*r**4 - 9*r**2 + r. Let l(p) = 6*i(p) + 7*s(p). Factor l(g).
g*(g - 1)**3*(g + 1)
Let c(h) be the first derivative of h**3/27 - h/9 - 17. Factor c(p).
(p - 1)*(p + 1)/9
Let d be ((-33)/4)/(6/(-16)). Let p be -4*(d/(-8) - -2). Let 16*n**3 + 1 + 0 + 6*n**4 + 12*n**2 - p = 0. What is n?
-1, 1/3
What is j in 6 + 3/5*j**2 - 33/5*j = 0?
1, 10
Suppose -2/13*u**4 + 0 - 2/13*u**2 + 0*u - 4/13*u**3 = 0. What is u?
-1, 0
Let g be (-63)/6*8/90. Let a = g - -4/3. Let -2/5*t**2 + 4/5 - a*t = 0. What is t?
-2, 1
Let m(h) = -h**3 + 4*h**2 + 6*h - 2. Let n be m(5). Suppose 4*p - y = 15 - 6, -n*y = p - 12. Solve 0*k + 0*k**2 + 0 - 2/7*k**p = 0.
0
Let z(b) be the first derivative of -b**5 - 9*b**4/2 - 7*b**3/3 + 3*b**2 - 7. Factor z(g).
-g*(g + 1)*(g + 3)*(5*g - 2)
Let k = 158/123 + 2/41. Factor 4/3*l - 1/3*l**2 - k.
-(l - 2)**2/3
Let n = -36/109 - -1196/981. Factor 4/3*p**2 - 8/9*p**3 + 2/9*p**4 - n*p + 2/9.
2*(p - 1)**4/9
Suppose 0 = 4*f + 5*j - 13, 4*f - f + 5*j = 11. Factor -7*n**3 - 5*n - n**5 - 10*n**f - 5*n**4 - n**3 - 5 + 4 - 2*n**3.
-(n + 1)**5
Let h(n) be the third derivative of n**7/3780 + n**6/180 + n**5/20 + n**4/4 - n**3/6 + 4*n**2. Let j(v) be the first derivative of h(v). Solve j(q) = 0.
-3
Let c(b) be the third derivative of -b**8/1176 - 2*b**7/735 + b**6/140 + 2*b**5/105 - b**4/21 + 4*b**2. Factor c(z).
-2*z*(z - 1)**2*(z + 2)**2/7
Factor -18*g**3 + 21*g**3 - 2*g - 3*g - g - 3*g**2.
3*g*(g - 2)*(g + 1)
Let t be (3 - (-34)/(-10))*-1. Let i(c) be the first derivative of -t*c**5 - 2 - 2/3*c - 1/3*c**4 + 8/9*c**3 + 2/3*c**2. Solve i(j) = 0.
-1, 1/3, 1
Let f(a) be the third derivative of -a**6/42 - 11*a**5/210 + a**4/84 + 2*a**3/21 - 9*a**2. Let f(d) = 0. What is d?
-1, -1/2, 2/5
Suppose 0*a + 12 = 4*a. Suppose a*n - 4 = n. Factor 0 + 4/3*r + 2/3*r**n.
2*r*(r + 2)/3
Let x(t) be the first derivative of 343*t**6/18 + 98*t**5/5 + 7*t**4 + 8*t**3/9 - 39. Solve x(n) = 0 for n.
-2/7, 0
Let z(y) be the first derivative of -y**3/3 + 5*y**2 - 25*y + 8. Determine h so that z(h) = 0.
5
Let v(m) = -m**3 + 11*m**2 - 10*m + 2. Let p be v(10). Solve -2/3*o**3 + 2*o - 4/3 + 0*o**p = 0 for o.
-2, 1
Let 1/3*h**2 + h + 2/3 = 0. What is h?
-2, -1
Solve 2/3*q**3 - 2/3*q - 4/3*q**2 + 4/3 = 0.
-1, 1, 2
Determine u, given that 3*u**5 + 24*u - 6*u**4 + 12 + 0*u**5 + u**4 - 15*u**3 + 3*u**2 + 2*u**4 = 0.
-1, 2
Let o(q) be the first derivative of -7 + q**3 + 0*q + 0*q**2 - 3/4*q**4. Solve o(d) = 0.
0, 1
Let a(z) = -3*z**2 - 8*z - 4. Let b(g) = -4*g**2 - 8*g - 5. Let p(w) = 5*a(w) - 4*b(w). Let i be p(8). Factor v**3 + i*v + 0 - 3/4*v**4 + v**2.
-v**2*(v - 2)*(3*v + 2)/4
Suppose -4*i + 4 + 16 = 0. Let d(t) be the second derivative of 1/36*t**4 + 1/60*t**i - 1/6*t**2 - t - 1/18*t**3 + 0. Factor d(h).
