). Solve 25*f**d - 36*f**2 + 22*f**3 - 26*f**4 + 14*f + 6*f**5 - 2 - 3*f**3 = 0.
1/3, 1
Let n be 0/((-14 - -2)/6). Let z(a) be the third derivative of 0*a + 1/420*a**6 - 1/70*a**5 + n*a**3 + 0*a**4 + a**2 + 0. Find u, given that z(u) = 0.
0, 3
Suppose 0 = -2*m + m + 3. Let d(q) be the second derivative of 1/9*q**4 + 1/9*q**2 + 1/135*q**6 - 2*q + 0 + 2/45*q**5 + 4/27*q**m. Factor d(u).
2*(u + 1)**4/9
Suppose 0 = y - 8 + 2. Find o, given that -o**2 - y + 11*o**2 - 9*o + 5*o**2 = 0.
-2/5, 1
Let p(u) = -u**2 + 4*u + 5. Let j be p(4). Suppose i**4 + i - 2*i**3 + 0*i**4 + 3*i**2 - 5*i**2 + 1 + i**j = 0. What is i?
-1, 1
Suppose 0 = -l + 16 - 13, -5*u + 3 = l. Let j(a) be the second derivative of 1/39*a**4 - 4*a + 0*a**2 + 0 + u*a**3 + 1/130*a**5. Find b, given that j(b) = 0.
-2, 0
Let m(p) be the second derivative of p**6/165 - p**5/110 + p. Factor m(b).
2*b**3*(b - 1)/11
Let z(v) be the third derivative of v**6/90 + v**5/30 + v**4/24 + 2*v**3/3 - 2*v**2. Let a(j) be the first derivative of z(j). Let a(c) = 0. What is c?
-1/2
Suppose 2*d = -3*d + 15. Suppose 0 = d*v - 12, -2*h - 4*v + 7 = -5*h. Find j, given that 6*j**2 + 3*j**4 + j**2 - 6*j**h - 4*j**2 = 0.
0, 1
Let z(f) be the second derivative of 9*f - 1/18*f**4 + 0 - 1/3*f**2 + 2/9*f**3. Factor z(d).
-2*(d - 1)**2/3
Let u(j) = -j**3 - 2*j**2 + 4*j. Let b(i) = i**3 + 2*i**2 - 3*i. Let c(g) = 5*b(g) + 4*u(g). Find y, given that c(y) = 0.
-1, 0
Let c(r) be the third derivative of 0 + 1/90*r**5 + 3*r**2 + 0*r**3 + 0*r**6 - 1/315*r**7 + 1/1008*r**8 + 0*r - 1/72*r**4. Factor c(h).
h*(h - 1)**3*(h + 1)/3
Factor 189*d**2 + 8 + 6*d - 188*d**2 + 0*d.
(d + 2)*(d + 4)
Let d(n) be the third derivative of -1/8*n**4 + 0 + 1/120*n**5 - 2*n**2 + 3/4*n**3 + 0*n. Factor d(h).
(h - 3)**2/2
Let n = -7 - -12. Let -2*h + h**2 - 17 + 17 + 3*h**2 - 4*h**4 + 2*h**n = 0. What is h?
-1, 0, 1
Let i = 53 - 38. Find z such that i*z**2 + 1 - 20*z**3 + 5*z**2 + 1 - 10*z + 10*z**4 - 2*z**5 = 0.
1
Let w(j) = j + 20. Let s be w(-18). Factor -4/5*c + 2/5 + 2/5*c**s.
2*(c - 1)**2/5
Factor 1/2 + 9/4*j + 7/4*j**2.
(j + 1)*(7*j + 2)/4
Suppose 0 = -0*s - 4*s. Solve 2/11*z**2 + 6/11*z**4 - 2/11*z**5 + 0 - 6/11*z**3 + s*z = 0.
0, 1
Let o(g) = g**2 + g. Let i(k) = 2*k**3 + 11*k**2 + 9*k. Let n(b) = i(b) - 5*o(b). Let n(u) = 0. Calculate u.
-2, -1, 0
Let d(w) be the third derivative of w**6/100 - 4*w**5/75 + w**4/20 + 2*w**3/15 + 6*w**2. Factor d(r).
2*(r - 2)*(r - 1)*(3*r + 1)/5
Let j(v) be the first derivative of v**7/70 + v**6/20 - 3*v**5/20 - v**4/2 + 2*v**3 + 5*v**2/2 + 4. Let o(i) be the second derivative of j(i). Factor o(l).
3*(l - 1)**2*(l + 2)**2
Let f(o) = o**3 - 5*o**2 + 2*o + 8. Let j be f(4). Solve j + 0*u + 2/7*u**3 - 2/7*u**2 = 0 for u.
