2 + 0*z + t*z**4 - 2/3*z**3.
-2*z**2*(z - 1)**2*(3*z + 1)/3
Let c(o) = -o**2 + 5*o - 1. Let s be c(4). Let t(k) = k**3 - 7*k**2 - 8*k + 2. Let q be t(8). Suppose b**q + b**2 + 2*b - 1 - 2*b**s - 1 = 0. Calculate b.
-1, 1
Let u(a) be the third derivative of a**5/20 - a**4/8 - 3*a**3 - 59*a**2. Solve u(g) = 0.
-2, 3
Factor 191*t**2 + 4 + 4*t**4 - 97*t**2 - 102*t**2.
4*(t - 1)**2*(t + 1)**2
Let w(q) = -12*q**2 + 6*q - 10. Let x(l) = l**2 + 1. Let i(v) = -2*w(v) - 20*x(v). Let i(b) = 0. Calculate b.
0, 3
Let j(p) = 15*p**4 + 12*p**3 + p**2 - 7*p - 11. Let s(f) = 4*f**4 + 3*f**3 - 2*f - 3. Let q(a) = 6*j(a) - 22*s(a). Factor q(m).
2*m*(m + 1)**3
Let o = 211/2 - 105. Suppose o*d - 1/4*d**2 - 1/4 = 0. What is d?
1
Let p(d) = -24*d**2 - 129*d - 96. Suppose -8*s + 13*s = -165. Let t(q) = 3*q**2 + 16*q + 12. Let b(g) = s*t(g) - 4*p(g). Factor b(a).
-3*(a + 2)**2
Let j(v) = -v**2 - 5. Let i(q) = -q**2 - 5. Let h(d) = 6*i(d) - 7*j(d). Let k(w) = -w**2 - 1. Let r(f) = h(f) + 3*k(f). Factor r(o).
-2*(o - 1)*(o + 1)
Let x = -424/145 + 108/29. Solve 0*a + 6/5*a**3 + 0 - 2/5*a**5 + 0*a**4 - x*a**2 = 0.
-2, 0, 1
Find r such that -15/2*r**3 + 7/4*r**4 + 9*r**2 + 0 - 2*r = 0.
0, 2/7, 2
Let g(f) be the third derivative of 1/105*f**7 + 0*f**3 + 1/30*f**5 + 1/30*f**6 + 0*f + 0*f**4 - f**2 + 0. Factor g(r).
2*r**2*(r + 1)**2
Let c(h) be the third derivative of -h**8/84 + 2*h**7/105 + h**6/30 - h**5/15 - 13*h**2. Find s such that c(s) = 0.
-1, 0, 1
Let s(f) be the third derivative of f**5/120 + f**4/16 - f**3/3 - 19*f**2. Find d, given that s(d) = 0.
-4, 1
Factor -5*u + 57*u**3 - 20*u**2 - 52*u**3 + 5 + 15.
5*(u - 4)*(u - 1)*(u + 1)
Let o(d) be the first derivative of -6*d**2 + 2*d - 6 - 18/5*d**5 + d**4 + 4/3*d**6 + 16/3*d**3. Solve o(x) = 0.
-1, 1/4, 1
Factor -12*c - 229 + 39*c + 253 + 3*c**2.
3*(c + 1)*(c + 8)
Let o(x) be the third derivative of x**9/30240 + x**8/3360 + x**7/840 + x**6/360 + x**5/20 - x**2. Let r(z) be the third derivative of o(z). Solve r(t) = 0.
-1
Suppose -5*m + 142 = 3*c, -5*m - 4*c = -150 + 4. Let t = m - 76/3. Factor 0 - 2/3*b**3 + 2/3*b**4 + t*b - 2/3*b**2.
2*b*(b - 1)**2*(b + 1)/3
Suppose -2*c - 73 = 3*a, -3*a + 2*c = 11 + 78. Let w = a - -30. What is n in 1/4*n**2 + 0 + 0*n + 3/4*n**4 + 1/4*n**5 + 3/4*n**w = 0?
-1, 0
Let b(k) = 2*k - 2. Let g be b(7). Suppose 5*t = -u + 6, 4*u - g = 2*u + t. Solve 12*l + u + 12*l**3 - l**4 + 4*l**4 - 3 + 18*l**2 = 0.
-1
Let u = 13 + -11. Let r(z) be the first derivative of 0*z**u - 2 + 0*z + 1/6*z**3. Factor r(t).
t**2/2
Suppose -15 = -0*v - 3*v. Factor 50*t**v - 49*t**5 + 2*t**4 - t**4.
t**4*(t + 1)
Factor 0*z + 2*z - 4 - z**2 + 3*z + 0*z.
