h) be the first derivative of n(h). Factor w(t).
t**3*(3*t + 2)
Let p = 10 + -8. Suppose p*j - 10 - 2 = 0. Solve -2 + k**3 + 6*k - j*k**2 + 3 + k**3 - 3 = 0.
1
Let h(k) be the second derivative of k**4/54 - 9*k. Factor h(p).
2*p**2/9
Let u(t) be the third derivative of -3/2*t**4 - 3/20*t**6 + 13/20*t**5 + 0*t + 2*t**3 + 1/70*t**7 + 8*t**2 + 0. Let u(f) = 0. What is f?
1, 2
Let t(c) = 5*c + 3*c - c**3 + 5*c**2 + 3 - 2*c. Let b be t(6). Factor 1 - 2 + 2*k + 0 - b + 2*k**2.
2*(k - 1)*(k + 2)
Suppose 25*s = 8*s. Determine z, given that -z**3 + s*z + 0 + 1/2*z**2 = 0.
0, 1/2
Let z be ((-21)/(-7) - 4)/(-2). Factor 1 - z*u + 1/2*u**3 - u**2.
(u - 2)*(u - 1)*(u + 1)/2
Let w(f) be the second derivative of 1/110*f**5 + 2/33*f**3 - 4*f + 0*f**2 + 0 + 1/22*f**4. What is k in w(k) = 0?
-2, -1, 0
Let q(t) be the first derivative of -t**6/3 + 18*t**5/5 - 15*t**4 + 92*t**3/3 - 33*t**2 + 18*t + 60. Factor q(a).
-2*(a - 3)**2*(a - 1)**3
Let a(h) be the first derivative of -h**6/225 - 3*h**5/100 - h**4/30 - 2*h**3/3 + 3. Let r(u) be the third derivative of a(u). Factor r(d).
-2*(d + 2)*(4*d + 1)/5
Let g(w) = 4*w**2 - 15. Let d(v) = -v**2 + 4. Let a(s) = -22*d(s) - 6*g(s). Find f, given that a(f) = 0.
-1, 1
Find y, given that -8 - 28*y**2 - 20*y**2 + 18*y + 2*y**3 + 36*y**2 = 0.
1, 4
Let n(j) = -j**2 - j - 1. Let p(m) = -m**3 - 8*m**2 - 7*m - 8. Let z(t) = 24*n(t) - 3*p(t). Factor z(q).
3*q*(q - 1)*(q + 1)
Solve -32/9*i**2 - 14/9*i**5 + 0 + 2/3*i**3 + 8/9*i + 32/9*i**4 = 0 for i.
-1, 0, 2/7, 1, 2
Let r(d) = 2*d - 4. Suppose 4*k - 9 - 3 = 0. Let h be r(k). Let 0*m + 0*m**3 + 1/2*m**4 + 0 - 1/2*m**h = 0. Calculate m.
-1, 0, 1
Let y(w) = -56*w - 52. Let f(j) = j**2. Let q(h) = 4*f(h) - y(h). Factor q(m).
4*(m + 1)*(m + 13)
Let f(r) be the second derivative of -1/30*r**4 + 0 + 3*r + 0*r**3 + 1/5*r**2. Factor f(o).
-2*(o - 1)*(o + 1)/5
Let v = 6298567/40 - 157456. Let n(q) be the second derivative of -q - 7/4*q**7 - 9/2*q**4 - v*q**5 - q**3 - 63/10*q**6 + 0*q**2 + 0. Solve n(o) = 0 for o.
-1, -2/7, 0
Let y(a) be the third derivative of a**5/60 + a**4/24 - a**3/3 - 3*a**2 + 2*a. Factor y(t).
(t - 1)*(t + 2)
Let o(g) be the second derivative of 3*g**5/5 - g**4/3 - 3*g**2 - 4*g. Let p(m) be the first derivative of o(m). Determine x, given that p(x) = 0.
0, 2/9
Factor -58/9*m**3 - 2*m**4 - 10/3*m - 4/9 - 22/3*m**2.
-2*(m + 1)**3*(9*m + 2)/9
Factor 0*c + 1/2*c**3 + c**2 + 0.
c**2*(c + 2)/2
Let i(x) be the third derivative of -32*x**7/105 + 4*x**6/5 - 3*x**5/5 + x**4/6 - 8*x**2. Suppose i(a) = 0. What is a?
0, 1/4, 1
Let a(k) be the third derivative of -k**10/151200 - k**9/90720 + k**8/60480 + k**5/30 - 2*k**2. Let n(t) be the third derivative of a(t). Solve n(p) = 0.
-1, 0, 1/3
Let j be (-10)/(-30) + 5/3. Factor -6/5*m + 2/5*m**j + 0.
