et t(m) be the second derivative of -8*m + 0*m**3 + 0 + 0*m**2 - 1/336*m**7 + 0*m**4 - 1/160*m**5 - 1/120*m**6. Determine w, given that t(w) = 0.
-1, 0
Let x(y) be the first derivative of y**5/240 - y**4/96 + 9*y**2/2 - 20. Let i(k) be the second derivative of x(k). Find l, given that i(l) = 0.
0, 1
Factor -315 + y**2 - 56*y + 9*y**2 + 111 - 6*y**2.
4*(y - 17)*(y + 3)
Let t(d) be the third derivative of d**6/420 - d**5/42 - d**4/14 - 6*d**2 + 2*d. Find c such that t(c) = 0.
-1, 0, 6
Suppose 8*r - 32*r + 46 = -r. Factor 2/7*f**r - 2/7 + 0*f.
2*(f - 1)*(f + 1)/7
Suppose 3*q = -11*q + 28. Factor -v**2 + 2*v**3 + 6*v**2 + 6*v - 2*v**2 + 20 - 15*v**q.
2*(v - 5)*(v - 2)*(v + 1)
Let p(w) = -w**3 - 14*w**2 + 9. Let x be p(-14). Factor 12*l + l**2 + x*l - 18*l.
l*(l + 3)
Let r = -236 + 422. Let s = -183 + r. Let 0*n - 2/5*n**2 + 2/5*n**s + 0 = 0. Calculate n.
0, 1
Let a(v) be the third derivative of v**8/120960 - v**6/4320 + v**5/60 - 7*v**2. Let m(h) be the third derivative of a(h). Solve m(q) = 0 for q.
-1, 1
Let o(z) be the first derivative of 0*z - 1/120*z**6 - 5 - 1/30*z**5 + 1/24*z**4 - 3*z**2 + 1/3*z**3. Let i(k) be the second derivative of o(k). Factor i(f).
-(f - 1)*(f + 1)*(f + 2)
Let y(a) be the third derivative of a**8/336 - 2*a**7/105 + a**6/30 - 5*a**2 - 3*a. Factor y(k).
k**3*(k - 2)**2
Let h = 29 - 29. Suppose 2*z - 7*z + 10 = h. What is w in -5 + 3*w**2 + 3 + 0*w**z - 1 = 0?
-1, 1
Let q(r) be the third derivative of r**8/8064 - r**7/504 + r**6/72 - r**5/12 - 19*r**2. Let k(p) be the third derivative of q(p). Factor k(c).
5*(c - 2)**2/2
Let i(s) = 7*s**3 - 7*s**2 - 9*s. Let m(t) = 4*t**3 - 4*t**2 - 5*t. Suppose -3 = h - 8. Suppose h*z - 48 = 2. Let w(a) = z*m(a) - 6*i(a). Solve w(g) = 0.
-1, 0, 2
Let l be 20/75 - (-3 + 39/12). Let n(h) be the second derivative of -l*h**6 + 0 + 0*h**3 + 3/40*h**5 - 1/12*h**4 - 8*h + 0*h**2. What is v in n(v) = 0?
0, 1, 2
Let x = 32 + -30. Suppose -3*h - x = -4*h. Solve 27/5 + 3/5*n**h + 18/5*n = 0.
-3
Let p(k) be the third derivative of k**5/45 - 29*k**4/9 + 1682*k**3/9 + 11*k**2. What is q in p(q) = 0?
29
Factor 4 + 0 - 5*b**5 - 4*b + 2*b**5 - 9796*b**2 + b**4 + 9787*b**2 + 11*b**3.
-(b - 1)**3*(b + 2)*(3*b + 2)
Factor -s**2 - 19 + 3*s + 21 - 4.
-(s - 2)*(s - 1)
Factor -7/2*w**3 + w**4 - 7*w**2 - 5/2*w + 0.
w*(w - 5)*(w + 1)*(2*w + 1)/2
Let u(o) be the second derivative of o**2 + 1/12*o**4 + 1/12*o**5 + 0 + 0*o**3 - 7/120*o**6 + 4*o. Let i(r) be the first derivative of u(r). Factor i(p).
-p*(p - 1)*(7*p + 2)
Let z(d) = -26*d**2 - 26*d - 16. Suppose c + 0 = -16. Let t(u) = -5*u**2 - 5*u - 3. Let o(m) = c*t(m) + 3*z(m). Find f such that o(f) = 0.
-1, 0
Let p(g) = 5*g**2 - 986*g + 49001. Let w(b) = 60*b**2 - 11830*b + 588010. Let u(o) = -25*p(o) + 2*w(o). Determine y, given that u(y) = 0.