(h - 1)*(h + 1)**2/3
Let z(r) = 5*r**2 - 4*r + 7. Let o = 16 - 11. Let l(a) = 6*a**2 - 4*a + 8. Let j(p) = o*z(p) - 4*l(p). What is q in j(q) = 0?
1, 3
Factor 23 + 5*h**2 - 28 + 0*h**2.
5*(h - 1)*(h + 1)
Let a(b) = 10*b**5 - 8*b**3 - 4*b**2 + 6*b - 4. Let r(t) = -t**5 + t**2. Let y(n) = -a(n) - 8*r(n). Factor y(p).
-2*(p - 1)**3*(p + 1)*(p + 2)
Let v = 33 - 33. Let w(h) be the third derivative of -1/60*h**5 + 0*h**4 + v*h + 3*h**2 + 0 + 0*h**3. Factor w(n).
-n**2
Suppose -8 = -13*t + 9*t. Let -1/5*a**t - 2/5*a - 1/5 = 0. Calculate a.
-1
Let c(f) be the second derivative of 0 + 0*f**3 - 1/42*f**7 + 0*f**2 - 1/20*f**5 + 1/15*f**6 - 3*f + 0*f**4. Determine k, given that c(k) = 0.
0, 1
Factor 9/2*i**3 + 1/2*i**4 + 8*i + 0 + 12*i**2.
i*(i + 1)*(i + 4)**2/2
Suppose -p = 24*p - 50. Factor -15/2*d**p + 0 - 3*d + 21/2*d**3.
3*d*(d - 1)*(7*d + 2)/2
Let m(n) be the first derivative of 5*n**3/3 + n**2 + 7*n + 5. Let a(o) = 2*o**2 + o + 3. Let c be 6/(-9) - 80/6. Let t(f) = c*a(f) + 6*m(f). Factor t(h).
2*h*(h - 1)
Let n(v) be the second derivative of 3*v + 0 - 3/4*v**3 + 3/2*v**2 + 1/8*v**4. Let n(i) = 0. What is i?
1, 2
Let k be (0 + -2)*2/772. Let b = k - -393/1351. Determine u, given that 8/7*u**2 - b + 6/7*u = 0.
-1, 1/4
Suppose 4*k = 4, 4*v = 2*v - 2*k + 2. Let d(q) be the first derivative of -2 + v*q - q**2 - 1/2*q**4 + 4/3*q**3. Factor d(r).
-2*r*(r - 1)**2
Solve -7 - 8*m**3 - 56*m - 48*m**2 - m**3 + m**3 + 4*m**4 - 13 = 0 for m.
-1, 5
Suppose -8 = -3*x + 7. Suppose 5*b - x = -0. Let d(i) = -1. Let m(v) = -2*v**2 + 4*v + 6. Let f(k) = b*m(k) + 8*d(k). Factor f(a).
-2*(a - 1)**2
Let s(w) be the third derivative of -1/24*w**4 - 1/60*w**5 + 0*w + 0 - 2*w**2 + 1/6*w**3 + 1/120*w**6. Factor s(m).
(m - 1)**2*(m + 1)
Let l(q) = 3*q - 3. Let x be l(-5). Let j = 20 + x. Suppose -3/5*f**3 + 2/5*f**4 + 0 + 0*f**j + 1/5*f = 0. What is f?
-1/2, 0, 1
Suppose -2 = -x - 4*l, -2*x - 3*l = -4*x + 4. Factor t**3 + 0*t**2 - 8*t**x + 8*t**2.
t**3
Let a(m) be the second derivative of m**6/90 - m**5/60 + 5*m. Factor a(v).
v**3*(v - 1)/3
Let y be ((-21)/112)/((-2)/8). Let h = -13 - -16. Factor 1/4 - 1/4*g**h - 3/4*g + y*g**2.
-(g - 1)**3/4
Let t be (3/(-3) - -4) + -3. Let p(w) be the second derivative of 1/12*w**4 - 1/6*w**3 - 2*w + t + 0*w**2. Factor p(u).
u*(u - 1)
Suppose 0*p - 4*p - i + 17 = 0, i = -3*p + 13. Factor 2*r**2 + 8*r + 0*r**2 - 8 - p*r**2.
-2*(r - 2)**2
Let f be 0 + 61/20 + -3. Let b(g) be the second derivative of 0*g**4 + 4*g - f*g**5 + 0*g**3 + 0 + 0*g**2. Let b(l) = 0. What is l?
0
Factor -1/2*i**2 + 0*i + 1/2.
-(i - 1)*(i + 1)/2
Let d(y) be the third derivative of y**6/30 + y**5/15 - y**4/3 + 16*y**2. Factor d(i).
