t x(s) = 2*s**3 - 3*s**2 - 3. Let j(b) = b**3 - 3*b**2 - b - 3. Let p(z) = 3*j(z) - 2*x(z). Let m(f) be the first derivative of p(f). Factor m(h).
-3*(h + 1)**2
Let s(l) = l**2 + 7*l + 6. Let t(n) = -2*n**2 - 14*n - 12. Let q(r) = -7*s(r) - 4*t(r). Factor q(j).
(j + 1)*(j + 6)
Let w(d) be the first derivative of -d**6/180 + d**5/30 - d**4/12 + d**3 + 2. Let f(m) be the third derivative of w(m). Factor f(q).
-2*(q - 1)**2
Let k be 2/(-1)*(-1 - 0). Let k*d**2 + 0*d - 5*d**2 + 3*d + 6 = 0. What is d?
-1, 2
Let t(q) be the first derivative of q**8/840 + 3*q**7/560 + q**6/120 + q**5/240 - 2*q**3/3 - 4. Let y(h) be the third derivative of t(h). Factor y(a).
a*(a + 1)**2*(4*a + 1)/2
Let w = 29/122 + 3/244. Determine t so that 3/4 + 1/2*t - w*t**2 = 0.
-1, 3
Let t(p) be the third derivative of -4*p**2 + 1/10*p**5 + 0*p - 1/8*p**6 + 0*p**3 + 0*p**4 + 1/35*p**7 + 0. Factor t(x).
3*x**2*(x - 2)*(2*x - 1)
Let x(c) be the first derivative of -2*c**3/33 + 2*c**2/11 + 12. Factor x(w).
-2*w*(w - 2)/11
Let t = 3 - -1. Suppose -5*a + 14 = -4*a - t*o, 2*a + 3*o = -5. Find y such that -1/2 + 1/2*y**a + 1/2*y**3 - 1/2*y = 0.
-1, 1
Let o(p) be the second derivative of -p**5/30 - p**4/18 + p**3/9 + p**2/3 - 6*p. Factor o(v).
-2*(v - 1)*(v + 1)**2/3
Let i(u) be the second derivative of 3*u**5/10 + 9*u**4/8 + 3*u**3/2 + 3*u**2/4 + 15*u. Let i(m) = 0. Calculate m.
-1, -1/4
Determine u, given that 0*u + 4/9*u**3 + 0 - 2/9*u**4 - 2/9*u**2 = 0.
0, 1
Let g(w) be the second derivative of -w**6/42 - w**5/20 - w**4/42 + 8*w. Solve g(r) = 0.
-1, -2/5, 0
Let v(o) be the first derivative of o**4/5 + o**3/3 - 7*o**2/10 - 2*o/5 + 11. Determine j, given that v(j) = 0.
-2, -1/4, 1
Let j(l) be the third derivative of -l**6/600 - l**5/100 + 2*l**3/15 - 10*l**2. Factor j(z).
-(z - 1)*(z + 2)**2/5
Let t be 0/(-2 + (2 - 2)). Factor -4*u**2 + 2*u**3 - 4*u + 6*u + t*u**3.
2*u*(u - 1)**2
Factor -m**4 + 92*m**2 - 92*m**2 - 3*m**3.
-m**3*(m + 3)
Let k = 100 - 100. What is v in 2/5*v**2 + k*v - 2/5 = 0?
-1, 1
Factor 14/9*n - 2/9*n**2 - 4/3.
-2*(n - 6)*(n - 1)/9
Let c(o) = o**2 - 5*o + 6. Suppose -3*f + 26 - 8 = 0. Let g(s) = 2*s**2 - 11*s + 13. Let w(j) = f*g(j) - 13*c(j). Factor w(d).
-d*(d + 1)
Suppose 5*q - 12 = q. Let u = q + 1. Find h such that h**2 + 0 - u*h + 1 + 2*h = 0.
1
Suppose 2*w + 49 = 51. Factor -w - 1/2*j**3 + 1/2*j + j**2.
-(j - 2)*(j - 1)*(j + 1)/2
Let u = 229 + -229. Find s, given that u + 2*s - 4*s**2 - 5/2*s**3 = 0.
-2, 0, 2/5
Let b(i) be the third derivative of -i**5/10 - 5*i**4/12 - 2*i**3/3 - 4*i**2. Let b(c) = 0. Calculate c.