0, 1
Let g(a) = a**2 + 2*a + 3. Let h be g(0). Factor 25 - 25 - 6*r**2 + h*r**3.
3*r**2*(r - 2)
Let l(u) be the second derivative of -u**7/3780 - u**6/405 - u**5/135 - 5*u**3/6 - 4*u. Let t(j) be the second derivative of l(j). Find k such that t(k) = 0.
-2, 0
Let u(n) = 17*n**4 + 8*n**3 - 21*n**2 - 13*n + 4. Let r(o) = -9*o**4 - 4*o**3 + 11*o**2 + 7*o - 2. Let k(y) = 10*r(y) + 6*u(y). Factor k(t).
4*(t - 1)*(t + 1)**2*(3*t - 1)
Let z(y) be the third derivative of 0 + 0*y**3 + 1/336*y**8 + 0*y + 1/20*y**6 - 2/105*y**7 + 1/24*y**4 - 1/15*y**5 + 3*y**2. Solve z(a) = 0.
0, 1
Let -69 - 10*i + 64 - 2*i**2 - 3*i**2 = 0. What is i?
-1
Factor -j**2 + 9 + 2*j**2 + 36*j - 42*j.
(j - 3)**2
Let v(l) be the second derivative of l**6/720 + l**5/240 + l**3/6 - l. Let k(n) be the second derivative of v(n). Factor k(a).
a*(a + 1)/2
Let f = 26 + -16. Find c such that 53*c**3 - 44*c**3 - f*c - 2*c + 3*c**4 = 0.
-2, 0, 1
Suppose 3*y + 6 = 0, -2*z + 60 = z - 3*y. Let m be ((-2)/z)/(2/(-12)). Find h, given that -4/3*h**2 - m - 2*h = 0.
-1, -1/2
Let u(d) be the second derivative of 1/3*d**3 - 1/10*d**5 - 1/3*d**4 + 0 - 2*d + 2*d**2. Factor u(n).
-2*(n - 1)*(n + 1)*(n + 2)
Suppose 3*n - 50 = 4*c, c - 6 = -2. Let r be 48/n + 42/(-231). Factor 0*b + 2/3 - 2/3*b**r.
-2*(b - 1)*(b + 1)/3
Factor 5/2*j**2 - 1/2*j**3 + 2 - 4*j.
-(j - 2)**2*(j - 1)/2
Let y = 43 + -257/6. Let m(l) be the second derivative of 0 - 3*l + 1/3*l**2 + 1/3*l**3 + 1/30*l**5 + y*l**4. Suppose m(g) = 0. Calculate g.
-1
Let x(y) be the third derivative of -y**7/105 - 13*y**6/300 - 3*y**5/50 + y**4/60 + 2*y**3/15 + y**2. Factor x(f).
-2*(f + 1)**3*(5*f - 2)/5
Determine y, given that -39*y**2 + 70*y**3 - 41*y**2 + 188*y**4 + 0*y - 203*y**4 + 10*y + 15 = 0.
-1/3, 1, 3
Factor 0*l - 2/3*l**3 - 2/3*l**5 + 0*l**2 - 4/3*l**4 + 0.
-2*l**3*(l + 1)**2/3
Let z = -15 + 17. Factor 1/2*s**3 + 0*s + z - 3/2*s**2.
(s - 2)**2*(s + 1)/2
Let t(u) = u**2 - 3*u + 2. Let f(b) = -b**3 + 3*b**2 + 5*b - 6. Let o be f(4). Let p(r) = -5*r**2 + 16*r - 11. Let h(s) = o*p(s) - 11*t(s). Factor h(m).
-m*(m - 1)
Let g(d) be the second derivative of d**6/90 + d**5/30 + d**4/36 + 5*d. Determine o so that g(o) = 0.
-1, 0
Let q(r) be the first derivative of r**6/180 - r**4/12 - r**3/3 + 2. Let o(y) be the third derivative of q(y). Let o(x) = 0. What is x?
-1, 1
Let s be (-24)/12 + 2 + 3/6. Let b - 1/2 - s*b**2 = 0. What is b?
1
Let y(b) be the second derivative of b**7/210 + b**6/60 + b**5/60 + b**2/2 - 2*b. Let h(s) be the first derivative of y(s). Factor h(t).
t**2*(t + 1)**2
Let o(d) = -d**5 - d**4 - d + 1. Let g(k) = 9*k**5 + 6*k**4 + 8*k - 8. Let q(i) = -3*g(i) - 24*o(i). Determine y, given that q(y) = 0.
