. Let r be 8/3*6/4. Let h(f) = -2*f**2 + 8*f + 2. Let g(m) = r*p(m) - 11*h(m). Factor g(z).
-2*(z - 1)**2
Let y(b) be the first derivative of -b**7/420 + b**6/45 - b**5/12 + b**4/6 + b**3 + 1. Let d(c) be the third derivative of y(c). Find w such that d(w) = 0.
1, 2
Let g(v) be the third derivative of 7/120*v**5 + 11/240*v**6 + 0*v**3 + 1/84*v**7 - v**2 + 0 + 0*v + 1/48*v**4. Factor g(m).
m*(m + 1)**2*(5*m + 1)/2
Solve 2 - p**3 - 2*p**2 + 0*p + 2*p**3 + 6*p**2 + 5*p = 0 for p.
-2, -1
Let u(i) be the first derivative of 0*i + 2/9*i**3 + 1/3*i**4 + 0*i**2 + 2/15*i**5 - 1. What is v in u(v) = 0?
-1, 0
Suppose 10*o - 12 = 7*o. Find p such that 12/5*p**2 + 0 + 0*p + 12/5*p**3 + 3/5*p**o = 0.
-2, 0
Let d(b) be the second derivative of -b**5/20 + b**4/4 + 3*b**3/2 + 5*b**2/2 - 4*b - 8. Factor d(z).
-(z - 5)*(z + 1)**2
Let p be 2*(-5)/(-75)*(1 - -11). Factor 2/5*o**2 + 8/5 + p*o.
2*(o + 2)**2/5
Let r(t) = t**3 - 18*t**2 - t + 23. Let h be r(18). Let s(i) be the second derivative of -2*i + 0*i**2 - 1/10*i**h + 0 + 1/3*i**4 - 1/3*i**3. Factor s(k).
-2*k*(k - 1)**2
Let l(y) be the third derivative of 6250*y**7/21 - 3500*y**6/3 + 520*y**5 - 304*y**4/3 + 32*y**3/3 + y**2 - y. Suppose l(c) = 0. Calculate c.
2/25, 2
Let q = 6 - 2. Let 2*i**3 - i**3 + 2*i**2 + 0*i**3 - i - i**2 - i**q = 0. What is i?
-1, 0, 1
Let w be (-1)/(((-6)/(-2))/(-6)). Let y be (2/(-4))/((-1)/4). Determine s, given that -s**2 + 0*s**w - s + y*s = 0.
0, 1
Let i(y) be the third derivative of y**11/1496880 + y**10/226800 + y**9/136080 + y**5/60 + 5*y**2. Let l(m) be the third derivative of i(m). Factor l(r).
2*r**3*(r + 1)*(r + 2)/9
Let p be 2*((-3)/(-3) - (-4)/(-5)). Suppose -4/5*d - 2/5*d**2 - p = 0. What is d?
-1
Let b(l) be the third derivative of l**8/23520 - l**7/2205 + l**6/630 + l**4/8 + 2*l**2. Let w(c) be the second derivative of b(c). Factor w(g).
2*g*(g - 2)**2/7
Let h(l) be the second derivative of -l**5/4 + 5*l**4/2 - 15*l**3/2 + 10*l**2 + 22*l. Factor h(y).
-5*(y - 4)*(y - 1)**2
Suppose -2*k - 5*q = -31, -q + 1 = 2*k - 10. Suppose -2 - 3*p**k - 5 + 7 = 0. Calculate p.
0
Factor -15/2 + 27/2*a + 3*a**2.
3*(a + 5)*(2*a - 1)/2
Let i = 17 + -15. Suppose -10 = 4*h - i*x, x + 15 = -h + 4*x. What is o in 2/3*o**4 + 0*o**2 + 2/3*o**3 + h*o + 0 = 0?
-1, 0
Factor -12 + 21/4*h**2 + 15/2*h - 3/4*h**3.
-3*(h - 8)*(h - 1)*(h + 2)/4
Let p(k) be the second derivative of k**6/420 - k**4/84 - k**2 - 2*k. Let n(l) be the first derivative of p(l). Factor n(i).
2*i*(i - 1)*(i + 1)/7
Let w(g) = 2*g**2 - 4*g + 3*g**2 + 3 + 2*g**2. Let v(d) = 20*d**2 - 11*d + 8. Let c(n) = -3*v(n) + 8*w(n). Factor c(q).
-q*(4*q - 1)
Let v = 7 - 4. Let t(y) = -3 + 2*y**2 + 11*y - 2*y**2 - 6 - 2*y**2. Let g(q) = q**2 - 5*q + 4. Let r(b) = v*t(b) + 7*g(b). Factor r(p).
(p - 1)**2
Factor -4/5*s + 1/5*s**2 + 4/5.
