be the second derivative of a**6/30 - a**4/6 + a**2/2 + 7*a. Determine b, given that x(b) = 0.
-1, 1
Let p = 69/7 - 65/7. Factor p*k + 1/7*k**3 + 4/7*k**2 + 0.
k*(k + 2)**2/7
Let k(v) be the second derivative of v**6/1800 - v**5/200 + v**4/60 - v**3/2 + 5*v. Let u(r) be the second derivative of k(r). Determine s, given that u(s) = 0.
1, 2
Let m(i) be the first derivative of -i**5/210 + i**3/21 + 3*i**2 - 3. Let v(d) be the second derivative of m(d). Let v(s) = 0. What is s?
-1, 1
Let z(b) = -2*b**5 + 4*b**4 + 4*b**2 - 6*b. Let i(x) = -x**4 + x**3 - x**2 + x. Let t(r) = -4*i(r) - z(r). Solve t(n) = 0.
-1, 0, 1
Let r(x) be the third derivative of x**7/210 - x**6/72 - x**5/180 + 5*x**4/72 - x**3/9 - x**2. What is a in r(a) = 0?
-1, 2/3, 1
Let w(m) = 3*m + 6. Let r(n) = n**2 - 3*n - 6. Let h(d) = 3*r(d) + 2*w(d). Factor h(y).
3*(y - 2)*(y + 1)
Suppose 2*p - 26 = -6. Let t be (-2)/(-7) + p/14. Determine d so that 3*d - 11*d**3 - 4*d - t + 4*d**4 + 12*d**2 - 3*d**2 = 0.
-1/4, 1
Suppose -183*v**2 + 187*v**2 - 4 + 0 = 0. What is v?
-1, 1
Suppose 24 = -2*g + 2*t, -g + 9 = -5*t + 29. Let s be (3 - 0)*g/(-15). Factor 1/3*j**4 + 0*j + 0*j**3 - 1/3*j**s + 0.
j**2*(j - 1)*(j + 1)/3
Let p(s) be the third derivative of 3*s**2 + 1/60*s**6 - 1/42*s**5 + 0*s - 4/21*s**3 + 0 - 4/21*s**4. Factor p(f).
2*(f - 2)*(f + 1)*(7*f + 2)/7
Let h(a) be the first derivative of -a**5/3 + 5*a**4/8 + 35*a**3/18 - 5*a**2 + 10*a/3 + 31. Solve h(v) = 0 for v.
-2, 1/2, 1, 2
Let s(h) be the third derivative of 0*h**4 + 0 - 3*h**2 + 0*h + 0*h**3 + 0*h**5 + 1/525*h**7 - 1/300*h**6. Suppose s(i) = 0. What is i?
0, 1
Let m(s) = 90*s**3 - 69*s**2 - 90*s + 69. Let z = 43 + -70. Let h(q) = -13*q**3 + 10*q**2 + 13*q - 10. Let x(d) = z*h(d) - 4*m(d). Factor x(b).
-3*(b - 1)*(b + 1)*(3*b - 2)
Suppose m**2 + m**4 - 5 - 377*m + 3 + 374*m + 3*m**3 = 0. Calculate m.
-2, -1, 1
Solve s**4 + 0*s**2 - 4/9*s + 0 + 2/9*s**5 + 11/9*s**3 = 0 for s.
-2, -1, 0, 1/2
Suppose 3*w - 15 = -0*w + 3*y, -5*y - 19 = -2*w. Factor -p + p**5 + 0*p**5 + w*p**4 + 0*p + p**2 - 3*p**2.
p*(p - 1)*(p + 1)**3
Let i(s) be the second derivative of -1/15*s**6 + 0 + 0*s**2 + 2*s + 3/10*s**5 - 1/2*s**4 + 1/3*s**3. Factor i(l).
-2*l*(l - 1)**3
Let p(t) = -t**2 + 7*t - 1. Let v be p(7). Let w be (-24)/(-20) - (0 - v). Solve w*y - 1/5*y**3 + 0*y**2 + 0 = 0.
-1, 0, 1
Let x be 0 - (2 - (-18)/(-7)). Let a(z) be the second derivative of 1/42*z**4 + 4/21*z**3 + z + 0 + x*z**2. Factor a(m).
2*(m + 2)**2/7
Let i(j) be the first derivative of 3*j**4 + 20*j**3/3 + 4*j**2 + 5. Factor i(h).
4*h*(h + 1)*(3*h + 2)
Let s be (42/(-63))/((-10)/6). Factor -12/5*a**3 + 8/5*a**4 - s*a**5 + 0 - 2/5*a + 8/5*a**2.
