 Let d(g) be the first derivative of v*g**2 + 2/3*g + 1 - 1/9*g**3. Factor d(i).
-(i - 2)*(i + 1)/3
Let a(j) be the first derivative of -j**4/66 + j**3/11 - 2*j**2/11 + j + 3. Let k(c) be the first derivative of a(c). Solve k(m) = 0 for m.
1, 2
Suppose -4 = 10*n - 34. Let v(t) be the second derivative of -n*t + 1/48*t**4 - 1/8*t**3 + 0 + 1/4*t**2. Factor v(l).
(l - 2)*(l - 1)/4
Let p be (-5)/((-90)/4)*3. Let u = -51/5 + 173/15. What is x in 2/3*x**4 - p*x**5 - u*x**2 - 2/3*x + 2/3 + 4/3*x**3 = 0?
-1, 1
Let t(c) = -12*c**4 + 2*c**3 - 10*c + 10. Let a(m) = -m**4 - m + 1. Let i(k) = 10*a(k) - t(k). Factor i(u).
2*u**3*(u - 1)
Let n be (-3)/(-5) - 333/(-495). Suppose -18/11*t**2 + 4/11 - n*t = 0. What is t?
-1, 2/9
Let a = 10 - 10. Suppose -8*l + 3*l = a. Let -1/3*b**2 + l + 8/3*b**3 - 5/3*b**4 - 2/3*b = 0. Calculate b.
-2/5, 0, 1
Let t(l) be the first derivative of l**5/15 - l**4/6 + l**3/9 - 3. Factor t(k).
k**2*(k - 1)**2/3
Factor -4/3 + 16/3*s - 5/3*s**2 - 25/3*s**3.
-(s + 1)*(5*s - 2)**2/3
Let r(j) be the third derivative of j**8/6720 - j**7/280 + 3*j**6/80 + j**5/10 - 4*j**2. Let i(a) be the third derivative of r(a). Let i(k) = 0. What is k?
3
Let k(j) = j - 2. Let g be k(4). Solve 0*c**g + 3*c**2 - c**2 = 0 for c.
0
Factor 0 + 0*j - 2/11*j**4 + 4/11*j**3 - 2/11*j**2.
-2*j**2*(j - 1)**2/11
Let j(a) = 2*a - 2. Let f be j(3). Factor 2*l**2 - 4*l**2 + 4*l - 4*l**f - 5*l + 7*l**3.
-l*(l - 1)**2*(4*l + 1)
Let k be ((-8 + 6)*1)/(12/(-14)). Factor w**3 + 0*w + 4/3 - k*w**2.
(w - 2)*(w - 1)*(3*w + 2)/3
Let c(y) be the first derivative of -1 + 1/12*y**3 + 1/4*y - 1/4*y**2. Determine w, given that c(w) = 0.
1
Let a(d) be the first derivative of -d**7/21 - d**6/25 + d**5/25 - 2*d - 2. Let y(q) be the first derivative of a(q). Factor y(b).
-2*b**3*(b + 1)*(5*b - 2)/5
Suppose 9 = 7*h - 12. Let l(u) be the first derivative of 2/21*u**h - 1 + 2/7*u - 2/7*u**2. Let l(f) = 0. Calculate f.
1
Suppose 38*u**3 - 2*u - 79*u**3 + 6*u**4 - 6*u**2 + 43*u**3 = 0. Calculate u.
-1, -1/3, 0, 1
What is f in 12*f + 7*f**3 + 4*f**2 + 4 - 3*f**3 + 10*f**2 - 2*f**2 = 0?
-1
Suppose 0 = 2*n - n - 4. Factor -3*u - 4*u**2 + u + 4 - n*u.
-2*(u + 2)*(2*u - 1)
Suppose -10 - 7 = q. Let v(n) = -2*n - 29. Let i be v(q). Factor -2*y + 8/5*y**4 + 2/5*y**i - 4/5 - 4/5*y**2 + 8/5*y**3.
2*(y - 1)*(y + 1)**3*(y + 2)/5
Suppose 14 = 5*u - 1. Suppose -u*g = 2*g - 10. Suppose -4/3*c**5 + 1/3*c**g + 0*c - 1/3*c**4 + 0 + 4/3*c**3 = 0. Calculate c.
-1, -1/4, 0, 1
Let d = -8 + 401/50. Let n(k) be the second derivative of 0 + 0*k**2 - d*k**6 - 1/70*k**7 + 0*k**3 + 1/20*k**4 + 3/100*k**5 + 2*k. Factor n(p).
-3*p**2*(p - 1)*(p + 1)**2/5
Let z(t) = 5*t**3 - 4*t**2 + t + 2. Let m(w) = 4*w**3 - 3*w**2 + 1. Suppose 3*v = 2*v - 4. Let q(j) = v*m(j) + 3*z(j). Factor q(x).
