 v(g) be the second derivative of g**7/168 - g**6/120 - 3*g**5/80 + g**4/48 + g**3/12 + 10*g. Factor v(m).
m*(m - 2)*(m - 1)*(m + 1)**2/4
Let l = -14881/92560 + -2/1157. Let s = l - -9/16. Find h such that -2*h**2 - s - 4/5*h**3 - 8/5*h = 0.
-1, -1/2
Let h(u) = 6*u**2 - 4*u + 4. Let i(a) = -7*a**2 + 4*a - 5. Let q(x) = -5*h(x) - 4*i(x). Factor q(p).
-2*p*(p - 2)
Let i(m) = -2*m + 6. Let t be i(5). Let h = 7 + t. Factor -4*l**h + l**2 + 3*l**3 + 2*l**3.
l**2*(l + 1)
Let g(r) be the second derivative of -2*r**7/49 + 4*r**6/21 - 3*r**5/35 + 12*r. Factor g(n).
-4*n**3*(n - 3)*(3*n - 1)/7
Let s(i) be the third derivative of 1/15*i**6 + 0*i + 2/3*i**3 - 2/15*i**5 - 1/84*i**8 + 2/105*i**7 + 0 + 9*i**2 - 1/6*i**4. Suppose s(c) = 0. Calculate c.
-1, 1
Factor 3*u**4 - 5*u**3 + 8*u**3 - 4*u**3 + u**5 + 2*u**3 - 2*u - 3*u**2.
u*(u - 1)*(u + 1)**2*(u + 2)
Let m(w) be the first derivative of 5/6*w**4 + 8/15*w**5 + 0*w**2 - 1 + 0*w + 2/9*w**3. Factor m(x).
2*x**2*(x + 1)*(4*x + 1)/3
Let k(d) be the second derivative of d**6/80 - 3*d**5/40 + 3*d**4/32 + 40*d. Find l, given that k(l) = 0.
0, 1, 3
Suppose 15/8*r**2 + 3/8*r**3 + 3*r + 3/2 = 0. Calculate r.
-2, -1
Suppose 0 = -7*v + 11*v. Let u(y) be the second derivative of 0*y**2 - 2*y + v - 1/18*y**3 - 1/18*y**4 - 1/60*y**5. Let u(k) = 0. What is k?
-1, 0
Let x(o) be the third derivative of -1/48*o**4 + 0*o**3 - 3*o**2 + 1/240*o**5 + 0*o + 0. Factor x(d).
d*(d - 2)/4
Factor 0 + j**2 + 1/3*j + 1/3*j**4 + j**3.
j*(j + 1)**3/3
Suppose 3*q = -19 + 7, 3*q + 4 = -4*o. Solve -10*c**o + 3*c - 4*c**4 + 12*c**3 - 2*c**2 + c = 0.
0, 1
Factor 0*a**3 + 0*a + 0*a**2 + 1/3*a**5 + 0 + 1/3*a**4.
a**4*(a + 1)/3
Let a = 3 - 3. Solve -s**5 - 2*s**2 + s + s**4 + 2*s**3 + a*s**2 - 2*s + 1 = 0.
-1, 1
Factor -12/11 - 6/11*p**5 - 96/11*p**2 - 54/11*p - 84/11*p**3 - 36/11*p**4.
-6*(p + 1)**4*(p + 2)/11
Let u(t) be the third derivative of 9*t**7/70 - 3*t**6/20 - t**5 - t**4 + 5*t**2. Find i such that u(i) = 0.
-2/3, 0, 2
Let a(h) be the second derivative of h**5/20 + h**4/8 + h**2 + h. Let s(y) be the first derivative of a(y). Solve s(r) = 0 for r.
-1, 0
Factor -3/2 - 5/2*b**2 + 1/2*b**3 + 7/2*b.
(b - 3)*(b - 1)**2/2
Let 2/7*f**4 + 6/7*f**3 + 0 + 6/7*f**2 + 2/7*f = 0. What is f?
-1, 0
Suppose 3*y + 6 = 24. Factor -t**3 + 6*t**2 - y*t**2.
-t**3
Let j(a) be the second derivative of -a**6/120 - a**5/30 + a**2/2 - 2*a. Let u(z) be the first derivative of j(z). Solve u(w) = 0.
-2, 0
Let n be -12*(7/28)/(6/(-8)). Let y(d) be the third derivative of -1/12*d**n + 0*d - 1/6*d**3 + 0 - 1/60*d**5 + 3*d**2. Factor y(q).
-(q + 1)**2
Let c be 434/72 - 2/(-9). Let w = c - 6. Solve -1/4 - w*l**4 - 3/2*l**2 - l - l**3 = 0 for l.