2*m*(m - 3)/5
Let n(b) = -b**3 + 11*b**2 + b - 10. Let d be n(11). Let v be (d + -4)/(6/(-4)). Factor -a**2 - 2*a - 2*a - 9 - v*a.
-(a + 3)**2
Let c(s) = 2*s + s**2 - 2*s. Let y(p) be the third derivative of p**6/20 - 11*p**5/60 - p**4/12 + 2*p**3/3 + 3*p**2. Let l(w) = -3*c(w) - y(w). Solve l(u) = 0.
-2/3, 1
Let n(u) be the second derivative of -1/24*u**4 - 1/6*u**3 + 0*u**2 - 3*u + 0. Factor n(p).
-p*(p + 2)/2
Let d be (0 - 1/(-12))*46/161. Let f(b) be the second derivative of 1/105*b**6 - 2/7*b**2 + 2*b - 1/7*b**3 + d*b**4 + 0 + 3/70*b**5. Factor f(o).
2*(o - 1)*(o + 1)**2*(o + 2)/7
Let q(g) be the first derivative of -3*g**4/4 + 10*g**3/3 + 4*g**2 + 13. Solve q(w) = 0.
-2/3, 0, 4
Let z(n) = n**3 - 4*n**2 - 5*n. Let o be z(5). Let h(c) be the third derivative of 1/6*c**4 + o - c**2 + 0*c**3 + 0*c + 7/30*c**5. Factor h(t).
2*t*(7*t + 2)
Let w(i) be the first derivative of -i**4/36 + i**3/9 - i**2/9 - 3. Let w(k) = 0. What is k?
0, 1, 2
Let s(g) be the second derivative of g**4/6 - g**3 + 2*g**2 + 18*g. Factor s(j).
2*(j - 2)*(j - 1)
Let q(h) be the second derivative of -3/20*h**5 + 0*h**3 + 0*h**2 + 0 + 1/30*h**6 + 1/6*h**4 + 4*h. Find l, given that q(l) = 0.
0, 1, 2
Let i(z) be the first derivative of 3/2*z**3 - 3/2*z**2 + 1/2*z + 2. Factor i(o).
(3*o - 1)**2/2
Solve 32*u**5 + 29*u**5 - 64*u**5 = 0 for u.
0
Solve 1/3 + 1/3*h + 1/3*h**5 + 1/3*h**4 - 2/3*h**3 - 2/3*h**2 = 0.
-1, 1
Let o = -7 - -15. Let s be (4/o*0)/(-3). Factor s*p**2 - 1/4 + 1/2*p - 1/2*p**3 + 1/4*p**4.
(p - 1)**3*(p + 1)/4
Suppose 28*p - 26*p - 7 = -3*t, p = 2*t. Factor 2/7*i - 2/7*i**p + 4/7.
-2*(i - 2)*(i + 1)/7
Let s(a) be the second derivative of -a**6/120 - a**5/20 - a**4/8 - a**3/6 - a**2/2 - a. Let m(y) be the first derivative of s(y). Factor m(u).
-(u + 1)**3
Let x(f) be the second derivative of -125*f**7/252 + 5*f**6/6 - f**5/2 + f**4/9 - f - 16. Factor x(j).
-j**2*(5*j - 2)**3/6
Let v be (-6)/8 + 45/12. Solve v*r - 27*r**2 + 3*r**2 - 4*r - 48*r**3 - 2*r = 0 for r.
-1/4, 0
Let q be ((-220)/(-35))/((-6)/(-119)). Let l = 128 - q. Find j such that -l*j + 8/3*j**2 - 2/3*j**3 + 4/3 = 0.
1, 2
Suppose 4*x = -3 + 11. Suppose 0 = -x*c + c. Factor 2/3*b**2 + c*b - 2/3.
2*(b - 1)*(b + 1)/3
Let j(n) be the second derivative of n**7/14 + 7*n**6/10 + 57*n**5/20 + 25*n**4/4 + 8*n**3 + 6*n**2 - 57*n. Suppose j(b) = 0. What is b?
-2, -1
Let u(l) be the third derivative of -l**7/140 + 7*l**5/40 + 3*l**4/8 + 19*l**2. Factor u(b).
-3*b*(b - 3)*(b + 1)*(b + 2)/2
Let c(q) = 5*q + 1. Let h be c(4). Suppose -j = -4*j - h. Let m(r) = 7*r**3 + 9*r**2. Let o(b) = 10*b**3 + 13*b**2. Let x(u) = j*m(u) + 5*o(u). Factor x(k).
k**2*(k + 2)
Let z(q) = -q**2 + 4*q + 2. Let r be z(4). Suppose -10 = -3*b - r*y, 0 = 4*b - 3*y - 1 - 1. Factor -9*t**b - 7*t**2 + 18*t**2 + 4*t.