-1, -2/3
Let i(d) = -d**2 - d + 1. Let a be (2 + -1)*0/4. Suppose a = -5*c + 5. Let p(g) = 27*g**2 + 21*g - 12. Let w(n) = c*p(n) + 6*i(n). Let w(b) = 0. Calculate b.
-1, 2/7
Let g(b) be the first derivative of -81*b**7/490 - 9*b**6/70 - b**5/35 - 5*b**2 + 6. Let u(l) be the second derivative of g(l). Factor u(s).
-3*s**2*(9*s + 2)**2/7
Let b(n) = n**2 + 3*n + 4. Let w be b(-3). Factor 5*u**3 + 0*u**2 - 16*u**w + 6*u**2 - 7*u**2 + 3*u**3.
-u**2*(4*u - 1)**2
Factor 25/3 + 1/3*i**2 - 10/3*i.
(i - 5)**2/3
Let j(x) be the third derivative of x**5/15 + 8*x**4/3 + 128*x**3/3 + 6*x**2. Solve j(b) = 0 for b.
-8
Let b(u) be the third derivative of u**5/180 - u**4/36 + u**3/18 - 4*u**2. Find v, given that b(v) = 0.
1
Let w(t) be the first derivative of 6*t - 15/4*t**4 - 5 + 15/2*t**2 - 9*t**3 + 21/5*t**5. Factor w(v).
3*(v - 1)**2*(v + 1)*(7*v + 2)
Let h(b) be the first derivative of 2*b**5/35 + b**4/7 + 2*b**3/21 + 17. Factor h(s).
2*s**2*(s + 1)**2/7
Let o be (-2 - 4)/((-9)/6). Let t be (-1)/((-10)/o - -2). Factor -t*r - r**3 - r**2 - r**3 - 3*r**2.
-2*r*(r + 1)**2
Factor s - 144 - 49*s - 15*s**2 + 23*s**2 - 12*s**2.
-4*(s + 6)**2
Factor 3/5*h + 0 + 3/5*h**2.
3*h*(h + 1)/5
Solve 14 + f - 4 + 5*f**2 - 16*f = 0.
1, 2
Let y(g) = 4*g**2 - 2*g - 3. Let d be y(-3). Let w be d/60 - 1/4. Let 4/5 - w*s**2 + 2/5*s = 0. Calculate s.
-1, 2
Let l = -4 - -9. Let q(a) = a**3 - 6*a**2 + 6*a - 2. Let c be q(l). What is t in 0 + 1/2*t**4 - 1/4*t**5 + 0*t**c + 1/4*t - 1/2*t**2 = 0?
-1, 0, 1
Suppose 0 = -2*t - 70 + 76. Factor 0*u**2 + 0*u - 1/2*u**t + 0.
-u**3/2
Let x(j) be the first derivative of -3*j**5/80 + j**4/16 + j**3/8 - 3*j**2/8 - 4*j - 2. Let m(i) be the first derivative of x(i). Factor m(g).
-3*(g - 1)**2*(g + 1)/4
Let l(z) = -7*z - 2 - 1 + 23*z**2 + 1 + 3. Let x(o) = 8*o**2 - 2*o. Let s(p) = 6*l(p) - 17*x(p). Solve s(c) = 0.
1, 3
Let b be ((-70)/20)/((-42)/24). Determine a so that 5/2*a - b*a**3 - 2*a**4 + a**2 + 1 - 1/2*a**5 = 0.
-2, -1, 1
Find y, given that 6*y**4 - 32 + 64*y**2 + 72*y**3 - 32*y + y**4 + 11*y**4 = 0.
-2, -2/3, 2/3
Factor -f**2 - 21*f**3 + 24*f**3 - 4*f**4 - 3*f + 2 + 3*f**4.
-(f - 2)*(f - 1)**2*(f + 1)
Let p(f) be the third derivative of f**7/315 - f**6/90 - 22*f**2. Factor p(h).
2*h**3*(h - 2)/3
Suppose -4*j + 6 + 16 = 2*d, -14 = -2*d - 2*j. Find h, given that 30*h**4 - 6*h**3 + 4*h**d - 6 + 19*h**3 + 9*h**5 + 13*h**3 - 15*h = 0.