-(x - 2)*(x + 1)**2
Let z(m) be the third derivative of 0*m**7 - 1/1008*m**8 - 1/24*m**4 - 1/90*m**5 + 1/90*m**6 + 0*m + 1/9*m**3 - 3*m**2 + 0. Determine l, given that z(l) = 0.
-2, -1, 1
Let a(n) be the first derivative of n**4/30 + 46*n**3/45 + 143*n**2/15 + 242*n/15 - 31. Find k, given that a(k) = 0.
-11, -1
Suppose 0*s = 5*z + 3*s, 0 = -z + 5*s. Factor -1/2*w**5 + 0*w**2 - 1/2*w**3 + w**4 + 0 + z*w.
-w**3*(w - 1)**2/2
Suppose -2*d + 1 = s - 5, 4*s - 2 = 3*d. Let 10/7*q**3 - 18/7*q**4 + 4/7*q + 18/7*q**d - 2*q**5 + 0 = 0. Calculate q.
-1, -2/7, 0, 1
Let f(u) = 8*u**2 - 15*u + 1. Let b(p) = 40*p**2 - 74*p + 4. Suppose -2 = -2*z + 2, 5*z - 1 = -3*h. Let d(c) = h*b(c) + 16*f(c). Solve d(l) = 0 for l.
1/4, 2
Let h(t) be the second derivative of 5*t**4/3 + 13*t**3/6 + t**2 + 11*t. Factor h(o).
(4*o + 1)*(5*o + 2)
Let o(b) = b**3 - 12*b**2 - b + 7. Let k be o(12). Let p be k/15 + 21/9. Let 0*y + 0 + 1/2*y**3 - 1/2*y**p = 0. Calculate y.
0, 1
Let m(w) be the third derivative of -w**7/280 - w**6/40 - w**5/20 - w**3/3 - 3*w**2. Let n(r) be the first derivative of m(r). Suppose n(o) = 0. Calculate o.
-2, -1, 0
Let s(w) be the first derivative of -w**6/120 + w**5/10 - w**4/2 + w**3/3 - 4. Let k(r) be the third derivative of s(r). What is q in k(q) = 0?
2
Factor 2/7*v**2 - 2/7*v + 0.
2*v*(v - 1)/7
Let k(y) = -y - 4. Let g be k(-8). Solve 0*b + 2/3*b**3 - 1/3*b**g - 1/3*b**2 + 0 = 0 for b.
0, 1
Let w = -99/41 - -21797/9061. Let b = 460/1989 + w. Factor 2/9*n - 2/9*n**2 + 2/9*n**4 + 0 - b*n**3.
2*n*(n - 1)**2*(n + 1)/9
Let h = 2/11929 + -894683/47716. Let c = -501/28 - h. Let -c*q + 2/7*q**2 + 4/7 = 0. What is q?
1, 2
Let r be ((-27)/(-6))/(-9)*140. Let q be ((-4)/(-7))/((-20)/r). Solve -5/4*t**4 - 1/2 + 7/4*t**q + 3/4*t**3 - 3/4*t = 0.
-1, -2/5, 1
Let p = -1237/3 - -413. Determine r, given that 4/3*r - p*r**4 + 2/3 + 0*r**2 - 4/3*r**3 = 0.
-1, 1
Let b(c) = -20*c**3 - 2*c**2 - 8*c + 2. Let q(i) = 7*i**3 + i**2 + 3*i - 1. Let j(u) = -5*b(u) - 14*q(u). Let j(m) = 0. Calculate m.
-1, 1, 2
Suppose -4*z + 24 = 5*c + 12, -5*c + 5*z - 15 = 0. Factor c*u + 1/6*u**2 - 1/6.
(u - 1)*(u + 1)/6
Let b be (-16)/(-8) + 2/(-8). Factor 0 - 3/2*w**3 - 1/4*w - b*w**2.
-w*(w + 1)*(6*w + 1)/4
Let o(h) be the first derivative of -h**5/40 + h**4/24 - 3*h - 2. Let i(v) be the first derivative of o(v). Factor i(n).
-n**2*(n - 1)/2
Let o = -144 - -721/5. Factor -1/5*c + o*c**2 - 2/5.
(c - 2)*(c + 1)/5
Factor 14/5*j - 2*j**2 + 2/5*j**3 - 6/5.
2*(j - 3)*(j - 1)**2/5
Let b(a) be the second derivative of a**7/105 + a**6/75 - a**5/50 - a**4/30 + 7*a. What is x in b(x) = 0?
-1, 0, 1
Let i(f) be the third derivative of -7*f**6/540 - 4*f**5/27 - 17*f**4/36 + 2*f**3/3 + 3*f**2. Solve i(t) = 0.