(s - 2)**2/5
Determine s so that 2*s - 21*s**2 - s + 20*s**2 = 0.
0, 1
Let u(i) be the third derivative of 0*i - 2*i**2 + 0 - 1/60*i**6 + 0*i**3 + 0*i**4 - 1/30*i**5. Factor u(a).
-2*a**2*(a + 1)
Let d(h) be the first derivative of h**6/180 - h**5/180 - h**2/2 + 2. Let k(c) be the second derivative of d(c). Factor k(g).
g**2*(2*g - 1)/3
Suppose -1 = k - 3. Suppose 14 = 5*c - 0*t - 2*t, 0 = c - 3*t - 8. Determine n so that 2*n - 8*n**3 - 5 + c - n**k - 5*n**4 + 3 = 0.
-1, 0, 2/5
Let i(s) be the third derivative of s**6/360 - s**5/180 - s**4/36 + 6*s**2. Let i(a) = 0. What is a?
-1, 0, 2
Let p(o) be the first derivative of 3*o**4/20 + 3*o**3/5 + 9*o**2/10 + 3*o/5 - 24. Determine h so that p(h) = 0.
-1
Suppose -2 + 10 = 4*f. Suppose -f - 4 = -3*x. Factor -b**x + 2*b + 2*b + 3*b**2.
2*b*(b + 2)
Factor -2*i**3 + 7*i**3 + 8*i**2 + 0*i**3 - i**3.
4*i**2*(i + 2)
Let b = 58 - 55. Solve -9/2*n + b + 3/2*n**2 = 0.
1, 2
Let y(s) = s + 8. Let r be y(-8). What is b in 4/9*b**3 - 2/9*b - 2/9*b**5 + r*b**2 + 0*b**4 + 0 = 0?
-1, 0, 1
Let a(u) be the first derivative of -u**2 - 1/3*u**3 - u - 3. Factor a(i).
-(i + 1)**2
Let u = -2 - 1. Let j = 1 - u. Suppose d**4 - d**5 - 2*d**2 + d**j + 2*d**3 - d**5 = 0. What is d?
-1, 0, 1
Factor -2608*d + 2608*d + 8*d**3 + d**5 + 5*d**4 + 4*d**2.
d**2*(d + 1)*(d + 2)**2
Let i(v) be the first derivative of -8*v**3/9 - 7*v**2/3 + 4*v/3 + 15. Factor i(j).
-2*(j + 2)*(4*j - 1)/3
Let f(w) be the first derivative of w**7/195 - w**6/390 + 5*w**2/2 - 1. Let d(l) be the second derivative of f(l). Solve d(a) = 0 for a.
0, 2/7
Let j(s) be the second derivative of 1/6*s**3 + s + 0 + 0*s**2 - 1/12*s**4. Factor j(o).
-o*(o - 1)
Let c(a) = -a**2 - a - 1. Let q(b) = 21*b**2 + 24*b + 9. Let p(z) = -18*c(z) - q(z). What is n in p(n) = 0?
-3, 1
Determine c so that 0*c + 4/7*c**2 + 2/7*c**3 - 6*c**4 + 0 = 0.
-2/7, 0, 1/3
Let n(y) = -y**3 + 7*y**2 - 6*y + 2. Let o be n(6). Suppose 5*t - 12 = -o. Determine q, given that 8/9*q**3 + 8/9*q - 2/9 - 2/9*q**4 - 4/3*q**t = 0.
1
Let j(h) = 3*h**3 + 8*h**2 + 4. Let z(w) be the second derivative of w**5/5 + 3*w**4/4 + w**3/6 + 5*w**2/2 - 2*w. Let v(m) = 5*j(m) - 4*z(m). Factor v(b).
-b*(b - 2)**2
Factor -9/7 - 3*g - 3/7*g**3 - 15/7*g**2.
-3*(g + 1)**2*(g + 3)/7
Let d = 181 - 179. Factor 0 + 1/4*g**4 - 1/4*g**5 + 0*g**d + 1/2*g**3 + 0*g.
-g**3*(g - 2)*(g + 1)/4
Factor -30/11*n**4 + 36/11*n**3 + 6/11*n**5 + 24/11*n**2 - 48/11*n + 0.
6*n*(n - 2)**3*(n + 1)/11
Let j be (-2 - -4) + (6 - (4 - -1)). Factor -4/3*a**4 + 2/3*a + 0*a**j + 0 + 4/3*a**2 - 2/3*a**5.
-2*a*(a - 1)*(a + 1)**3/3
Factor -4/3*s**3 + 0 + 4/3*s**5 + 4/3*s**2 - 4/3*s**4 + 0*s.
4*s**2*(s - 1)**2*(s + 1)/3
Let i be ((-18)/(-2))/(-3) + 6. Let k be i/((-3)/(-4)) - 0. Determine m, given that 2/9 + 4/9*m**2 - 2/3*m + 2/9*m**5 + 4/9*m**3 - 2/3*m**k = 0.
