e of q**7/210 + q**6/90 - q**5/15 - q**3 - 5. Let r(c) be the third derivative of x(c). Factor r(l).
4*l*(l - 1)*(l + 2)
Let a = 18 + -18. Let o(k) be the third derivative of 0*k**4 + 0*k**3 + 2*k**2 + 0*k**6 + 1/630*k**7 + a*k - 1/180*k**5 + 0. Solve o(z) = 0 for z.
-1, 0, 1
Let o = 42 - 38. Let b(v) be the second derivative of 0*v**2 + 1/50*v**5 + 0 - 1/105*v**7 - 1/75*v**6 + 2*v + 0*v**3 + 1/30*v**o. Determine z so that b(z) = 0.
-1, 0, 1
Let p be (-10)/(-15) - 546/2385. Let x = -2/53 + p. Factor -2/5*u**2 - 4/5*u - x.
-2*(u + 1)**2/5
Let o be 1/(-2) + 5/2. Suppose -4*y + 1 + 7 = 0. Suppose -o + h**3 + h**2 + y = 0. What is h?
-1, 0
Let u(g) be the first derivative of -g**3/27 - g**2/9 + 8. Factor u(x).
-x*(x + 2)/9
Let l be (-46)/345 - (-64)/30. Find v such that 27/4*v**4 + 39/4*v**l - 18*v**3 - 3/2*v + 0 = 0.
0, 1/3, 2
Let s(b) be the second derivative of b**5/120 + b**4/8 + 2*b**3/9 + 13*b. Factor s(g).
g*(g + 1)*(g + 8)/6
Suppose -s + 2*y = 3, -8 = -2*y - 2. Let u(a) be the first derivative of 2/5*a**5 + 26/3*a**3 - 2 + s*a**4 + 12*a**2 + 8*a. Determine k, given that u(k) = 0.
-2, -1
Let n(u) be the second derivative of u**7/336 - u**6/240 - u**5/160 + u**4/96 - 3*u. Factor n(z).
z**2*(z - 1)**2*(z + 1)/8
Let t(h) be the third derivative of 15*h**6/4 + 19*h**5/2 + 16*h**4/3 + 4*h**3/3 - 72*h**2. Suppose t(s) = 0. What is s?
-1, -2/15
Let m(a) be the third derivative of a**6/360 + a**5/90 + a**4/72 - 36*a**2. Factor m(p).
p*(p + 1)**2/3
Let x(b) be the third derivative of 1/30*b**5 + 7/180*b**6 + b**2 - 1/6*b**3 + 0 + 0*b + 0*b**4. Let q(w) be the first derivative of x(w). Factor q(n).
2*n*(7*n + 2)
Let g(u) = -3*u**2 + u - 2. Suppose -3*t + 5*b + 0 = -13, -t = 4*b - 27. Let l(w) = 16*w**2 - 5*w + 11. Let c(i) = t*g(i) + 2*l(i). Factor c(z).
-z*(z - 1)
Solve 4*f + 6*f - 4*f - 5*f**2 + 3*f**2 = 0 for f.
0, 3
Let i be (5 - (-52)/(-12))*2/4. Factor -1/3*z**2 + 0 + 1/3*z**4 + i*z**3 - 1/3*z.
z*(z - 1)*(z + 1)**2/3
Let k(j) be the second derivative of j**6/10 + 3*j**5/10 - 11*j**4/4 - 6*j**3 + 54*j**2 + 34*j. Factor k(a).
3*(a - 2)**2*(a + 3)**2
Let t(w) be the third derivative of 0 + 0*w - 1/210*w**7 + 1/24*w**4 - 1/120*w**6 + 1/20*w**5 - 1/3*w**3 - 3*w**2. Find h such that t(h) = 0.
-2, -1, 1
Let z(o) = o - 5. Let b be z(7). Factor -5*h**4 - 4*h**3 + h**4 + b*h + 2*h + 2*h**4 + 2.
-2*(h - 1)*(h + 1)**3
Let u(o) be the third derivative of o**9/21168 + o**8/3920 + o**7/1960 + o**6/2520 + 4*o**3/3 + 4*o**2. Let b(w) be the first derivative of u(w). Factor b(n).
n**2*(n + 1)**3/7
Let b be (13 + -1)/((-6)/(-4)). Solve b*t**2 - 8*t**3 + 6 - 5*t**5 + 0*t**5 - 12*t**4 - 2 + 12*t + t**5 = 0.
-1, 1
Let g(o) = o**3 - o**2 - 5*o + 2. Let u be g(3). Suppose 2*q = u*s + 25, 4*q + 4*s + 17 = -3. Let q + 2/3*h**3 + 0*h - 2/3*h**2 = 0. Calculate h.