-2*a*(a - 1)**4/5
Let s(m) = m**2 + 5*m + 2. Let d be s(-5). Suppose -9 = -5*j + d*j. Factor -8 + 0*p**2 + 5*p**3 + 16*p - 10*p**2 - j*p**3.
2*(p - 2)**2*(p - 1)
Let d(u) be the first derivative of u**4/16 - u**3/6 - 3*u**2/8 - 7. Factor d(k).
k*(k - 3)*(k + 1)/4
Let h(y) be the second derivative of -y**7/280 + y**5/40 - y**3/6 - 2*y. Let k(d) be the second derivative of h(d). Find j such that k(j) = 0.
-1, 0, 1
Let o be ((-30)/20)/((-3)/10). Let f(m) be the second derivative of 2/15*m**6 + 2/5*m**o + 0*m**2 + 5/12*m**4 - 3*m + 0 + 1/6*m**3. Factor f(w).
w*(w + 1)*(2*w + 1)**2
Suppose 2*s - 69 = -65. Let n(j) be the first derivative of 1/6*j**3 + 3 + 1/2*j - 1/2*j**s. Factor n(l).
(l - 1)**2/2
Factor -1/4*q**2 + 1 + 1/4*q**3 - q.
(q - 2)*(q - 1)*(q + 2)/4
Factor 4/11 + 74/11*r**2 - 78/11*r.
2*(r - 1)*(37*r - 2)/11
Let k(b) be the third derivative of b**7/3780 + b**6/540 + b**5/270 + 2*b**3/3 + 4*b**2. Let f(d) be the first derivative of k(d). What is n in f(n) = 0?
-2, -1, 0
Let q be (-5)/6*27/(-135). Let j(w) be the first derivative of -q*w**3 + 0*w - 3 - 1/4*w**2. Determine m, given that j(m) = 0.
-1, 0
Factor 1/2 - 3/4*n - 1/4*n**4 + 3/4*n**3 - 1/4*n**2.
-(n - 2)*(n - 1)**2*(n + 1)/4
Factor 0 + 3*b**3 - 1/2*b**4 - 6*b**2 + 4*b.
-b*(b - 2)**3/2
Let h(n) be the first derivative of 0*n + 9 - 2*n**2 + 2/3*n**3. Suppose h(q) = 0. Calculate q.
0, 2
Let y = -35/8 + 207/40. Factor 0 + 2/5*l - y*l**2 + 2/5*l**3.
2*l*(l - 1)**2/5
Factor 30 - 32 - 14*n**3 + 2*n - n - 11*n + 26*n**2.
-2*(n - 1)**2*(7*n + 1)
Factor -5/7*j - 4/7*j**2 - 1/7*j**3 - 2/7.
-(j + 1)**2*(j + 2)/7
Let p(j) be the first derivative of 9 + 2/7*j - 3/7*j**4 + 6/7*j**2 - 2/21*j**3. Find v, given that p(v) = 0.
-1, -1/6, 1
Let t = 2 + 0. Find z such that 0*z - 2*z**5 - t*z**4 + 2*z**2 - 2*z**3 + 0*z + 4*z**5 = 0.
-1, 0, 1
Factor 9*s - s**2 + 9*s**3 - 5*s**2 - 8*s**3.
s*(s - 3)**2
Factor 41*w - 2*w**3 + 5*w**3 + 3*w**2 - 47*w.
3*w*(w - 1)*(w + 2)
Factor -17 + 13 - 6 + 5*y**2 - 5*y.
5*(y - 2)*(y + 1)
Let f(j) = -j**2 - 3*j - 1. Let a be f(-4). Let y = a + 5. Solve 0*g - 2/5*g**2 + y = 0.
0
Let v(p) be the first derivative of p**6/15 + 14*p**5/25 + 3*p**4/2 + 6*p**3/5 + 11. Factor v(b).
2*b**2*(b + 1)*(b + 3)**2/5
Let b(s) = s**4 + s**3 - s**2 - 1. Let z(o) = 8*o**4 + 4*o**2 + 12. Let g be (3/(-3))/(3/36). Let h(a) = g*b(a) - z(a). Suppose h(m) = 0. What is m?
-1, 0, 2/5
Let a(z) be the third derivative of z**5/240 - z**4/96 - 2*z**2. Find b, given that a(b) = 0.
0, 1
Let c(d) be the third derivative of d**7/105 - d**6/12 + 7*d**5/30 - d**4/4 - 10*d**2. Let c(t) = 0. What is t?
0, 1, 3
Let b(j) be the third derivative of j**7/1050 + j**6/200 + j**5/150 + 5*j**2. Determine k, given that b(k) = 0.
-2, -1, 0
Factor -f**2 + 4*f + f - 7*f.
-f*(f + 2)
Let b(p) be the third derivative of p**5/150 - 4*p**3/15 - 5*p**2. Suppose b(v) = 0. What is v?