-(z - 4)*(z - 1)
Let z(i) be the first derivative of -i**9/3024 - i**8/840 + i**6/180 + i**5/120 + i**3 - 2. Let u(d) be the third derivative of z(d). Factor u(t).
-t*(t - 1)*(t + 1)**3
Let g = 0 + 2. Let w(j) be the second derivative of -2/9*j**3 + 0 - 77/60*j**5 + 8/9*j**4 + 0*j**2 + g*j + 49/90*j**6. Determine q so that w(q) = 0.
0, 2/7, 1
Suppose -l = -3*l + 12. Factor 3 + 7*u + 5*u - l*u + 3*u**2.
3*(u + 1)**2
Suppose 6*x = x + 10. Suppose 4*n**2 - 6*n**3 + 2*n**5 - 3*n**2 - 6*n**x + n**2 = 0. What is n?
-1, 0, 2
Let m(f) be the first derivative of 4*f**5 - 25*f**4/4 - 5*f**3 + 25*f**2/2 - 5*f + 10. Factor m(x).
5*(x - 1)**2*(x + 1)*(4*x - 1)
Suppose -c = 2*r, 4*c + 6 - 17 = 3*r. Let g(t) be the first derivative of 4 + 4*t - t**c - 2/3*t**3. Suppose g(a) = 0. What is a?
-2, 1
Suppose 3*u + 15 = 0, u = 3*w - w - 109. Factor -x**2 - x**4 - 3*x**3 - w + 5*x**3 + 52.
-x**2*(x - 1)**2
Let y(i) = i**3 - 65*i**2 + 187*i - 59. Let u be y(62). Factor -4/5*s**u + 3/5*s + 2/5 - 2/5*s**2 + 1/5*s**5 + 0*s**4.
(s - 2)*(s - 1)*(s + 1)**3/5
Let y(u) be the first derivative of -9/16*u**4 - 3 + 3/2*u + 9/8*u**2 - 1/2*u**3. Factor y(t).
-3*(t - 1)*(t + 1)*(3*t + 2)/4
Let n(z) be the second derivative of 2*z**6/15 - z**5 + 8*z**4/3 - 8*z**3/3 + 8*z. Factor n(r).
4*r*(r - 2)**2*(r - 1)
Suppose 0 = 4*z + 1 - 17. Suppose -3*r + z*r = 2. Factor -3/4*a - 1/4*a**r - 1/2.
-(a + 1)*(a + 2)/4
Let b(z) be the third derivative of -z**6/120 - z**5/30 + z**4/8 + 3*z**2. Let w be b(-3). What is a in 0*a**2 + 2/5*a**3 + 0*a + w = 0?
0
Let u(h) be the third derivative of 5*h**8/336 + h**7/14 + h**6/8 + h**5/12 - 2*h**2 - 2*h. Suppose u(b) = 0. Calculate b.
-1, 0
Factor 0 - 2/9*l + 2/9*l**2.
2*l*(l - 1)/9
Let b(c) = c**2 - 6*c - 16. Let n be b(-2). Find y, given that -2/3 + 2/3*y**2 + n*y = 0.
-1, 1
Let m(y) be the second derivative of -y**7/105 + y**6/25 + y**5/50 - 7*y**4/30 + 4*y**2/5 + 43*y. What is f in m(f) = 0?
-1, 1, 2
Let x = -3 + 80. Let y be 3/5 + x/(-245). Factor 8/7*r - y - 6/7*r**2.
-2*(r - 1)*(3*r - 1)/7
Let j(a) = a**2 + 16*a - 15. Let k be j(-17). Let l(y) be the first derivative of 0*y**2 + 8*y + 3/2*y**4 - 14/3*y**3 - k. Let l(v) = 0. Calculate v.
-2/3, 1, 2
Let w be (-120)/(-105)*39/6. Let -4/7 + w*f**4 - 30/7*f**5 + 4/7*f**3 - 48/7*f**2 + 26/7*f = 0. Calculate f.
-1, 1/3, 2/5, 1
Let j(t) = t**3 + t**2 - 2*t. Let p(o) = -o**3 + o. Let i(x) = -3*j(x) - 6*p(x). Factor i(z).
3*z**2*(z - 1)
Let f(i) be the first derivative of 2*i**2 + 5 - 1/3*i + 16/3*i**4 - 16/3*i**3. Solve f(s) = 0 for s.
1/4
Let v(q) be the third derivative of q**6/8 - q**5/60 - q**4/2 + 2*q**3/3 + q**2 - 13*q. Factor v(a).
(a + 1)*(3*a - 2)*(5*a - 2)
Let z(q) be the second derivative of 1/7*q**3 + 4*q + 0 - 5/42*q**4 + 2/7*q**2. Find n such that z(n) = 0.
-2/5, 1
Let b be (-2154)/(-28) - (-18)/(-42). Let i = b + -75. Let -3*r - i*r**2 + 0 = 0. What is r?