99
Let j(q) be the first derivative of -9 + 0*q**2 + 5/27*q**3 - 1/36*q**4 + 0*q. Factor j(b).
-b**2*(b - 5)/9
Let a(m) be the third derivative of -m**7/420 - m**6/48 + 7*m**5/60 + 929*m**2. Factor a(r).
-r**2*(r - 2)*(r + 7)/2
Let k(c) be the third derivative of -1/90*c**5 - 8*c**2 - 1/60*c**6 + 0*c + 0 + 1/18*c**4 + 0*c**3. Find j, given that k(j) = 0.
-1, 0, 2/3
Find t such that 9/5*t**3 - 3/5 - 9/5*t - 12/5*t**4 + 3*t**2 = 0.
-1, -1/4, 1
Let v(x) = 17*x**2 - 1141*x - 285. Let q(m) = 18*m**2 - 1139*m - 285. Let n(i) = -3*q(i) + 2*v(i). Find w such that n(w) = 0.
-1/4, 57
Let t(v) be the second derivative of 4/3*v**3 + 0*v**2 + 3 + v + 1/6*v**4. Factor t(b).
2*b*(b + 4)
Let -44/7*s**2 + 10/7*s**4 + 24/7*s + 16/7 - 6/7*s**3 = 0. What is s?
-2, -2/5, 1, 2
Let j be -3 + (-567)/(-77) + -4. Find f, given that 0 + 2/11*f**2 - j*f + 2/11*f**3 = 0.
-2, 0, 1
Let d(h) = -2*h**3 + 14*h**2 - h + 9. Let c be d(7). Factor -c*f**4 - 20*f**3 + 4*f**4 - 104 + 176 + 74*f**2 - 120*f.
2*(f - 3)**2*(f - 2)**2
Factor -6*l - 158 + 13*l - 420 - 2*l**2 + 61*l.
-2*(l - 17)**2
Let c(k) be the second derivative of -k**3/6 - 8*k. Let n be c(-2). Factor 22 + 3*a**n - 22 + 3*a**3.
3*a**2*(a + 1)
Let l(s) be the first derivative of 7*s**4 + 12/5*s**5 - 2 + 32*s - 24*s**2 - 8*s**3. Let l(j) = 0. What is j?
-2, 2/3, 1
Let c(f) be the third derivative of 0 + 3*f**2 - 1/10*f**5 - 5/6*f**3 + 0*f - 1/24*f**4. Let x(u) = -u**2 - 1. Let g(a) = -3*c(a) + 15*x(a). Factor g(s).
3*s*(s + 1)
Let j(x) be the second derivative of x**7/84 + x**6/45 - x**5/60 - 14*x**3/3 - 18*x. Let l(g) be the second derivative of j(g). Factor l(a).
2*a*(a + 1)*(5*a - 1)
Let u(i) be the first derivative of -i**4/12 - i**3/3 + 3*i**2/2 - 10*i - 1. Let n(w) be the first derivative of u(w). Solve n(p) = 0.
-3, 1
Let j(i) be the third derivative of 0*i**3 + 1/70*i**7 + 0*i - 1/10*i**5 + 0*i**4 - 1/40*i**6 + 0 - 2*i**2. Factor j(q).
3*q**2*(q - 2)*(q + 1)
Let s(v) = -6080*v**3 - 6704*v**2 - 640*v - 16. Let b(i) = 6081*i**3 + 6705*i**2 + 640*i + 16. Let n(d) = -4*b(d) - 3*s(d). Solve n(t) = 0.
-1, -2/39
Let s(k) = 9*k**3 + 6*k**2 + 4*k + 4. Let b(n) = 10*n**2 + 25 + 25*n + 38*n**3 - 2*n**3 + 25*n**2 + 19*n**3. Let f(a) = 4*b(a) - 25*s(a). Solve f(t) = 0 for t.
-2, 0
Suppose 1284*p - 1423*p + 278 = 0. Factor -70/9*u**3 + 0 + 4/3*u - 22/9*u**p.
-2*u*(5*u + 3)*(7*u - 2)/9
Let s(x) be the first derivative of -x**4/14 - 8*x**3/7 + 27*x**2/7 - 4*x + 71. Find m, given that s(m) = 0.
-14, 1
Let i(y) = -2*y**3 + 16*y**2 - 5*y - 16. Let h be i(7). Factor 41 + 20*o - 7*o + 5*o**3 + h*o - 81 - 30*o**2.
5*(o - 2)**3
Let c(n) be the third derivative of -1/540*n**6 - 1/135*n**5 + 6*n**2 + 0*n**3 + 0*n + 0 - 1/108*n**4. Suppose c(m) = 0. What is m?