-1, 1
Let o(w) be the second derivative of w**9/5040 - w**8/1120 + w**6/120 - w**5/40 - w**4/6 - 6*w. Let q(m) be the third derivative of o(m). Factor q(p).
3*(p - 1)**3*(p + 1)
Let v be (-5 + (-93)/(-18))/((-2)/(-4)). Find z, given that 1/3*z**2 + 0*z + v*z**5 + z**3 + 0 + z**4 = 0.
-1, 0
Let q(z) = 8*z**4 - 16*z**3 + 8*z - 4. Let c(i) = i**4 - i**3 + i**2 - i - 1. Let x(n) = 4*c(n) - q(n). Let x(u) = 0. Calculate u.
-1, 0, 1, 3
Suppose 2*b + 5 = -3, -2*n - 4*b + 108 = 0. Let h be n/22 - (-30)/165. Let -4/9*q**4 - 2/3*q - 2/3*q**5 - 4/9 + 4/3*q**h + 8/9*q**2 = 0. What is q?
-1, -2/3, 1
Let p = -4 - -24. Suppose 5*n + p = 45. What is f in -5/2*f**3 + 0*f - 3/2*f**n + 0 - 1/2*f**2 - 7/2*f**4 = 0?
-1, -1/3, 0
Let v(k) be the second derivative of 1/18*k**4 + 0 + 3*k + 0*k**3 + 0*k**5 - 1/45*k**6 + 0*k**2. Let v(d) = 0. Calculate d.
-1, 0, 1
Let r(j) be the second derivative of -j**8/13440 + j**6/480 + j**5/120 + j**4/3 - j. Let d(l) be the third derivative of r(l). Factor d(a).
-(a - 2)*(a + 1)**2/2
Suppose -7 + 15 = 4*y. Factor -96*i - 12 - 8*i**3 - 11 + 8 - 21 - 52*i**y.
-4*(i + 3)**2*(2*i + 1)
Let b(k) = 3*k**4 + k**3 - 3*k**2 + k. Let g(u) = -16*u**4 - 6*u**3 + 16*u**2 - 5*u. Let n(q) = 11*b(q) + 2*g(q). Factor n(s).
s*(s - 1)**2*(s + 1)
Let s(j) be the first derivative of -2*j**3/3 - 2*j**2 + 6*j - 32. Factor s(m).
-2*(m - 1)*(m + 3)
Let c be (1 - (-4)/(-12))/2*1. Let z(k) be the first derivative of c*k**6 - 2/5*k**5 + 0*k**2 - 2 + 0*k + 0*k**4 + 0*k**3. Factor z(u).
2*u**4*(u - 1)
Suppose -5*k = -3*b + 29, -4*b - 5*k = 7 + 1. Let p be 2/8 - 30/(-8). Factor 0*g - b + 1 - 9*g - p*g**2.
-(g + 2)*(4*g + 1)
Let l(s) be the third derivative of -s**5/360 + s**4/16 + 5*s**3/18 + 8*s**2 + 4*s. Let l(m) = 0. Calculate m.
-1, 10
Let v = 3 + -27. Let u = v - -26. Let -1/2*a**u + 2*a - 2 = 0. What is a?
2
Factor -40*j**4 - 3*j**3 + 15*j**4 + 2*j**2 - 42*j**3 + 8*j**2.
-5*j**2*(j + 2)*(5*j - 1)
Let s(a) = -a - 1. Let v(c) = -c**2 - 8*c - 11. Let r(o) = 22*s(o) - 2*v(o). Find t, given that r(t) = 0.
0, 3
Let c be ((-2)/5)/((-4)/5). Let f(t) = -t**3 - 3*t**2 - 2*t + 2. Let u be f(0). Factor -c*o + 0*o**4 - 1/2*o**5 + 0*o**u + 0 + o**3.
-o*(o - 1)**2*(o + 1)**2/2
Let g(k) be the first derivative of 1/15*k**5 - 1/18*k**6 + 1/3*k**2 + 1/4*k**4 + 0*k - 5/9*k**3 + 7. Suppose g(f) = 0. Calculate f.
-2, 0, 1
Suppose -i + 7 = 3. Factor -4*d**3 - 3*d**2 - 12*d**2 + 6*d**i + 0*d**4 + d**3 - 6*d.
3*d*(d - 2)*(d + 1)*(2*d + 1)
Factor 1/5*j**2 + 0 + 0*j - j**4 + 1/5*j**3 + 3/5*j**5.
j**2*(j - 1)**2*(3*j + 1)/5
Let l(n) be the first derivative of 2/5*n**5 - 4/3*n + 7/6*n**4 + 2/3*n**3 - n**2