**3 + 4*f**2 + 6*f + 1. Let l(d) = -d**4 - 7*d**3 + 5*d**2 + 7*d + 1. Let m(a) = 5*b(a) - 4*l(a). Determine i, given that m(i) = 0.
-1, 1
Let n(m) be the third derivative of -m**6/300 + m**5/30 - m**4/20 - 3*m**3/5 - 12*m**2. Determine x, given that n(x) = 0.
-1, 3
Let u(r) be the second derivative of r**6/210 + r**5/28 + 14*r. Factor u(z).
z**3*(z + 5)/7
Let d(r) be the second derivative of -r**9/11340 + r**8/3360 - r**6/1080 - r**4/3 + r. Let z(t) be the third derivative of d(t). Let z(j) = 0. What is j?
-1/2, 0, 1
Let d(a) be the first derivative of a**5/180 - a**4/9 + 8*a**3/9 - 3*a**2/2 - 4. Let s(k) be the second derivative of d(k). Determine b, given that s(b) = 0.
4
Let g = 5161/9 - 573. Determine l, given that 2/9*l**3 + 2/9*l**5 - 2/3*l**4 - g*l + 2/3*l**2 + 0 = 0.
-1, 0, 1, 2
Let o(s) be the second derivative of s**6/30 - s**4/6 + s**2/2 + 3*s. Let c(f) be the first derivative of o(f). Let c(b) = 0. What is b?
-1, 0, 1
Let x(f) be the first derivative of -18/7*f**2 - 32/21*f**6 + 7 + 8*f**3 - 73/7*f**4 + 32/5*f**5 + 0*f. Suppose x(j) = 0. Calculate j.
0, 3/4, 1
Let i(r) be the third derivative of r**6/60 - r**5/10 + r**4/6 - 9*r**2. Factor i(t).
2*t*(t - 2)*(t - 1)
Let l(q) be the third derivative of q**8/3360 - q**7/560 + q**6/240 + q**5/15 + 2*q**2. Let z(t) be the third derivative of l(t). What is x in z(x) = 0?
1/2, 1
Find g such that 1/2*g + 3/2*g**3 - 1/2 + 5/2*g**2 = 0.
-1, 1/3
Let k be 88/(-16)*(-8)/22. Factor -k*s + 2/3*s**3 + 4/3 + 0*s**2.
2*(s - 1)**2*(s + 2)/3
Let j(s) = 5*s**4 + 5*s**3 + 19*s**2 + 29*s - 7. Let c(d) = 2*d**4 + 2*d**3 + 6*d**2 + 10*d - 2. Let i(l) = 17*c(l) - 6*j(l). Factor i(z).
4*(z - 1)**2*(z + 1)*(z + 2)
Let u(b) be the second derivative of b**7/10 + b**6/8 - 4*b**5/5 + b**4/2 + 3*b**2/2 + b. Let z(x) be the first derivative of u(x). Factor z(l).
3*l*(l - 1)*(l + 2)*(7*l - 2)
Let t(v) be the second derivative of -5*v**4/12 - v**3 - v**2/2 + 4*v. Factor t(n).
-(n + 1)*(5*n + 1)
Solve -12*o**2 + 608*o**4 - 2*o**5 + 0*o + 4*o**3 - 2*o + 6 - 602*o**4 = 0.
-1, 1, 3
Suppose -9 = -b + k, -6*b + 23 = -3*b - 2*k. Suppose 4 = 2*w + a, -3*a - 1 - b = 0. Suppose 1 - 4*z**2 + 0*z**2 + w*z**2 = 0. What is z?
-1, 1
Suppose 9 = 4*i + 1. Let j(q) be the third derivative of -1/60*q**5 + 0 + 0*q**3 + 0*q**4 + 2*q**i + 0*q. Find x, given that j(x) = 0.
0
Let a = 43 + -128/3. Factor -2/3 + 1/3*z**3 - z**2 + a*z**4 - 5/3*z.
(z - 2)*(z + 1)**3/3
Let g(t) be the second derivative of t**4/36 + t**3/6 - 24*t. Factor g(n).
n*(n + 3)/3
Let g be 36/(-2)*((-124)/60 - -2). Solve 2/5*b**2 + g*b + 4/5 = 0 for b.
-2, -1
Let f(o) = -o**5 + o**3 + o**2 - o + 1. Let m(d) = -2*d**5 + 2*d**4 + 7*d**3 - 3*d**2 - 14*d - 5. Let w(q) = -f(q) + m(q). Factor w(u).
-(u - 3)*(u - 2)*(u + 1)**3
Let -282 + 60 - 278 - 4*y**3 - 300*y - 60*y**2 = 0. Calculate y.