-1, 0
Let i(p) = 7*p**4 - 28*p**3 - 85*p**2 - 70*p. Let v(j) = -48*j**4 + 195*j**3 + 597*j**2 + 489*j. Let m(a) = 27*i(a) + 4*v(a). Factor m(g).
-3*g*(g - 11)*(g + 1)*(g + 2)
Let c(j) = -j**3 - 37*j - 136. Let t be c(-3). Suppose 0 - 1/2*h + 3/4*h**t = 0. Calculate h.
0, 2/3
Let l(c) be the second derivative of 0*c**2 + 5/12*c**4 - 1/6*c**6 + 0 + 5*c - 1/2*c**5 + 5/3*c**3. Factor l(x).
-5*x*(x - 1)*(x + 1)*(x + 2)
Let n be (140/16)/(-5)*185/(-35). Factor 21/4*x**3 - n*x + 25/2*x**2 + 3/2.
(x + 3)*(3*x - 1)*(7*x - 2)/4
Let w(j) be the second derivative of -j**6/120 + 7*j**5/40 - 11*j**4/16 - 14*j**3/3 - 8*j**2 + j - 2. Determine k, given that w(k) = 0.
-1, 8
Let f(n) be the second derivative of n**5/90 + 13*n**4/18 + 169*n**3/9 + 2197*n**2/9 - 2*n + 27. Factor f(c).
2*(c + 13)**3/9
Let u(y) be the third derivative of -y**6/120 + 5*y**5/12 - 143*y**4/24 - 169*y**3/6 - 83*y**2. Factor u(a).
-(a - 13)**2*(a + 1)
Let r be ((-1)/15)/((-7464)/268524). Let o = r - -1/622. Factor -8/5*d + o*d**2 - 4/5*d**3 + 0.
-4*d*(d - 2)*(d - 1)/5
Let g = -278 - -264. Let v be ((-34)/g + -2)/((-93)/(-62)). Factor 1/7*p**2 - 3/7 - v*p.
(p - 3)*(p + 1)/7
Solve 4/3*m**4 + 40/3*m + 0 - 76/3*m**2 + 32/3*m**3 = 0.
-10, 0, 1
Let f(a) be the first derivative of -14*a**5/5 - 11*a**4/2 + 16*a**3 + 44*a**2 + 32*a + 17. Suppose f(b) = 0. Calculate b.
-2, -1, -4/7, 2
What is j in 0 + 6/13*j**3 - 32/13*j**2 + 2/13*j**4 + 24/13*j = 0?
-6, 0, 1, 2
Let i(o) be the second derivative of -o**5/4 - 205*o**4/4 - 8405*o**3/2 - 344605*o**2/2 - 261*o. Solve i(n) = 0.
-41
Let r(o) be the third derivative of o**8/8400 - o**7/1800 - o**6/1800 + 11*o**4/24 - 14*o**2. Let w(l) be the second derivative of r(l). Factor w(q).
q*(q - 2)*(4*q + 1)/5
Let u(o) be the second derivative of -o**4/60 + 3*o**3/5 - 81*o**2/10 - 352*o. Suppose u(n) = 0. What is n?
9
Let r(g) be the third derivative of 2*g**6/75 - 46*g**5/75 + 89*g**4/120 - 11*g**3/30 + 109*g**2. Factor r(o).
(o - 11)*(4*o - 1)**2/5
Let k(x) be the second derivative of x**7/630 - x**6/60 + x**5/15 + 5*x**4/12 + x. Let c(d) be the third derivative of k(d). Determine v so that c(v) = 0.
1, 2
Let l(p) be the first derivative of 35*p**3/3 - 30*p**2 - 20*p + 60. Suppose l(n) = 0. Calculate n.
-2/7, 2
Let m = 136 - -2. Factor -d**2 - 55*d**2 + m*d**3 + 50*d**5 - 78*d**4 + 8*d - 62*d**4.
2*d*(d - 1)**2*(5*d - 2)**2
Let j(p) be the second derivative of -p**5/10 - 5*p**4/6 + 13*p**3/3 - 7*p**2 - 2*p + 64. Determine i so that j(i) = 0.
-7, 1
Suppose 423 = -5*q + 1173. Let a = q + -446/3. Factor -a + 8/3*x + 1/3*x**3 - 5/3*x**2.
(x - 2)**2*(x - 1)/3
Let s = 89 + -86. Suppose -6*f**s + 4*f**2 + 253*f - 237*f - 6*f**3 = 0. What is f?
-1, 0, 4/3
Let i(r) = -3*r**2 - 18*