4*i*(i - 1)*(i + 2)
Let x(t) = -2*t - 2*t + 52*t**2 - 53*t**2 + 7. Let d be x(-5). Factor 0 + 2*g**4 + 16/3*g**3 + 14/3*g**d + 4/3*g.
2*g*(g + 1)**2*(3*g + 2)/3
Factor -1/3*z**5 + 2/3 + 2/3*z**2 + 5/3*z - 4/3*z**3 - 4/3*z**4.
-(z - 1)*(z + 1)**3*(z + 2)/3
Let k(s) = 10*s**3 - 5*s**2 - 45*s - 25. Let a(p) = 9*p**3 - 5*p**2 - 46*p - 26. Let c(w) = 5*a(w) - 6*k(w). Let c(q) = 0. What is q?
-1, -2/3, 2
Let j(m) = -m**5 - 8*m**4 - 3*m**3 + 4*m**2. Let f(v) = v**5 + 7*v**4 + 3*v**3 - 3*v**2. Let t be 2/4*(7 + 1). Let p(b) = t*j(b) + 5*f(b). Factor p(o).
o**2*(o + 1)**3
Let b = 29 - 43. Let l be (-4)/6 - b/21. Suppose 0*m**3 + l*m + 2/3 + 2/3*m**4 - 4/3*m**2 = 0. Calculate m.
-1, 1
Let o be (-4)/(-9)*12/40*5. Factor 4/3*g**3 + 0*g + 2/3*g**4 + 0 + o*g**2.
2*g**2*(g + 1)**2/3
Let a(g) be the first derivative of g**4/4 + g**3/3 - 5*g**2/2 + 3*g + 12. Suppose a(t) = 0. Calculate t.
-3, 1
Let t = 623/198 - 34/11. Let j(l) be the third derivative of 0 + l**2 - 1/24*l**4 + 1/60*l**5 + t*l**3 - 1/360*l**6 + 0*l. Let j(r) = 0. What is r?
1
Let g(i) be the third derivative of i**7/490 - i**6/140 - i**5/35 + i**4/28 + 3*i**3/14 + 21*i**2. Factor g(x).
3*(x - 3)*(x - 1)*(x + 1)**2/7
Let t be 4/(-12) - (-1)/3. Let c = 2 + t. Find s such that -2*s**4 - s**5 - 5*s**4 + 6*s**4 - 3*s**3 + s**c + 4*s**3 = 0.
-1, 0, 1
Let o(k) be the third derivative of k**8/336 + k**7/210 - k**6/20 + k**5/30 + 5*k**4/24 - k**3/2 - k**2 - 4*k. Factor o(w).
(w - 1)**3*(w + 1)*(w + 3)
Let k be (-17 - -17)/(-1 + -1). Let u(d) be the second derivative of 7/24*d**3 + 1/4*d**2 + 1/120*d**6 + k + 1/16*d**5 + 2*d + 3/16*d**4. Factor u(f).
(f + 1)**3*(f + 2)/4
Let u(w) be the first derivative of w**4/3 - 7*w**3/9 - 7*w**2/3 - w + 10. Factor u(p).
(p - 3)*(p + 1)*(4*p + 1)/3
Let b(c) be the second derivative of c**7/42 + c**6/30 - c**5/10 - c**4/6 + c**3/6 + c**2/2 - 20*c. Factor b(d).
(d - 1)**2*(d + 1)**3
Solve -12*v**4 + 10*v**2 + 10*v + 5*v**2 + 7*v**4 = 0.
-1, 0, 2
Let v(r) be the first derivative of r**7/630 - r**6/180 + 5*r**2/2 - 2. Let d(n) be the second derivative of v(n). Solve d(c) = 0 for c.
0, 2
Let y(n) be the first derivative of -n**6/540 - n**5/135 - n**4/108 + n**2 + 7. Let q(j) be the second derivative of y(j). Determine x, given that q(x) = 0.
-1, 0
Let n(t) be the second derivative of -t**4/126 + 40*t**3/63 - 400*t**2/21 + t + 20. Factor n(c).
-2*(c - 20)**2/21
Determine d, given that d + 0*d - 4*d - 3*d - 3 - 3*d**2 = 0.
-1
Let y = -6 + 11. Factor v**3 - 4*v**3 - 4*v**4 + 2*v**y + 5*v**3.
2*v**3*(v - 1)**2
Suppose 0 + 24 = 12*q. Factor 8/5*c + 8/5 - 6/5*c**q.
-2*(c - 2)*(3*c + 2)/5
Let z(j) be the second derivative of 3*j**4/28 - 10*j**3/7 + 18*j**2/7 - 36*j. What is h in z(h) = 0?
2/3, 6
Let b be -115 + 2 - (2 - 3). Let c = b - -343/3. Factor 0 - 2/3*n + n**5 - n**2 + n**3 + c*n**4.
n*(n + 1)**3*(3*n - 2