 in a(k) = 0?
-2, -2/9, -1/5
Let s(m) be the first derivative of m**5/20 + m**4/8 + 5*m**2 - 5. Let h(y) be the second derivative of s(y). Factor h(b).
3*b*(b + 1)
Let o(s) = -s**2 - s + 2. Let l be o(-3). Let k(i) = i**3 + 3*i**2 - 4*i + 3. Let n be k(l). Let -2/3*m + 0 + 2/3*m**n + 2/3*m**4 - 2/3*m**2 = 0. Calculate m.
-1, 0, 1
Let t(h) be the third derivative of 1/40*h**5 + 0 + 1/4*h**3 - 1/8*h**4 + 0*h - 5*h**2. Find f such that t(f) = 0.
1
Let h(c) = -c**3 + c**2 - c + 1. Let g(b) = -3*b**2 + 12*b**3 - 2 - 3*b**2 - 1 - 3*b**4. Let p(v) = g(v) + 6*h(v). Factor p(m).
-3*(m - 1)**3*(m + 1)
Let x(n) be the third derivative of n**8/168 + 4*n**7/105 + n**6/20 - 2*n**5/15 - n**4/3 - 5*n**2. Factor x(i).
2*i*(i - 1)*(i + 1)*(i + 2)**2
Let j be ((-1)/75)/((-10)/25). Let x(c) be the second derivative of 1/12*c**4 + 0 + 0*c**2 + 0*c**5 + 0*c**3 - j*c**6 - c. Suppose x(y) = 0. What is y?
-1, 0, 1
Factor -4*f + 2/5*f**2 + 10.
2*(f - 5)**2/5
Let n(l) = l**2 - l + 4. Let o(s) = s**2 - 2*s + 4. Let d(g) = 2*n(g) - 3*o(g). Solve d(r) = 0.
2
Let d(o) = 3*o**2 - 7*o**2 - 2*o**2 + 32. Let s(l) = -14*l**2 + l**2 + 21 + 9*l**2. Let n(g) = 5*d(g) - 8*s(g). Factor n(w).
2*(w - 2)*(w + 2)
Let i(c) be the first derivative of -c**5/15 - c**4/6 + c**3/9 + c**2/3 - 6. Let i(z) = 0. What is z?
-2, -1, 0, 1
Let f be (-8)/32 + (-1)/(-3). Let m(s) be the second derivative of 1/60*s**6 - f*s**3 + 0 - s + 1/40*s**5 - 1/24*s**4 + 0*s**2. Solve m(o) = 0 for o.
-1, 0, 1
Let j(v) be the second derivative of 2*v + 3/140*v**5 + 3/14*v**3 + 3/14*v**2 + 0 + 3/28*v**4. Factor j(u).
3*(u + 1)**3/7
Suppose 5*o - 18 = -3. Suppose -o*j - 2 = -8. Factor 2/5 + 1/5*h**j - 3/5*h.
(h - 2)*(h - 1)/5
Let s(n) be the second derivative of -n**7/3360 + n**6/720 - n**5/480 + n**3/6 + 5*n. Let w(l) be the second derivative of s(l). Suppose w(y) = 0. What is y?
0, 1
Let t be (-354)/18 + 1/(-3). Let r be (-5)/(-1)*(-8)/t. Factor 4/3 + 2/3*n - 16/3*n**r + 10/3*n**3.
2*(n - 1)**2*(5*n + 2)/3
Determine l so that -13*l**3 + 3*l**3 - 5 + 871*l**2 - 871*l**2 + 5*l**4 + 10*l = 0.
-1, 1
Suppose 16 = 16*i - 12*i. Let b be (-2 + 39/18)*2. Factor -2/3*w**3 - b*w**i + 0*w - 1/3*w**2 + 0.
-w**2*(w + 1)**2/3
Let n = 1669/34515 - 3/767. Let z(o) be the second derivative of 1/27*o**6 + 0 - n*o**5 - 2/189*o**7 - 4*o + 1/54*o**4 + 0*o**3 + 0*o**2. What is r in z(r) = 0?
0, 1/2, 1
Find g such that 0*g + 4/11*g**4 - 2/11*g**5 - 4/11*g**2 + 0 + 2/11*g**3 = 0.
-1, 0, 1, 2
Let c(z) be the third derivative of -z**8/110880 - z**7/27720 + z**6/1980 - z**5/30 + z**2. Let r(d) be the third derivative of c(d). Factor r(s).
-2*(s - 1)*(s + 2)/11
Solve 3/7*i**2 + 0*i**3 + 0*i - 3/7*i**4 + 0 = 0.
-1, 0, 1
Factor 0*j - 2/3*j**2 + 2/3.
-2*(j - 1)*(j + 1)/3
Suppose 10*w = 20*w - 18*w. Factor 0*o + 0 - 1/3*o**4 - 1/3*o**5 + 0*o**3 + w*o**2.