0, 2
Let f(w) be the third derivative of 1/210*w**5 - 1/21*w**3 + 1/84*w**4 + 5*w**2 - 1/420*w**6 + 0 + 0*w. Factor f(p).
-2*(p - 1)**2*(p + 1)/7
Let v(o) be the first derivative of 0*o**2 + 0*o**4 + 0*o + 2/5*o**5 + 0*o**3 - 3. Solve v(r) = 0 for r.
0
Let f(s) be the second derivative of s**7/14 - 3*s**5/10 + s**3/2 + 9*s. Factor f(l).
3*l*(l - 1)**2*(l + 1)**2
Suppose r - 5*w - 5 = 3*r, -5*r - w - 1 = 0. Determine p, given that 4/3*p + r - 2*p**2 = 0.
0, 2/3
Let t(u) = u - 3. Suppose -19*m + 17*m = -8. Let r be t(m). Factor r + 3/4*q**2 + 3*q - 5/4*q**3.
-(q - 2)*(q + 1)*(5*q + 2)/4
Let f(h) = -h**2. Let v(w) = -w**3 + 3*w**2 - 15*w + 9. Let i(r) = -4*f(r) + v(r). Factor i(a).
-(a - 3)**2*(a - 1)
Let x = -17 + 20. Let u = x - -1. Factor -6/5*y + 0 + 21/5*y**5 + 9*y**3 + 57/5*y**u + 3/5*y**2.
3*y*(y + 1)**3*(7*y - 2)/5
Let x(m) be the second derivative of m**7/315 - m**6/270 + m**5/720 - 2*m**3/3 - 5*m. Let n(r) be the second derivative of x(r). Determine g so that n(g) = 0.
0, 1/4
Let w(s) be the third derivative of -s**8/30240 - s**7/7560 + s**5/12 + 6*s**2. Let o(c) be the third derivative of w(c). Factor o(i).
-2*i*(i + 1)/3
Let l(r) be the second derivative of -r**4/8 - 3*r**3/2 + 37*r. Factor l(v).
-3*v*(v + 6)/2
Factor -1/4*h**2 + 1/4 + 1/4*h - 1/4*h**3.
-(h - 1)*(h + 1)**2/4
Let h(z) = -z**3 + 2*z**2 - z. Let y be h(1). Let t(x) be the second derivative of y*x**3 - x**2 + 0 + 1/6*x**4 - x. Suppose t(r) = 0. Calculate r.
-1, 1
Let c(x) be the first derivative of x**3 - 13. Factor c(m).
3*m**2
Let l be 4 - (4/(-12) - 0). Let a = 71/15 - l. What is k in a - 2/5*k**2 + 0*k = 0?
-1, 1
Let j(l) be the third derivative of 3*l**8/280 + l**7/175 - 11*l**6/300 - l**5/50 + l**4/30 - 4*l**2. Suppose j(a) = 0. What is a?
-1, -2/3, 0, 1/3, 1
Let 6*y**3 + 118*y + 3*y**2 + 3*y**4 + 116*y - 234*y = 0. What is y?
-1, 0
Let a(c) be the second derivative of 1/10*c**5 + 0 - 1/21*c**7 + 0*c**2 - 5*c + 0*c**3 + 1/15*c**6 - 1/6*c**4. Factor a(k).
-2*k**2*(k - 1)**2*(k + 1)
Let g(p) be the third derivative of -p**9/151200 + p**8/16800 - p**7/4200 + p**6/1800 + p**5/20 + 2*p**2. Let h(z) be the third derivative of g(z). Factor h(r).
-2*(r - 1)**3/5
Let f(n) = -9*n. Let b(a) = 1. Let w(g) = -2*b(g) + f(g). Let k be w(-2). Factor 22*i + 2*i**3 + k - 4*i + 12*i**2 + 6*i.
2*(i + 2)**3
Factor -63*y + 59*y + y**2 - 2 - 3.
(y - 5)*(y + 1)
Let m(v) = 2*v - 6. Let q be m(4). Let n(k) = -k**3 + 9*k**2 + k - 6. Let x be n(9). Factor 0 + 1/4*y + 1/4*y**x + 1/2*y**q.
y*(y + 1)**2/4
Let n(z) be the third derivative of z**7/630 - z**6/360 - z**5/180 + z**4/72 + 6*z**2. Factor n(a).
a*(a - 1)**2*(a + 1)/3
Suppose -12 = -y - 3*y. Factor -4*w**y + w**3 - 12 - 5*w**2 - 10*w**2 - 24*w.
-3*(w + 1)*(w + 2)**2
Let x(z) be the first derivative of 8/5*z**5 - 8/3*z**3 + 7 + z**2 + 0*z - 1/2*z**4. What is c in x(c) = 0?
-1