-5
Let f(c) be the first derivative of c**4/24 + c**3/12 + 3*c - 3. Let s(h) be the first derivative of f(h). Let s(w) = 0. Calculate w.
-1, 0
Let i(h) = 4*h**2 - 16*h + 8. Let t(j) = j. Let b(a) = i(a) + 4*t(a). What is r in b(r) = 0?
1, 2
Let j(n) be the first derivative of -3/5*n**5 + 1 + 0*n**2 + 0*n + n**3 + 0*n**4. Factor j(b).
-3*b**2*(b - 1)*(b + 1)
Let k(f) = -f**5 - 4*f**4 + 4*f**3 + 4*f**2 + 3. Let n(l) = -4*l**5 - 12*l**4 + 12*l**3 + 12*l**2 + 8. Let y(q) = -8*k(q) + 3*n(q). Factor y(t).
-4*t**2*(t - 1)*(t + 1)**2
Let a(y) = y**2 - 7*y - 8. Let d be a(8). Suppose -3*b + 0*b = d. Let b + 0*c - 2/7*c**4 - 2/7*c**2 - 4/7*c**3 = 0. What is c?
-1, 0
Let k(v) = -3 - 2*v + 0*v - 1. Let q be k(-3). What is z in -6*z**2 + 0*z + q*z + 4*z**2 + 4 = 0?
-1, 2
Let u(w) = w + 6. Let v be u(-5). Let q(k) = 3*k. Let n be q(v). Factor n*p**4 + 2*p + 3*p - 15*p**2 + 3*p**5 - 6*p - 5*p - 9*p**3.
3*p*(p - 2)*(p + 1)**3
Factor 2/11*t**5 + 4/11*t**2 + 8/11*t**4 + 0*t + 10/11*t**3 + 0.
2*t**2*(t + 1)**2*(t + 2)/11
Let s(z) be the third derivative of z**7/1260 + z**6/90 + z**5/15 + z**4/12 - 4*z**2. Let g(o) be the second derivative of s(o). Let g(j) = 0. Calculate j.
-2
Suppose -3*o = -2*o - 5. Suppose -v + 3*u = -2*u - 2, 68 = o*v + 4*u. Factor 8*c**4 + 2*c + v*c**3 + c**5 + c**5 + 12*c**2 - 4*c**2.
2*c*(c + 1)**4
Let u = 14/17 + -36/85. Factor -2/5*a - u*a**2 + 0.
-2*a*(a + 1)/5
Let q(c) = c - 6. Let y be q(10). Let m(o) be the first derivative of y*o + 2 + 8/3*o**3 - 9*o**2. What is p in m(p) = 0?
1/4, 2
Let q(k) be the third derivative of -k**5/15 - 2*k**4/3 - 8*k**3/3 + 8*k**2. Factor q(r).
-4*(r + 2)**2
Let h be ((-56)/21)/((-4)/6). Suppose h*a - 6 = a. Solve -1/2*l - 4*l**a - 5/2*l**3 + 1 = 0 for l.
-1, 2/5
Let l(f) be the first derivative of f**3/5 + 9*f**2/5 + 27*f/5 + 4. Let l(x) = 0. Calculate x.
-3
Let d = 643/2 + -321. Factor -1/3 + d*r - 1/6*r**2.
-(r - 2)*(r - 1)/6
Let o = 83 - 77. Let g(r) be the first derivative of 0*r - 7/15*r**o + 32/25*r**5 - 1 + 0*r**2 - 2/5*r**4 + 0*r**3. Find i, given that g(i) = 0.
0, 2/7, 2
Let d = -3/29 + 93/58. Factor d*i - 1 - 1/2*i**2.
-(i - 2)*(i - 1)/2
Let v be ((-1)/12)/((-2)/8). Determine b so that -v*b + 0 + 1/3*b**3 + 1/3*b**2 - 1/3*b**4 = 0.
-1, 0, 1
Let y(j) = -18*j - 24. Let w(s) = 14 + 4*s + 14*s - s**2 + 9. Let o(k) = 3*w(k) + 4*y(k). Factor o(l).
-3*(l + 3)**2
Let -60*f - 67 + 3*f**2 + 100 + 267 = 0. Calculate f.
10
Let l(i) = -8*i + 11. Let h be l(1). Suppose -1/3*c**5 - 2/3*c**4 + 0*c - 1/3*c**h + 0 + 0*c**2 = 0. What is c?
-1, 0
Let d(r) = -r**2 + 6*r + 3. Let p be d(6). Factor 3*u**5 - 6*u**p + 0*u**3 + 3*u**3.
3*u**3*(u - 1)*(u + 1)
Let v = 9 + -6. Let c be ((-1)/2)/((-2)/4). Find k such that 0 - 3 + c + 3*k**v + 3*k - 4*k**3 = 0.
