 b.
0
Suppose -4*p + 4*d + 12 = 0, 3*p - 3*d = -2*p + 15. Let b(c) be the second derivative of 0*c**2 - p*c - 1/30*c**4 + 1/15*c**3 + 0. Factor b(n).
-2*n*(n - 1)/5
Let r be (0/8)/(2 + 0)*-1. Let s(o) be the first derivative of -1/20*o**4 + r*o**3 + 6/25*o**5 + 0*o - 2 - 3/10*o**6 + 0*o**2. Find n, given that s(n) = 0.
0, 1/3
Let n(i) be the second derivative of -i**7/84 + i**6/15 - i**5/40 - 5*i**4/12 + i**3/3 + 2*i**2 + 9*i. What is k in n(k) = 0?
-1, 2
Let g be (1 - 14/10)*5. Let z(o) = -o**2 + 1. Let a(u) = -5 + 1 + 37*u - 39*u + 2. Let t(v) = g*a(v) - 2*z(v). Factor t(f).
2*(f + 1)**2
Factor 1/5*u**5 + 4/5*u**3 + 4/5*u**4 + 0*u + 0*u**2 + 0.
u**3*(u + 2)**2/5
Suppose -3*d + n = -18, 6 = -n - n. Suppose -5*h + 4 = -6. Find u, given that 3*u**3 - d*u**2 + 3 + 2*u**h - 3 = 0.
0, 1
Suppose 5*k - 12 + 2 = 0. Suppose -3*h + k*h = -7. What is l in -180*l**3 + 23*l**2 - 84*l**5 + 27*l**2 + 213*l**4 + h*l**2 - 6*l = 0?
0, 1/4, 2/7, 1
Let c(q) be the first derivative of -3/8*q**2 - 4 + 0*q - 3/16*q**4 + 1/2*q**3. Determine k, given that c(k) = 0.
0, 1
Let u(t) be the first derivative of 2*t**5/25 + t**4/10 - 6*t**3/5 + 11*t**2/5 - 8*t/5 - 4. Factor u(f).
2*(f - 1)**3*(f + 4)/5
Let n(z) be the third derivative of -z**7/35 + z**6/80 + 3*z**5/10 + 5*z**4/16 - z**3/2 - 2*z**2 + 38*z. Find r such that n(r) = 0.
-1, 1/4, 2
Let i(y) = y + 11. Let c be i(-9). Factor -6*m - m**2 - 2*m**c + 3*m.
-3*m*(m + 1)
What is k in 0*k - 4/3*k**5 + 4/3*k**3 + 0 - 2/3*k**2 + 2/3*k**4 = 0?
-1, 0, 1/2, 1
Let l(b) = 3*b**2 + 6. Let m(i) = -2*i**2 - 5. Let c(r) = -5*l(r) - 6*m(r). Factor c(f).
-3*f**2
Let b = 2 - -6. Let n(u) be the third derivative of -1/90*u**6 + 1/504*u**b + 2*u**2 + 1/36*u**4 + 1/45*u**5 + 0 - 1/9*u**3 + 0*u - 1/315*u**7. Factor n(t).
2*(t - 1)**3*(t + 1)**2/3
Let r(w) be the second derivative of -w**6/420 - w**5/70 - w**4/42 - 3*w**2/2 + 2*w. Let k(u) be the first derivative of r(u). Factor k(d).
-2*d*(d + 1)*(d + 2)/7
Let r(t) be the third derivative of 0*t**3 + 0*t**4 - 1/30*t**5 - 1/210*t**7 + 0*t + 0 - 1/40*t**6 - 6*t**2. What is n in r(n) = 0?
-2, -1, 0
Let l(s) be the third derivative of -3*s**2 - 3/8*s**4 + 0*s + 3/40*s**6 + 0*s**3 + 1/20*s**5 + 0 - 1/70*s**7. Factor l(u).
-3*u*(u - 3)*(u - 1)*(u + 1)
Let g(k) be the second derivative of k**6/135 - k**5/45 + k**4/54 - 8*k. Determine f, given that g(f) = 0.
0, 1
Find a, given that -255*a**4 + 42*a**2 - 5*a**3 + 225*a**5 - 3*a**3 - 4 - 21*a**3 + 21*a**2 = 0.
-1/3, 2/5, 1
Factor -4/15*j + 0 + 2/3*j**2.
2*j*(5*j - 2)/15
Let i = 25/12 - 7/3. Let p = 3/20 - i. Factor 0 - p*l**2 - 2/5*l.
-2*l*(l + 1)/5
Let h(c) be the first derivative of c**6/120 - c**4/24 - 2*c**2 + 3. Let q(b) be the second derivative of h(b). Factor q(w).
w*(w - 1)*(w + 1)
Let u(r) be the third derivative of 7*r**6/780 + r**5/78 - 4*r**4/39 + 4*r**3/39 + 16*r**2. Factor u(h).