-o**4*(o + 1)/3
Factor 3*d**2 + 2*d**4 - 4*d**4 - d**4.
-3*d**2*(d - 1)*(d + 1)
Suppose 2*h - k - 7 = 0, 0*h - 2*h - 3*k = -11. Factor 3 + 2*p**5 + 18*p**h - 3 - 16*p**4.
2*p**4*(p + 1)
Suppose -5*k + 5*y - 5 = 0, -3 = 11*k - 13*k + y. Let p(i) be the first derivative of -i**2 + 1/2*i - 1/6*i**3 - 4 + 1/2*i**k. Solve p(h) = 0 for h.
-1, 1/4, 1
Let m(p) = p + 1. Let c be m(2). Let d(k) = 1 - 2 + k**2 - 2*k + c*k. Let o(h) = -5*h**2 - 7*h + 3. Let i(z) = 3*d(z) + o(z). Factor i(r).
-2*r*(r + 2)
Let k(w) be the third derivative of -w**8/26880 + w**7/5040 - w**6/2880 + w**4/8 - 2*w**2. Let z(q) be the second derivative of k(q). Factor z(c).
-c*(c - 1)**2/4
Suppose -4*y = -4*o - 4, -4*o + 0*o - 5*y + 23 = 0. Factor 4/3 - 4/3*a**o - 2*a + 2*a**3.
2*(a - 1)*(a + 1)*(3*a - 2)/3
Let i be (234/(-27) - -9)*0. Suppose 1/4*d**3 + i + 0*d - 1/2*d**2 = 0. Calculate d.
0, 2
Let g = 25 - 25. Let q(n) be the third derivative of 1/60*n**6 - 3*n**2 + g + 0*n**5 + 0*n**4 + 0*n**3 - 1/42*n**7 + 0*n. Solve q(i) = 0.
0, 2/5
Suppose -5*f**2 - 10*f**3 + 8*f**4 + 10*f**3 + 9*f**3 - 2*f + 5*f**3 = 0. Calculate f.
-2, -1/4, 0, 1/2
Let q(w) be the first derivative of -5/24*w**3 - 3 - 1/80*w**5 + w + 1/12*w**4 + 1/4*w**2. Let o(v) be the first derivative of q(v). Let o(d) = 0. What is d?
1, 2
Let w = -9 - -13. Factor -2*v + 0*v**2 - 2*v + w*v**2 - 2*v**2.
2*v*(v - 2)
Let y be (-18)/2*2/(-24). What is r in y*r + 3/4*r**2 - 3/4*r**3 - 3/4 = 0?
-1, 1
Suppose 8 = -2*f + 4*w, -4*f + 4*w = 7 - 3. Factor -1/4*r + 1/4*r**f + 0.
r*(r - 1)/4
Let g = 3 + -1. Let p(m) = -m**2 + 8*m - 12. Let t be p(3). Determine h so that -1/2*h + 0 + 0*h**g + 1/2*h**t = 0.
-1, 0, 1
Factor -4*q - 1/2*q**3 - 7/2*q**2 + 8.
-(q - 1)*(q + 4)**2/2
Let b(v) = -10*v**2 - 4*v - 59 - v**3 + 53 - 6*v. Let p be b(-9). Suppose 0 - 3/4*d**5 + 0*d**p + 0*d**2 + 0*d + 0*d**4 = 0. What is d?
0
Let h(o) = o - 12. Let u be h(15). Suppose 4*m - 8 = l, m - 5*l + u*l + 5 = 0. Factor 0*x + 0 + 0*x**2 - 2/3*x**5 - 8/3*x**4 - 8/3*x**m.
-2*x**3*(x + 2)**2/3
Let t be (2 + 294)*(-6)/30. Let p = 60 + t. Suppose 0 - 2/5*o**3 + 0*o**2 + 0*o - 2/5*o**5 + p*o**4 = 0. Calculate o.
0, 1
Let a(y) be the third derivative of -y**5/540 - y**4/108 - y**3/54 - 6*y**2. Find s, given that a(s) = 0.
-1
Suppose 4*y = 2*y + 60. Factor g**4 - y*g**2 - 12*g**3 + 33*g**2 + 8*g**4.
3*g**2*(g - 1)*(3*g - 1)
Let z be 3/4 - (-86)/56. Factor 8/7 + 10/7*b**2 - 2/7*b**3 - z*b.
-2*(b - 2)**2*(b - 1)/7
Let q(k) = -k**3 + 2*k**2 + k. Suppose -2*z + 18 = 5*o, -5 = -z - 1. Let n be q(o). Find f, given that -1/3*f**n + 2/3*f - 1/3 = 0.