-2, 1
Let q(l) be the first derivative of 1/6*l**2 + 2*l + 2 + 1/36*l**4 - 1/9*l**3. Let p(m) be the first derivative of q(m). Suppose p(z) = 0. Calculate z.
1
Let i(w) = w + 1. Let s be i(-1). Factor s*t**4 - 2*t**4 + 2*t**4 - 2*t**4 + 2*t**2.
-2*t**2*(t - 1)*(t + 1)
Let r(f) = 6*f - 21 + f**3 + 9 + 10*f**2 + 0*f**3. Let v be r(-9). Determine b so that -50*b**2 - 5*b + 30*b - 8 + v*b = 0.
2/5
Let o(h) be the first derivative of -h**6/225 - h**5/150 + h**4/90 + h**3/45 + 5*h - 5. Let j(t) be the first derivative of o(t). Factor j(m).
-2*m*(m - 1)*(m + 1)**2/15
Let b = 10 - 10. Let d(h) be the third derivative of -2*h**2 + 0 + 0*h**3 + b*h**4 + 1/90*h**5 + 0*h + 1/360*h**6 - 1/630*h**7. Find m, given that d(m) = 0.
-1, 0, 2
Let t = -309 - -935/3. Let 2/3*b - t*b**4 + 0 - 8/3*b**2 + 2/3*b**5 + 4*b**3 = 0. What is b?
0, 1
Suppose 2*w - 2*x + 2 = 0, 3*w - 3*x = 2*x - 11. Factor 0*k + 20*k**5 - 19*k**5 - k**w + 0*k.
k**3*(k - 1)*(k + 1)
Let n(a) be the second derivative of 2/35*a**5 + 1/105*a**6 + 1/7*a**4 + 4/21*a**3 + 0 + 1/7*a**2 + 2*a. Solve n(g) = 0.
-1
Let v(w) be the third derivative of 7*w**8/96 - 3*w**7/10 + 11*w**6/240 + 59*w**5/60 - 5*w**4/4 + 2*w**3/3 + 2*w**2. What is q in v(q) = 0?
-1, 2/7, 1, 2
Suppose -3*q = u - 1 - 3, 5*u + 10 = 0. Factor 2/3 - 2/3*s**3 + 2*s**2 - q*s.
-2*(s - 1)**3/3
Let x = -10 - -17. Let m(t) be the third derivative of 0*t + 1/360*t**6 + 1/210*t**x + 1/9*t**3 + 0 + 2*t**2 - 1/36*t**5 - 1/72*t**4. Factor m(j).
(j - 1)*(j + 1)**2*(3*j - 2)/3
What is v in -3/4*v**2 - 3/2 - 15/4*v + 3/2*v**3 = 0?
-1, -1/2, 2
Let w be (4/28)/(1/(-15)). Let a = 17/7 + w. Factor -4/7*j + 0 + a*j**2.
2*j*(j - 2)/7
Factor 2/7*y + 1/7*y**2 - 1/7*y**3 + 0.
-y*(y - 2)*(y + 1)/7
Let x(j) = -j**4 + 4*j**3 - 5*j**2 - 4*j - 6. Let a(t) = -10*t**4 + 45*t**3 - 55*t**2 - 45*t - 65. Let u(f) = -6*a(f) + 65*x(f). Let u(d) = 0. Calculate d.
-2, -1, 0, 1
Let x = -57784/5 + 11432. Let q = -124 - x. Suppose -2/5*i**2 + q*i - 2/5 = 0. Calculate i.
1
Suppose v - 2*v = 4. Let h be 8/(-3)*6/v. Let -4*a**2 + 2*a - 2*a**5 + 0*a + 5*a**4 - a**h = 0. What is a?
-1, 0, 1
Let l(a) be the second derivative of 0 - 26/3*a**3 + 19/2*a**4 - 19/4*a**5 + 4*a + 4*a**2 + 5/6*a**6. Suppose l(m) = 0. Calculate m.
2/5, 1, 2
Let o = 513 + -5639/11. Let 2/11*u**2 + 2/11 + o*u = 0. What is u?
-1
Let a = 9/19 - 61/209. Solve a - 6/11*t - 2/11*t**3 + 6/11*t**2 = 0 for t.
1
Factor 0 - p**2 - 1/5*p**4 + 4/5*p**3 + 2/5*p.
-p*(p - 2)*(p - 1)**2/5
Let a(g) be the second derivative of 1/3*g**3 + 1/12*g**4 + 0 + 1/180*g**6 + 0*g**2 + g - 1/30*g**5. Let x(b) be the second derivative of a(b). Factor x(o).
2*(o - 1)**2
Let c(s) = -s**4 + s**3 - s**2 - s - 1.