2*(h - 1)*(h + 2)*(7*h - 2)/13
Let f be (-2)/(-3) + (-102)/153. Factor 0*y**2 - y**3 - 1/2*y**5 - 3/2*y**4 + 0*y + f.
-y**3*(y + 1)*(y + 2)/2
Let n(t) = -t + 1. Suppose 0 = -j + 4*j + 15. Let d be n(j). Solve -2*y + 2*y - 2*y**3 + d*y - 4*y = 0.
-1, 0, 1
Let z(f) be the second derivative of 0 + 4*f**2 + 4/3*f**4 - 1/5*f**5 + 5*f - 10/3*f**3. Factor z(m).
-4*(m - 2)*(m - 1)**2
Let v(y) = -2*y + 44. Let t be v(20). Let r(z) be the first derivative of 0*z**5 + 0*z + 3 - 1/9*z**2 - 1/27*z**6 + 1/9*z**t + 0*z**3. Factor r(j).
-2*j*(j - 1)**2*(j + 1)**2/9
Let p(a) = 8*a**2 + 37*a. Let j(n) = -4*n**2 - 18*n. Let w(i) = -5*j(i) - 2*p(i). Factor w(r).
4*r*(r + 4)
Let l = 24 + -19. Let f(h) be the second derivative of 1/2*h**4 + 1/5*h**l - 2/3*h**3 - 1/5*h**6 - 2*h + 0*h**2 + 0. Find v, given that f(v) = 0.
-1, 0, 2/3, 1
Let m(u) be the second derivative of -u**7/3024 - 13*u**6/4320 + u**5/120 + u**4/4 - 4*u. Let x(a) be the third derivative of m(a). Factor x(n).
-(n + 3)*(5*n - 2)/6
Let c(s) be the first derivative of 2*s**6/3 - 12*s**5/5 - 10*s**4 - 8*s**3/3 + 18*s**2 + 20*s + 33. What is d in c(d) = 0?
-1, 1, 5
Suppose 3*t + 7*p = 10*p + 6, 3*t - 6 = -p. Factor 3/4 + 3/2*v**3 - 3/2*v + 0*v**t - 3/4*v**4.
-3*(v - 1)**3*(v + 1)/4
Let q(t) = -6*t**3 + 14*t**2 - 2*t - 16. Let l(b) = 7*b**3 - 15*b**2 + 3*b + 16. Let w(f) = 2*l(f) + 3*q(f). Suppose w(s) = 0. Calculate s.
-1, 2
Let b(t) be the second derivative of 0 + 1/3*t**2 + 1/15*t**5 + 5*t + 5/18*t**4 + 4/9*t**3. Suppose b(o) = 0. Calculate o.
-1, -1/2
Let y be (-4)/(-1) - (1 + 0). Solve -y*d**5 - 7*d**3 + d**5 + 0*d**3 + 8*d**4 - d**3 = 0 for d.
0, 2
Let k(d) be the third derivative of d**6/40 - 3*d**5/20 - d**2. Find o such that k(o) = 0.
0, 3
Let w = 224/3 + -74. Factor -w - 2*h - 4/3*h**2.
-2*(h + 1)*(2*h + 1)/3
Suppose 88*o - 96*o = -16. What is j in -1/6*j**3 + 1/6*j - 1/6*j**o + 1/6 = 0?
-1, 1
Let t(n) be the second derivative of -n**6/90 + n**5/30 + n**4/36 - n**3/9 + 2*n. Factor t(u).
-u*(u - 2)*(u - 1)*(u + 1)/3
Let q(x) = 29*x**2 + 2*x**5 - 3*x**5 - 28*x**2 - 1 + x. Let n(p) = -4*p**5 + 2*p**4 + p**2 + 4*p - 3. Let a(c) = n(c) - 3*q(c). Factor a(w).
-w*(w - 1)**3*(w + 1)
Let j(u) = -2*u**4 + 4*u**3 - u**2 - u + 1. Let c(p) = -p**4 + p**3 - p**2 + p - 1. Suppose 2 = 3*q - 1. Let w(s) = q*j(s) + c(s). Factor w(a).
-a**2*(a - 1)*(3*a - 2)
Let l(x) = -x**2 - 4*x - 3. Let f(d) = d + 1. Let p(u) = 3*f(u) + l(u). Factor p(z).
-z*(z + 1)
Let l = 576 + -2876/5. Factor -l*n + 0 - 2/5*n**2.
-2*n*(n + 2)/5
Suppose k - 10 = -7. Factor 2*o**4 + 0*o**4 + 6*o**2 + 3*o**3 + 2*o + 0*o + 3*o**k.
2*o*(o + 1)**3
Let a(w) = 6*w**4 - 6*w**3 - 3*w**2 + w + 2. Let j(r) = 7*r**4 - 7*r**3 - 3*r**2 + r + 2. Let u(p) = -6*a(p) + 5*j(p). Factor u(b).