1
Let y be (11 - 13)/(2 - 8/3). Let r(w) be the second derivative of 0*w**2 + 4/105*w**6 - 4*w + 0 + 0*w**y + 1/14*w**5 + 1/147*w**7 + 1/21*w**4. Factor r(n).
2*n**2*(n + 1)**2*(n + 2)/7
Let p(o) = o**2 + 7*o. Let r(f) be the first derivative of f**3/3 + 3*f**2 - 4. Let v(h) = 6*p(h) - 7*r(h). Let v(j) = 0. Calculate j.
0
Let j(w) be the third derivative of -3*w**2 - 1/42*w**7 + 0 - 1/336*w**8 - 1/6*w**5 + 0*w - 1/12*w**6 - 1/6*w**3 - 5/24*w**4. Factor j(d).
-(d + 1)**5
Let u(r) = -2*r**3 + 6*r - 4. Let n(d) = -d**2 + d. Let h(w) = -w**2 + w + 4. Let g be h(0). Let f(o) = g*n(o) - u(o). What is a in f(a) = 0?
-1, 1, 2
Suppose 3*a + 14 = -0*k + 4*k, 0 = -2*a - 4. Determine s, given that -s**3 - 5*s**k + s**2 + 5*s**2 = 0.
0, 1
Let q(g) = g**2 + 9*g + 5. Let t be q(-8). Let d be (t/6)/(6/(-4)). Factor d*o - o**3 - 2/3*o**2 + 0.
-o*(o + 1)*(3*o - 1)/3
Let w(p) = 23*p**4 + 35*p**3 + 10*p**2 - 8*p - 3. Let x(n) = 45*n**4 + 70*n**3 + 20*n**2 - 15*n - 5. Let c(b) = 5*w(b) - 3*x(b). Suppose c(g) = 0. What is g?
-1, 0, 1/4
Let z(p) be the first derivative of 1/6*p**3 - 1/5*p**5 + 0*p**2 - 1 - 1/8*p**6 + 0*p + 1/16*p**4. Solve z(l) = 0 for l.
-1, 0, 2/3
Solve -2*v**5 + 4*v**3 + 4*v - 3*v - 3*v = 0.
-1, 0, 1
Let q(g) be the third derivative of -g**9/7560 - g**8/1680 - g**7/1260 + g**4/4 + 5*g**2. Let d(u) be the second derivative of q(u). Find y such that d(y) = 0.
-1, 0
Let z(h) be the first derivative of -h**2/2 + 2*h - 4. Let c be z(0). Solve 0*q + 2/7*q**5 + 6/7*q**4 + 2/7*q**c + 0 + 6/7*q**3 = 0.
-1, 0
Let z(w) be the third derivative of 1/120*w**5 + 0*w + 0 + w**2 + 1/48*w**4 + 0*w**3. Factor z(c).
c*(c + 1)/2
Suppose -18*b = -11*b - 21. Factor 0*m**b + 2/5*m**5 - 4/5*m**2 + 0 + 4/5*m**4 - 2/5*m.
2*m*(m - 1)*(m + 1)**3/5
Let p(i) = 3*i**2 + 4*i + 1. Let r(a) = a**2 + 1. Let v(u) = p(u) - 4*r(u). Factor v(t).
-(t - 3)*(t - 1)
Let k(q) be the third derivative of 5*q**8/336 - q**7/21 + q**6/24 + 11*q**2. Factor k(a).
5*a**3*(a - 1)**2
Let c(u) be the third derivative of -3*u**6/8 + 5*u**5/3 - 65*u**4/24 + 5*u**3/3 + 10*u**2. Determine t, given that c(t) = 0.
2/9, 1
Let z(j) be the third derivative of -j**6/1620 + j**5/540 + j**3/2 - j**2. Let c(b) be the first derivative of z(b). Solve c(p) = 0 for p.
0, 1
Let v(p) be the first derivative of -5*p**4/4 - 5*p**3/3 + 1. Let v(t) = 0. What is t?
-1, 0
Let o(u) be the second derivative of 0 + 0*u**2 + 0*u**5 - 2*u + 0*u**3 - 1/126*u**7 - 1/90*u**6 + 0*u**4. Determine x, given that o(x) = 0.
-1, 0
Let o(q) be the first derivative of q**3/18 - 2*q/3 - 45. Factor o(u).
(u - 2)*(u + 2)/6
Let w be 5/10 - (-13)/2. Suppose 3*i + w = k, -2*k - i - 13 = -5*k. Factor -6*p**k - 3*p**4 - 15*p**3 + 6*p**2 - p**4 - 11*p**4.
-3*p**2*(p + 1)*(7*p - 2)
Let a(p) be the first derivative of -2*p**5/65 + p**4/13 + 2*p**3/13 - 4*p**2/13 - 8*p/13 - 9. Let a(h) = 0. 