-1
Let f(c) = -7*c**2 - 3*c - 2. Let y(w) = 4*w - 7. Let t be y(6). Let s(q) = -20*q**2 - 8*q - 6. Let a(v) = t*f(v) - 6*s(v). Factor a(k).
(k - 2)*(k - 1)
Let j(r) be the third derivative of -2/15*r**6 + 0*r + 25/336*r**8 + 0*r**3 + 0*r**4 - 1/42*r**7 + 0 + 3*r**2 - 1/15*r**5. Find f, given that j(f) = 0.
-2/5, 0, 1
Let x(q) be the first derivative of 4*q**5/5 - 16*q**4 + 120*q**3 - 400*q**2 + 500*q + 38. Factor x(w).
4*(w - 5)**3*(w - 1)
Let g(k) be the second derivative of k**4/12 + 3*k. Factor g(j).
j**2
Let q(i) = i**2 + i - 9. Let w be q(3). Let -1/3*p**2 - 1/3*p**w + 0 + 0*p + 1/3*p**4 + 1/3*p**5 = 0. Calculate p.
-1, 0, 1
Suppose 3/7*g**3 + 6/7*g**2 - 12/7*g - 24/7 = 0. Calculate g.
-2, 2
Let o = -54 + 58. Let f(d) be the second derivative of 3*d + 0*d**2 + 0*d**3 + 0 - 1/36*d**o. Determine t, given that f(t) = 0.
0
Factor 1/2*c**2 + 3/2*c**3 + 3/2*c**4 + 0*c + 1/2*c**5 + 0.
c**2*(c + 1)**3/2
Suppose -9*v = -13*v. Let g(s) be the third derivative of s**2 + 0*s - 1/630*s**7 + 0 + v*s**3 - 1/72*s**4 + 1/360*s**6 + 1/180*s**5. Factor g(x).
-x*(x - 1)**2*(x + 1)/3
What is l in 0 + 3/2*l - 1/2*l**4 + 5/2*l**3 - 7/2*l**2 = 0?
0, 1, 3
Let o = -4198/49 + 31092/49. Let a = -548 + o. Factor -4/7*g + 0 + a*g**2 - 2/7*g**3.
-2*g*(g - 2)*(g - 1)/7
Let i be (-21)/9 - -3 - (-68)/(-120). Let a(k) be the second derivative of -1/3*k**3 - i*k**5 - 4*k + 1/3*k**4 + 0*k**2 + 0. Determine q, given that a(q) = 0.
0, 1
Let g(x) be the third derivative of -1/40*x**6 + 0*x + 3/10*x**5 - 9/8*x**4 - 7*x**2 + 0*x**3 + 0. Solve g(k) = 0 for k.
0, 3
Let h(m) be the second derivative of m**6/10 + 7*m**5/20 + m**4/4 - m**3/2 + 3*m**2 + 3*m. Let g(u) be the first derivative of h(u). Factor g(x).
3*(x + 1)**2*(4*x - 1)
Let j(l) be the first derivative of l**4/4 - l**3/6 + 2. Suppose j(p) = 0. What is p?
0, 1/2
Let u(o) be the second derivative of -o**7/105 + 2*o**6/75 - o**5/50 + 4*o. Factor u(c).
-2*c**3*(c - 1)**2/5
Let r(y) = -19*y**4 + 35*y**3 - 43*y**2 + 31*y + 9. Let b(w) = -9*w**4 + 17*w**3 - 21*w**2 + 15*w + 4. Let k(t) = 13*b(t) - 6*r(t). Let k(u) = 0. What is u?
2/3, 1
Let h(k) = -5*k**4 - k**3 + 17*k**2 - 11*k. Let g(j) = 3*j**4 - 9*j**2 + 6*j. Let l(u) = -7*g(u) - 4*h(u). Factor l(c).
-c*(c - 2)*(c - 1)**2
Let o(l) be the first derivative of -l**5/100 - l**4/60 + l - 3. Let z(v) be the first derivative of o(v). Let z(t) = 0. What is t?
-1, 0
Let g(n) be the third derivative of n**7/1050 - n**6/300 + n**5/300 - 5*n**2. Factor g(o).
o**2*(o - 1)**2/5
Let 2/7*h**3 + 0 + 2/7*h**4 + 0*h + 0*h**2 = 0. Calculate h.
-1, 0
Let l = 9 - -104. Let y = 793/7 - l. Solve 4/7*x - y*x**2 + 0 = 0 for x.
0, 2
Let q = -19 + 12. Let u be q/28*4/(-3). Find v such that 1/3 - 2/3*v + 2/3*v**3 + 0*v**2 - u*v**4 = 0.
-1, 1
Let i be (-47)/(-8) - (-1)/8. Let l(c) be the second derivative of 0*c**2 + 1/135*c**i + 0 + 0*c**4 - 3*c + 0*c**3 + 0*c**5. Factor l(b).