-(b - 2)*(b - 1)*(b + 1)**2
Let f(t) = t**2 + 8*t - 4. Let c be f(-9). Suppose -13 = -c*a - 3. Factor 0*r - 2/3*r**a + 2/3.
-2*(r - 1)*(r + 1)/3
Let p(b) = -b**3 + 5*b**2 - 6*b + 6. Let u(q) = q + 1. Let w(m) = p(m) - 2*u(m). Factor w(l).
-(l - 2)**2*(l - 1)
Let z(c) = c**3 - 6*c**2 - 6*c - 7. Let o be z(7). Suppose 4*p + 0*p = o. Factor 2/9*q**3 + p + 2/9*q - 4/9*q**2.
2*q*(q - 1)**2/9
Let r = 16085399/120716 - -2/30179. Let s = 134 - r. Factor 0 + 3/2*h + s*h**4 - 3/2*h**3 - 3/4*h**2.
3*h*(h - 2)*(h - 1)*(h + 1)/4
Let q = -18 - -28. Let g be 6/(-18) - q/(-12). Factor -p + 1/2 + g*p**2.
(p - 1)**2/2
Factor 0*j + 0 - 2/7*j**4 + 0*j**2 + 2/7*j**3.
-2*j**3*(j - 1)/7
Let u(y) be the third derivative of -y**7/70 + y**6/40 + y**5/10 - 2*y**2. Factor u(j).
-3*j**2*(j - 2)*(j + 1)
Suppose -k**3 - 18*k**5 + k**2 - k**4 + 2*k**3 + 17*k**5 = 0. What is k?
-1, 0, 1
Let l(y) = 21*y**3 - 6*y**2 - 15. Let h(o) = 3*o**3 - o**2 - 2. Suppose 3*d = -50 + 5. Let n(x) = d*h(x) + 2*l(x). Solve n(v) = 0.
0, 1
Factor 0 + 4/9*j**2 + 2/9*j**3 + 2/9*j.
2*j*(j + 1)**2/9
Suppose 0*f - 3*f - 30 = -5*x, 2*f - 18 = -3*x. Factor 0*y**4 + 3*y**4 - x*y**5 + 3*y**5.
-3*y**4*(y - 1)
Suppose -2*s = -3 - 3. Suppose 0*i + i - s = 0. Factor -5*t**2 + 3*t + 0*t**3 - 2*t**3 - t**2 + 5*t**i.
3*t*(t - 1)**2
Suppose v + 3*i + 24 = 2*v, v - i = 22. Let y = v - 21. Factor 0*c + 0*c**3 + 2/9*c**2 - 2/9*c**4 + y.
-2*c**2*(c - 1)*(c + 1)/9
Let u(w) = -w**2 - 4*w. Let k be u(0). Let q(v) be the third derivative of 1/270*v**5 + 0*v + 0 + k*v**4 - 1/27*v**3 - 3*v**2. Let q(m) = 0. What is m?
-1, 1
Let y(a) = a**2 - a - 1. Let b(d) = -2*d**3 + d**2 + d - 1. Let q(t) = 2*b(t) - 2*y(t). Factor q(r).
-4*r*(r - 1)*(r + 1)
Let b(n) be the second derivative of n**7/315 + n**6/180 - 3*n**2/2 - n. Let t(i) be the first derivative of b(i). What is h in t(h) = 0?
-1, 0
Let z(u) be the second derivative of u**5/90 - u**4/54 - 2*u**3/27 - 13*u. Factor z(k).
2*k*(k - 2)*(k + 1)/9
Let v = -40 - -42. Let h(n) be the first derivative of -1/12*n**4 + 4/3*n + 5/9*n**3 + 3 - 4/3*n**v. Find a such that h(a) = 0.
1, 2
Let r(y) = -y**3 + 5*y**2 + 7*y - 6. Let u be (4/3)/(2/9). Let z be r(u). Factor 1/3*g**2 + z - 1/3*g - 1/3*g**4 + 1/3*g**3.
-g*(g - 1)**2*(g + 1)/3
Let d = 7 - 3. Factor -2 - 3*m + 2*m + d + 2*m**2 - 3*m.
2*(m - 1)**2
Let r(m) be the first derivative of -m**6/15 - 4*m**5/25 - m**4/10 - 5. Let r(s) = 0. Calculate s.
-1, 0
Let r be 22/8 + 1/4. Factor 2*l**r + 4*l**5 + 3*l**4 + l**4 + 3*l**4 - l**2.
l**2*(l + 1)**2*(4*l - 1)
Let h be 1*(-1 + 2 + 2). Let f(b) = -2*b - 2. Let u be f(-2). Factor 4*n**u + 5*n + 9 + n**h + 0*n**2 - 7.
(n + 1)**2*(n + 2)