-3, 2/7
Factor -2/5*s**2 + 4/5 + 2/5*s.
-2*(s - 2)*(s + 1)/5
Solve -3*c + 51/4*c**2 + 3*c**5 + 0*c**3 + 0 - 51/4*c**4 = 0 for c.
-1, 0, 1/4, 1, 4
Let p(b) be the third derivative of -3*b**5/40 + 5*b**4/12 - b**3/3 + b**2. Factor p(v).
-(v - 2)*(9*v - 2)/2
Let m(r) = 5*r**3 + 5*r**2 - 5*r + 1. Let s(c) = -6*c**3 - 6*c**2 + 6*c - 2. Let a(d) = -4*m(d) - 3*s(d). Factor a(x).
-2*(x - 1)*(x + 1)**2
Let j(s) be the second derivative of -s**4/24 - 3*s. Factor j(y).
-y**2/2
Let z = -22/9 + 8/3. Let g = 383/387 + -33/43. Suppose 0 + z*c**2 + g*c = 0. Calculate c.
-1, 0
Factor 0 + 16/7*o - 220/7*o**3 + 48/7*o**2.
-4*o*(5*o - 2)*(11*o + 2)/7
Let q(r) be the first derivative of 2*r - 1/2*r**3 - 2 + 3/20*r**5 + 0*r**4 + 0*r**2. Let j(s) be the first derivative of q(s). Factor j(p).
3*p*(p - 1)*(p + 1)
Let j = 63 - 63. Let c(b) be the third derivative of 0 + j*b + 0*b**3 + 2*b**2 - 1/60*b**5 + 1/48*b**4 + 1/240*b**6. Solve c(r) = 0 for r.
0, 1
Let x(w) be the second derivative of 0*w**2 - 4*w + 0 - 1/60*w**5 - 1/90*w**6 + 1/18*w**3 + 1/36*w**4. Factor x(i).
-i*(i - 1)*(i + 1)**2/3
Suppose 0*f = -2*f + 6. Suppose -f*u - 4*d + 27 + 7 = 0, 5*u - 72 = d. What is p in -p - u*p**4 - 43/2*p**3 + 0 - 17/2*p**2 = 0?
-1, -2/7, -1/4, 0
Let z(s) be the third derivative of -s**6/40 + s**5/5 - s**2. Factor z(h).
-3*h**2*(h - 4)
Let v(r) be the second derivative of 0 + 3/5*r**6 + 2*r + 4/3*r**4 + 9/5*r**5 - r**2 - 2/3*r**3. Find o such that v(o) = 0.
-1, -1/3, 1/3
Suppose -3*f - 2*f = -40. Let q be f/5*(-20)/(-4). Factor -1 - 1 + 2*s**2 + 0*s**3 - 8*s**3 + q*s.
-2*(s - 1)*(s + 1)*(4*s - 1)
Suppose 7*u - 9*u = -8. Let o(g) be the second derivative of 1/80*g**5 - 1/4*g**2 + 0 - 1/12*g**u - 3*g + 5/24*g**3. Factor o(n).
(n - 2)*(n - 1)**2/4
Let y(d) be the third derivative of -1/100*d**6 + 0*d**3 + 2/75*d**5 + 0*d - 2*d**2 + 0 - 1/60*d**4. Factor y(u).
-2*u*(u - 1)*(3*u - 1)/5
Let s(x) = x**2 - 7*x - 4. Let b be s(8). Suppose 0 = -2*a + b*a. Factor a - 1/5*j + 3/5*j**2.
j*(3*j - 1)/5
Let q(u) = 2*u + 0*u - 4 - 2 + 4. Let r be q(4). Factor -r*m + 6*m - m**2.
-m**2
Suppose w - 23 = -p - 1, -4*w = 5*p - 92. Suppose -4*v - v - 4*y + w = 0, -3*v - 4*y = -14. Factor -v*d**2 - 3*d**3 + 4*d**3 + d + 4*d**2.
d*(d + 1)**2
Let t(j) be the third derivative of -j**10/302400 + j**8/13440 - j**7/5040 - j**5/20 + 2*j**2. Let r(v) be the third derivative of t(v). What is m in r(m) = 0?
-2, 0, 1
Let f = 15/244 + -163067/1220. Let r = 134 + f. Factor 0 + 0*t - r*t**5 - 6/5*t**3 - 2/5*t**2 - 6/5*t**4.
-2*t**2*(t + 1)**3/5
Factor 0 + 2/9*q**3 + 2/9*q**4 + 0*q + 0*q**2.
2*q**3*(q + 1)/9
Let h(j) = j**3 - 2*j**2 + j. Let z be h(2). Factor -u - 11*u**2 + u**3 + 4*u**2 + 7*u**z.
u*(u - 1)*(u + 1)
Let k(d) be the first derivative of d**5/14 + d**4/