2*b**4/9
Let p be (-5 + 5)/(2 - 0). Let k(l) be the second derivative of l + 1/105*l**7 + p - 1/15*l**3 + 0*l**5 + 1/15*l**4 - 2/75*l**6 + 0*l**2. Factor k(g).
2*g*(g - 1)**3*(g + 1)/5
Suppose 0 = -3*u + 38 - 11. Let y = u + -5. Factor 0*c**3 + 0*c**2 + 0 + 1/4*c**y + 0*c.
c**4/4
Suppose 5*k + 2 = 4*y + 4, 3*y + 2 = 4*k. Solve 0 - 1/3*u**3 - 2/3*u + u**y = 0.
0, 1, 2
Let c(t) be the third derivative of 0*t + 0 - 3*t**2 - 1/120*t**5 + 0*t**4 + 1/12*t**3. Factor c(a).
-(a - 1)*(a + 1)/2
Let p be 3/6*-2 - -3. Let f be 1*p/(-12)*-8. Let f*k**3 + 0 + 0*k + 1/3*k**2 + 4/3*k**4 = 0. What is k?
-1/2, 0
Let m = 455 + -453. Factor 2*p**m - 8/3 + 0*p - 2/3*p**3.
-2*(p - 2)**2*(p + 1)/3
Determine y so that -33*y**3 + 25/2*y**5 - 4*y - 5/2*y**4 + 0 - 22*y**2 = 0.
-1, -2/5, 0, 2
Let g(s) be the second derivative of -s**7/168 - s**6/120 + s**5/80 + s**4/48 + 8*s. Factor g(o).
-o**2*(o - 1)*(o + 1)**2/4
Let g be (-1)/(3/(-36)*3). What is b in 18/5*b**3 + 0*b + 4/5*b**2 + 0 - 4/5*b**g - 18/5*b**5 = 0?
-1, -2/9, 0, 1
Let 121*y**3 - 12 - 118*y**3 - 2*y - 10*y + 3*y**2 = 0. What is y?
-2, -1, 2
Let l(k) be the third derivative of -k**8/8400 - k**7/1400 - k**6/900 - k**3/3 - 3*k**2. Let a(f) be the first derivative of l(f). Let a(b) = 0. Calculate b.
-2, -1, 0
Let v = -98 + 886/9. Solve v*j - 2/9 - 2/9*j**2 = 0 for j.
1
Let l be 16/24 - (-34)/3. Factor -14*p**3 + 7*p**3 - 8*p**3 + 6*p**2 + 0*p**4 + l*p**4 - 3*p**5.
-3*p**2*(p - 2)*(p - 1)**2
Let o = 19 + -19. Suppose o = -d + 4*d - 4*n - 12, 12 = -2*d - 4*n. Let d + 0*x + 3/4*x**3 + 3/2*x**2 = 0. What is x?
-2, 0
Let j be -1*(-6 - (-115)/20). Factor -j*b**3 + 0 - 3/4*b**2 - 1/2*b.
-b*(b + 1)*(b + 2)/4
Let q(l) be the second derivative of 10*l**6/21 - 16*l**5/7 - 76*l**4/21 - 32*l**3/21 + 7*l. Find h, given that q(h) = 0.
-2/5, 0, 4
Let 144*r + 4*r**3 + 48*r**2 - 82 + 82 = 0. What is r?
-6, 0
Let r be 136/102*(-6)/(-32). Factor -1/4*h**2 + r*h**3 + 0 - 1/2*h.
h*(h - 2)*(h + 1)/4
Suppose -4*n**4 + 27*n + 18*n - 8*n**3 + 4*n**2 - 37*n = 0. Calculate n.
-2, -1, 0, 1
Let f(l) be the first derivative of l**7/63 - l**5/10 - l**4/9 + 5*l + 4. Let j(u) be the first derivative of f(u). Determine m, given that j(m) = 0.
-1, 0, 2
Suppose -17 + 3 = -7*t. Factor 4/7 + 0*p**t + 6/7*p - 2/7*p**3.
-2*(p - 2)*(p + 1)**2/7
Let p be (-4)/((-7)/((-42)/(-12))). Let y(q) = -q + 11. Let x be y(6). Factor -10/3*o**4 + 20/3*o**3 - 2/3 - 20/3*o**p + 10/3*o + 2/3*o**x.
2*(o - 1)**5/3
Let j be 3*123/63 + -3. Factor -j*p**3 - 2/7 - 10/7*p - 20/7*p**2 - 10/7*p**4 - 2/7*p**5.
-2*(p + 1)**5/7
Suppose 4*m - 1 - 11 = 0. Suppose -4*j + s + 15 = -2*s, 0 = -m*j - 4*s + 5. Factor 0 - 1/2*n - 1/2*n**4 + 1/2*n**j + 1/2*n