0, 1
Let t(a) be the third derivative of -a**8/7560 + a**7/1260 - a**6/810 - a**3/3 - a**2. Let s(d) be the first derivative of t(d). Suppose s(m) = 0. What is m?
0, 1, 2
Let h(i) be the first derivative of -i**3/21 - 4. Find t such that h(t) = 0.
0
Suppose -3*t = s - 11, -2*s - 3*t + 17 = -8. Find v, given that -4 + 8 + 4*v**3 + s*v + 14*v**2 + 0*v**2 = 0.
-2, -1, -1/2
Let l(o) be the third derivative of 6*o**2 + 0*o + 1/15*o**5 + 0*o**4 + 0*o**3 + 0. Solve l(q) = 0.
0
Let j(y) be the second derivative of 5*y + 0*y**2 - 1/25*y**5 + 0*y**3 - 1/30*y**4 + 0 - 1/75*y**6. Determine w, given that j(w) = 0.
-1, 0
Let d(v) be the third derivative of v**8/6720 - v**7/420 + v**6/60 - v**5/15 - 5*v**2. Let c(j) be the third derivative of d(j). Suppose c(o) = 0. Calculate o.
2
Let v(y) be the first derivative of -3*y**5 - 39*y**4/4 - 4*y**3 + 6*y**2 + 4. Factor v(w).
-3*w*(w + 1)*(w + 2)*(5*w - 2)
Let w = -1564/9 + 174. Factor -4/9*l - 2/9*l**4 + w + 0*l**2 + 4/9*l**3.
-2*(l - 1)**3*(l + 1)/9
Let z = 12 + -12. Let m(s) = -s**3 + 5*s**2 - 5*s + 4. Let t be m(4). Factor 0*b - 2/3*b**3 + z + t*b**2 + 2/3*b**4.
2*b**3*(b - 1)/3
Let p(x) be the third derivative of -x**6/420 - x**5/15 - 25*x**4/84 - 4*x**3/7 - 4*x**2 + 6*x. Factor p(z).
-2*(z + 1)**2*(z + 12)/7
Let f(u) = -u**2 + 7*u. Let i be f(7). Let r(a) be the third derivative of i*a + 0*a**3 + 1/48*a**4 + 0 - 2*a**2 - 1/120*a**5. Factor r(j).
-j*(j - 1)/2
Suppose 24*q**4 + 26*q**2 - 58*q**2 + 32*q**2 - 8*q**3 + 14*q**5 = 0. What is q?
-2, 0, 2/7
Let q(r) be the third derivative of -5*r**8/112 + 16*r**7/105 - 19*r**6/120 + r**5/30 - 32*r**2. Factor q(z).
-z**2*(z - 1)**2*(15*z - 2)
Let x = 5 - 5. Find g, given that x + 2*g**3 + 2/5*g**4 + 8/5*g + 16/5*g**2 = 0.
-2, -1, 0
Let a(m) be the second derivative of -m**4/12 + m**3/2 + 31*m. Find p such that a(p) = 0.
0, 3
Let k be ((-8)/(-10))/(1/5). What is y in -k*y**3 + 12*y**2 + 8*y**3 - 12*y**3 - 4*y**3 - 3*y = 0?
0, 1/2
Let v = -4/21 - -5/14. Factor -1/3 + 1/2*k - v*k**2.
-(k - 2)*(k - 1)/6
Suppose 2*v + 0 - 2 = 0. Solve 2*z**3 - 3*z**3 - z**2 + v - 3*z + 0*z**3 + 4*z**2 = 0 for z.
1
Solve 3/4*u**3 + 0*u + 1/4*u**5 + 0 - 3/4*u**4 - 1/4*u**2 = 0.
0, 1
Let d(p) be the first derivative of 4*p**5/5 + p**4/4 + p**2 - 1. Let z(j) = 5*j**4 + j**3 + 3*j. Let n(f) = -3*d(f) + 2*z(f). Factor n(y).
-y**3*(2*y + 1)
Let x(h) be the first derivative of -h**3/3 + 5*h**2 - 5*h + 1. Let r be x(9). Factor -2 - 4*c**3 - 12*c**2 + 9*c + 5*c**3 + r*c**3.
(c - 1)**2*(5*c - 2)
Factor 1/3 + 1/6*p**2 - 5/6*p + 1/3*p**3.
(p - 1)*(p + 2)*(2*p - 1)/6
Suppose 0 = -v - 4 + 8. Let -5*j**v + 3*j + 2*j**4 + 0*j - 3*j**3 + 3*j**2 = 0. What is j?
