + 3)**2/7
Let h(r) be the second derivative of -r**6/90 + 2*r**5/15 - 2*r**4/3 - 7*r**3/6 + 4*r. Let b(a) be the second derivative of h(a). Solve b(d) = 0 for d.
2
Factor -12912*z - z**2 + 12922*z - 4*z**2.
-5*z*(z - 2)
Factor 110*f**3 + 7*f + 18*f**5 - 2*f + 40*f**2 + 120*f**4 + 27*f**5.
5*f*(f + 1)**2*(3*f + 1)**2
Let r(s) = -s**3 - s**2 + 5*s - 1. Let o(m) = 5*m**3 + 3*m**2 - 21*m + 4. Let g(h) = 4*o(h) + 18*r(h). Factor g(l).
2*(l - 1)**3
Factor -2/15*s**2 + 2/15*s + 0.
-2*s*(s - 1)/15
Let d(r) be the second derivative of -128*r**5/5 - 16*r**4 - 4*r**3 - r**2/2 + 3*r. What is p in d(p) = 0?
-1/8
Suppose -8 = -2*s - 0*s. Let u(k) be the first derivative of -k**2 + 1/5*k**5 - 1/3*k**3 + 0*k + 1 + 1/2*k**s. Let u(v) = 0. Calculate v.
-2, -1, 0, 1
Let j = -497 - -499. What is i in -3/2*i**3 + 15/8*i**j + 21/8*i - 3/4 = 0?
-1, 1/4, 2
Let i(t) be the third derivative of t**5/30 + t**4/12 - 2*t**3/3 - t**2. Factor i(g).
2*(g - 1)*(g + 2)
Let o be (-1*1)/(6/(-18)). Suppose 2*w - w**5 + w**4 - 2*w**4 - o*w**3 + 2*w**5 + w**2 + 0*w = 0. Calculate w.
-1, 0, 1, 2
Let r(v) be the first derivative of 1/4*v**4 + 2 + 1/2*v**2 - 2/3*v**3 + 0*v. Factor r(w).
w*(w - 1)**2
Let m(u) = -u**3 - 4*u**2 - 2*u - 5. Let w(i) = -4*i**2. Let p be w(-1). Let a be m(p). Let -6*k + a*k + 2*k**4 - 2 + 4*k**3 - k = 0. Calculate k.
-1, 1
Let g be ((-18)/(-27))/((-1)/9). Let j(b) = 9*b**2 + 15*b + 12. Let d(i) = i**2 + i + 1. Let t(z) = g*d(z) + j(z). Factor t(s).
3*(s + 1)*(s + 2)
Let g(l) be the second derivative of 7*l**4/4 - 2*l**3 + 6*l**2/7 - 15*l. What is j in g(j) = 0?
2/7
Let r(t) be the third derivative of -t**6/108 - t**5/90 + t**4/9 - 4*t**3/27 - t**2. Factor r(p).
-2*(p - 1)*(p + 2)*(5*p - 2)/9
Factor -2/5*z**2 - 16/5*z - 32/5.
-2*(z + 4)**2/5
Let i(y) be the first derivative of -y**4/18 - 4*y**3/9 - 5*y**2/9 - 11. Factor i(g).
-2*g*(g + 1)*(g + 5)/9
Let m be (36/15)/((-4)/(-10)). Factor -b**3 - m*b**2 - 5*b + 2*b + 3*b**2 + 3*b**4 + 4*b**3.
3*b*(b - 1)*(b + 1)**2
Let t(l) be the second derivative of l**5/4 + 25*l**4/48 + 5*l**3/24 + 9*l. Factor t(m).
5*m*(m + 1)*(4*m + 1)/4
Let l(z) = -z. L