-2, 0
Let z(t) be the first derivative of 0*t + 2/33*t**3 - 2/55*t**5 + 1/11*t**2 - 1/22*t**4 + 5. Factor z(x).
-2*x*(x - 1)*(x + 1)**2/11
Let u(m) = -m**3 + 8*m**2 + 8*m + 11. Let o be u(9). Factor 17*r**2 - 48*r**2 - 48*r**o - 19*r**2 - 8 - 56*r.
-2*(7*r + 2)**2
Let d = 116 + -114. Let f(m) be the second derivative of -1/90*m**5 - 3*m + 1/54*m**4 + 0*m**d + 2/27*m**3 + 0. What is t in f(t) = 0?
-1, 0, 2
Let t = -42 + 48. Let s be (-9)/(-42) - t/(-21). Factor 0 + 1/2*l**2 - l**3 + l - s*l**4.
-l*(l - 1)*(l + 1)*(l + 2)/2
Let q(p) be the second derivative of -p**8/6720 + p**7/2520 - p**4/12 + p. Let b(g) be the third derivative of q(g). Factor b(v).
-v**2*(v - 1)
Suppose 5*k - 3 = 8*k. Let z be (-2)/72 - k/4. Let 0 - z*w**5 + 0*w + 2/9*w**2 - 2/9*w**4 + 2/9*w**3 = 0. Calculate w.
-1, 0, 1
Let p = -8 - -8. Suppose -2*n = 2*f + f + 2, p = f + 2. Factor 0 + 0*w + 2/5*w**n.
2*w**2/5
Suppose 30 = 2*i + 72. Let y be (i/(-14))/(1/2). Factor -1/5*t - 1/5 + 1/5*t**y + 1/5*t**2.
(t - 1)*(t + 1)**2/5
Let u(c) be the first derivative of c**5/10 + 2*c**4/3 + 5*c**3/3 + 2*c**2 + c - 1. Let w(t) be the first derivative of u(t). Factor w(s).
2*(s + 1)**2*(s + 2)
Let c = 6 + -1. Suppose -3*b = c*l - 0*l - 6, 5*b + 24 = 3*l. Suppose 0 - 1/3*y - 7/3*y**l - y**4 - 5/3*y**2 = 0. What is y?
-1, -1/3, 0
Let a(y) = 2*y**3 + y**2 - 2*y + 1. Let n be a(1). Let j be 1/2 + (-1)/n. Solve -2/5*d**3 + 0 + j*d**2 + 0*d - 3/5*d**4 = 0 for d.
-2/3, 0
Let h(p) be the second derivative of 1/189*p**7 + 1/9*p**3 + 0 + 2/9*p**2 - 1/27*p**4 + 0*p**6 + 6*p - 2/45*p**5. Factor h(m).
2*(m - 2)*(m - 1)*(m + 1)**3/9
Let a(b) be the second derivative of -b**4/12 + 5*b**3/3 - 7*b**2 + 7*b. Let x(d) = 4*d**2 - 49*d + 71. Let j(i) = 11*a(i) + 2*x(i). Solve j(v) = 0 for v.
2
Solve -3/7 + 3/7*u**2 + 3/7*u - 3/7*u**3 = 0.
-1, 1
Let r be (-4)/(-56) + (-3)/(-7). Let j(t) be the first derivative of -t**2 - 1 + r*t**4 + 0*t**3 + 0*t. Determine i so that j(i) = 0.
-1, 0, 1
Let b(p) be the third derivative of p**8/2016 + p**7/630 - p**6/360 - p**5/45 - 7*p**4/144 - p**3/18 + 14*p**2. Factor b(k).
(k - 2)*(k + 1)**4/6
Let t(s) be the third derivative of 1/2*s**3 + 0*s - 2*s**2 + 0 - 1/4*s**4 + 1/20*s**5. Factor t(g).
3*(g - 1)**2
Factor 3*o**2 - 11*o - 7*o + 18*o.
3*o**2
Let q(u) = -u - 7. Let p be q(-10). Determine b, given that -13*b**2 + 12*b**2 + 0 + b**p + 0 = 0.
0, 1
Let a(z) be the third derivative of -1/180*z**5 + 0 + 0*z**3 - z**2 + 0*z + 1/36*z**4. Find v such that a(v) = 0.
0, 2
Factor 182*a**3 + 12*a - 8*a**2 - 181*a**3 - 10 + 5*a.
(a - 5)*(a - 2)*(a - 1)
Let q(o) be the second derivative of -o**6/225 + o**5/50 - o**4/30 + o**3/45 + 6*o. Factor q(p).
-2*p*(p - 1)**3/15
Suppose 6*p - 6 = 4*p. Suppose 2*q - 