-1, 0, 1
Let t(n) = -10*n**4 - 10*n**3 - 6*n**2 + 2*n - 2. Let u(a) = a**5 - a**4 - a**2 + a - 1. Let m = -5 + 7. Let p(w) = m*u(w) - t(w). Factor p(l).
2*l**2*(l + 1)**2*(l + 2)
Let x(i) be the second derivative of -i**6/90 - i**5/45 + i**4/9 + 7*i**2/2 - 8*i. Let h(a) be the first derivative of x(a). Suppose h(s) = 0. What is s?
-2, 0, 1
Let k(c) be the second derivative of -c**5/60 + c**3/6 - c**2 - 3*c. Let q(v) be the first derivative of k(v). What is u in q(u) = 0?
-1, 1
Let g(y) = y + 23. Let u be g(-18). Let p(d) be the second derivative of 0 + d + 0*d**2 - 1/3*d**3 - 1/10*d**u - 1/3*d**4. Solve p(r) = 0 for r.
-1, 0
Let l(u) be the first derivative of -u**6/6 + 3*u**5/5 - u**4/2 - 2*u**3/3 + 3*u**2/2 - u + 4. Factor l(r).
-(r - 1)**4*(r + 1)
Let u be 36*((-12)/112)/(4/(-14)). Suppose -72*z**2 - u + 54*z + 32*z**3 = 0. What is z?
3/4
Let n(m) = -12*m**5 + 2*m**4 - 4*m**3 - 4*m**2 - 12*m + 16. Let a(j) = -j**5 - j + 1. Let v(y) = 28*a(y) - 2*n(y). Factor v(t).
-4*(t - 1)**2*(t + 1)**3
Let g be ((-8)/(-14) - 1) + (-6)/(-14). Determine d so that g*d**2 + 0*d + 0 + 2/9*d**3 - 2/9*d**4 = 0.
0, 1
Let b(n) = -17*n**4 - 17*n**3 + 27*n**2 + 7*n + 7. Let p(d) = -8*d**4 - 8*d**3 + 13*d**2 + 3*d + 3. Let a(m) = -3*b(m) + 7*p(m). Factor a(g).
-5*g**2*(g - 1)*(g + 2)
Factor -2/3*a**2 + 2/3 - 1/3*a + 1/3*a**3.
(a - 2)*(a - 1)*(a + 1)/3
Let b(i) be the second derivative of 0 - 1/12*i**3 - 1/4*i**2 - i + 1/24*i**4 + 1/40*i**5. Find j, given that b(j) = 0.
-1, 1
Let u be (-7 + 6)/(1/(-3)). Let w(r) be the third derivative of 0*r**3 + 0*r + 0 - 2/75*r**5 + u*r**2 + 1/60*r**4. Factor w(t).
-2*t*(4*t - 1)/5
Let x(j) be the second derivative of -j**6/150 + j**4/30 - j**2/10 + 3*j. Solve x(g) = 0 for g.
-1, 1
Let d = 62/5 + -12. Factor -4/5*z - d*z**2 + 0.
-2*z*(z + 2)/5
Let p = 4 - 2. Let 12*r**5 + 9*r - 5*r**5 - 4*r**p - 16*r**3 - 9*r - 5*r**4 = 0. What is r?
-1, -2/7, 0, 2
Let x(n) be the first derivative of -n**3/18 + 5*n**2/12 + n + 20. Find g, given that x(g) = 0.
-1, 6
Let p = 134 + -932/7. Determine h so that 0 + 3/7*h**2 + p*h = 0.
-2, 0
Let x(n) be the second derivative of -n**5/90 + n**4/27 - n**3/27 - 4*n. Let x(m) = 0. Calculate m.
0, 1
Let u = 66 - 63. Factor 12*o**2 + 1/2 + 9/2*o + 8*o**u.
(o + 1)*(4*o + 1)**2/2
Let t = -2/65 - -404/455. Factor 2/7*c + 6/7*c**2 + t*c**3 + 0 + 2/7*c**4.
2*c*(c + 1)**3/7
Let n(b) be the second derivative of -b**4/24 + b**3/12 - 7*b. Factor n(i).
-i*(i - 1)/2
Let z(t) be the third derivative of -t**7/525 - t**6/25 - 23*t**5/75 - t**4 - 5*t**3/3 - 4*t**2 - 7*t. Determine a, given that z(a) = 0.
-5, -1
Let d be 0/(-1)*(-1)/(-2). Suppose d = -4*z + 3 + 1. Solve z + 6*a**2 - a**3 - 3*a**3 - 3 = 0.
-1/2, 1
Let b(z) = -815*z**2 + 990*z - 175. Let f(c) = -37*c**2 + 45*c - 8. Let y(s) = -2*b