-2, 2
Let l = -664 - -2020/3. Factor l*f**3 + 6*f + 4/3 + 32/3*f**2 + 4*f**4 + 2/3*f**5.
2*(f + 1)**4*(f + 2)/3
Let c(z) = z**2 + 5*z - 4. Let m be c(-6). Suppose 3*d - 11 = -5. Find w such that w + m*w + 3*w**d + 0*w = 0.
-1, 0
Solve 0 + 1/5*o**2 - 2/5*o = 0 for o.
0, 2
Let g be 6/(3 + 0) - 8. Let n(c) = 7*c**2 - 8*c - 5. Let q(r) = 6*r**2 - 7*r - 4. Let i(p) = g*q(p) + 5*n(p). Factor i(v).
-(v - 1)**2
Let x(m) be the first derivative of 2*m**6/3 - 4*m**4 - 8*m**3/3 + 6*m**2 + 8*m + 47. Factor x(c).
4*(c - 2)*(c - 1)*(c + 1)**3
Let n(a) be the third derivative of -a**6/540 - a**5/270 + a**4/108 + a**3/27 - 12*a**2. Factor n(t).
-2*(t - 1)*(t + 1)**2/9
Let q(g) be the third derivative of -g**5/90 - g**4/12 - 2*g**3/9 + 7*g**2. Find x, given that q(x) = 0.
-2, -1
Let d(l) be the third derivative of l**8/840 - l**7/420 + l**3/2 + 2*l**2. Let x(h) be the first derivative of d(h). Let x(r) = 0. Calculate r.
0, 1
Let c be 3/(-6)*(-4)/((-8)/(-2)). Find r, given that c*r**2 + 0 - 1/4*r = 0.
0, 1/2
Let f(l) be the first derivative of -l**5/300 - l**4/40 - l**3/15 + 5*l**2/2 + 6. Let v(m) be the second derivative of f(m). Determine u so that v(u) = 0.
-2, -1
Let f(w) be the third derivative of 0*w**4 - 2*w**2 + 0 + 1/90*w**6 + 1/90*w**5 + 0*w + 1/315*w**7 + 0*w**3. What is o in f(o) = 0?
-1, 0
Let d(f) be the first derivative of -f**2/2 + 6*f - 2. Let u be d(5). Let r**2 + 1 - 3*r**3 - u - r**5 + 3*r**4 = 0. What is r?
0, 1
Let n(j) be the second derivative of -j**6/30 - j**5/15 + 5*j**4/6 - 2*j**3 + 5*j**2/2 + 4*j. Let r(c) be the first derivative of n(c). Factor r(h).
-4*(h - 1)**2*(h + 3)
Suppose -2*f = -2*h, 4*h - 1 = -f + 19. Solve s - 1 - 1 - h*s - 2*s**2 - s = 0.
-1
Suppose 8*d - 9*d = d. Factor 2/11*a**3 + 0 + d*a + 2/11*a**2.
2*a**2*(a + 1)/11
Let 3*n**4 - 3*n**2 - 5*n + 10*n**3 - 7*n**3 + 2*n = 0. Calculate n.
-1, 0, 1
Find a such that -6*a**3 + 0*a - 8*a**4 - 4/3*a**2 + 0 - 10/3*a**5 = 0.
-1, -2/5, 0
Let 7*m**5 - 8*m + m**3 - 23*m**2 + 19*m**4 + m**3 + 4 - m**3 = 0. What is m?
-2, -1, 2/7, 1
Suppose 5*r - 93 = -3*y, -15 = -0*r - 5*r. Suppose 23*j = y*j - 9. What is w in -3/2*w + 0 - j*w**3 + 9/2*w**2 = 0?
0, 1/2, 1
Suppose -4*w - 2*a + 4*a = 6, -5*a = -3*w - 22. Let m be 4 - (8 + (w - 5)). Factor m*k + 2/3*k**2 - 2/3.
2*(k - 1)*(k + 1)/3
Let f(p) be the first derivative of -1/2*p**2 - 4 - 2*p + 1/3*p**3. Factor f(w).
(w - 2)*(w + 1)
Let d(h) = -5*h**2 - 40*h - 80. Let i(w) = 55*w**2 + 440*w + 880. Let a(p) = 65*d(p) + 6*i(p). Factor a(r).
5*(r + 4)**2
Let w be -1 + 3 - 0/1. What is m in w - 1 - 2*m**2 - 1 + 2*m**3 = 0?
0, 1
Factor 2/5*g**3 - 2/5 + 2/5*g**2 - 2/5*g.
2*(g - 1)*(g + 1)**2/5
Let w(j) be the second derivative of -2*j + 0*j**4 + 0*j**2