2*t*(t + 2)
Let u(j) be the third derivative of j**5/30 - j**4/6 + j**3/3 + j**2. Solve u(x) = 0.
1
Suppose 6*u - 7*u = 0. What is n in -2*n**2 + u + 1/2*n = 0?
0, 1/4
Let v be (-456)/(-88) - 5 - 8/44. Find p, given that -6/5*p**2 - 4/5*p + v = 0.
-2/3, 0
Factor -4000/3 - 400*j - 40*j**2 - 4/3*j**3.
-4*(j + 10)**3/3
Let i(g) = 2*g**2 + 8*g + 2. Let l(v) be the third derivative of -v**5/60 - v**4/24 - v**3/6 + 9*v**2. Let u(h) = -i(h) - 4*l(h). Suppose u(w) = 0. Calculate w.
1
Factor 81 + 72*s**3 + 34*s**4 + 35*s - 21*s**3 + 46*s - 135*s**2 - 40*s**4.
-3*(s - 3)**3*(2*s + 1)
Factor -1/5*f + 1/5*f**3 - 2/5 + 2/5*f**2.
(f - 1)*(f + 1)*(f + 2)/5
Let 11*z - 18*z**2 + 5*z**3 - 3*z**3 - 54 + 0*z**3 + 43*z = 0. Calculate z.
3
Let j(i) be the third derivative of i**5/150 - i**4/30 + 4*i**2. What is b in j(b) = 0?
0, 2
Let h(a) be the second derivative of -2*a - 28/3*a**3 + 49/15*a**6 + 0 - 15/2*a**4 - 4*a**2 + 14/5*a**5. Let h(b) = 0. What is b?
-1, -2/7, 1
Let b(f) be the third derivative of 1/300*f**6 + 2*f**2 + 0 + 0*f + 1/15*f**3 + 1/50*f**5 + 1/20*f**4. Solve b(d) = 0.
-1
Suppose 1 = -f - 2*u, 4*f - 5 = 5*u + 17. Factor -2/11*t**4 + 0*t - 2/11*t**5 + 0*t**2 + 4/11*t**f + 0.
-2*t**3*(t - 1)*(t + 2)/11
Let f be 0*(-6 - (-1 - 6)). Factor -u + 1/2*u**2 + f.
u*(u - 2)/2
Factor 1/6*x**2 + 2/3 + 2/3*x.
(x + 2)**2/6
Let a(o) be the first derivative of -o**6/180 + o**5/60 + o**3 - 2. Let s(t) be the third derivative of a(t). Determine v so that s(v) = 0.
0, 1
Solve d**4 + 2*d**3 - 48*d**2 + 0*d**4 + 49*d**2 = 0.
-1, 0
Let b = 4 - 3. Let p = 9 - b. Find j such that -2 + 4 + 13*j + 32*j**2 + p*j**4 + 38*j**3 + 5*j**5 + 14*j**4 = 0.
-1, -2/5
Suppose -4*u - 227 = -235. Suppose 2/3 + 4/3*s + 2/3*s**u = 0. What is s?
-1
Factor 4/5*v + 16/15 + 2/15*v**2.
2*(v + 2)*(v + 4)/15
Let l(n) be the first derivative of -2*n**5/55 + n**4/22 + 2*n**3/11 - n**2/11 - 4*n/11 - 5. What is h in l(h) = 0?
-1, 1, 2
Suppose -2*o - 6 = -5*r, 4*r + 2*o - 3*o = 6. Suppose 0 = -3*v + r + 4. Factor f**3 + 5*f**2 + 2*f + f**3 - f**v.
2*f*(f + 1)**2
Let s(v) be the first derivative of v**6/15 + 3*v**5/10 + v**4/3 - 3*v + 2. Let m(k) be the first derivative of s(k). Factor m(n).
2*n**2*(n + 1)*(n + 2)
Let o(b) = b**3 - 8*b**2 - b + 10. Let i be o(8). Factor 1/2 - 3/4*l - 5/4*l**i.
-(l + 1)*(5*l - 2)/4
Let l be (15/(-6) - -3)*284. Suppose 0 = -4*f + 8*f - 3*d - l, -f - 5*d = -47. Find w such that f*w**4 + 24*w + 13*w**4 + 12*w**2 - 60*w**3 + 8 - 34*w**2 = 0.
-2/5, 1
Let x = -627/5 + 41383/330. Let w(v) be the third derivative of x*v**5 + 0*v - 1/33*v**3 + v**2 + 0*v**4 + 0. Factor w(h).
2*(h - 1)*(h + 1)/11
Suppose -4*a - 8 = -4*w, 0*w - a = 4*w + 17. Let x be ((-6)/w)/(2