-1, 2/3
Let u(s) be the third derivative of s**5/60 + s**4/12 + s**3/6 - 3*s**2. Factor u(r).
(r + 1)**2
Let j(y) = y**3 - 4*y**2 - 2*y + 1. Let v be j(4). Let b be (7 - v)*(-2)/(-7). Factor -6/5*s**3 + 0*s**2 + 0 + 2/5*s**b + 8/5*s.
2*s*(s - 2)**2*(s + 1)/5
Let w(f) be the second derivative of f**6/120 - 2*f**2 - 3*f. Let y(l) be the first derivative of w(l). Suppose y(v) = 0. Calculate v.
0
Let r(q) be the third derivative of 9*q**8/392 - 3*q**6/70 + 4*q**5/105 - q**4/84 - 24*q**2. Solve r(z) = 0 for z.
-1, 0, 1/3
Let n be -3*-2*(-3)/(-6). Find i, given that 2*i + 4 + 2*i**2 - n - 4*i**2 + 3*i**2 = 0.
-1
Let k(g) be the third derivative of g**6/600 - g**5/100 + g**4/40 - 2*g**3/3 - 4*g**2. Let q(d) be the first derivative of k(d). Factor q(n).
3*(n - 1)**2/5
Let u(v) = -v**3 - v**2 + v. Let k(q) = -5*q**5 - 10*q**4 - 2*q**3 + 3*q**2 - 3*q. Let o(t) = -k(t) - 3*u(t). Suppose o(w) = 0. Calculate w.
-1, 0
Let h(t) = 4*t**4 - 7*t**3 + 5*t. Let i = 5 - 0. Let z(k) = 2*k**4 - 4*k**3 + 3*k. Let m(j) = i*z(j) - 3*h(j). Factor m(l).
-l**3*(2*l - 1)
Factor 1/2*l**5 + l**3 + 3/2*l**4 - l**2 - 1/2 - 3/2*l.
(l - 1)*(l + 1)**4/2
Let c(w) = -w**4 + w**3 + w**2 - w + 1. Let p(l) = 27*l**4 - 96*l**3 + 102*l**2 - 18*l - 6. Let o(m) = 6*c(m) + p(m). Factor o(i).
3*i*(i - 2)**2*(7*i - 2)
Let w(b) be the first derivative of -b**6/12 - b**5/5 + b**4/4 + 2*b**3/3 - b**2/4 - b + 9. What is g in w(g) = 0?
-2, -1, 1
Let y(g) be the third derivative of -g**8/48 - 8*g**7/105 - 11*g**6/120 - g**5/30 + 7*g**2. Determine p, given that y(p) = 0.
-1, -2/7, 0
Let h(y) be the second derivative of y**6/600 - y**5/100 + y**4/40 - y**3/30 + y**2 + 2*y. Let v(x) be the first derivative of h(x). Factor v(k).
(k - 1)**3/5
Solve 5/2*r**4 - 11/2*r**2 - 13/2*r**3 + 3 + 13/2*r = 0.
-1, -2/5, 1, 3
Let s(c) be the third derivative of -c**6/480 + 3*c**5/80 - 9*c**4/32 + 9*c**3/8 + 4*c**2. Let s(b) = 0. Calculate b.
3
Let w = 171 - 165. Let l = 6 - -8. Suppose w*d**2 + 13*d**3 - 4*d**3 - 10*d**4 + 4 - l*d + 5*d**3 + 0 = 0. What is d?
-1, 2/5, 1
Let a(l) = l**2 + 13*l + 12. Let x(g) = g + 1. Let s(c) = -2*a(c) + 18*x(c). Factor s(b).
-2*(b + 1)*(b + 3)
Let w(x) be the third derivative of 0*x**3 - 2/21*x**4 - 2*x**2 - 19/42*x**6 + 34/105*x**5 + 5/21*x**7 + 0*x + 0. Factor w(d).
2*d*(5*d - 2)**2*(7*d - 2)/7
Let h(x) be the third derivative of -x**8/28 - 10*x**7/21 - 37*x**6/15 - 94*x**5/15 - 17*x**4/2 - 6*x**3 - 5*x**2. Let h(b) = 0. Calculate b.
-3, -1, -1/3
Let s(t) = -5*t**5 + 9*t**4 - 4*t**3 - t**2 + 9*t - 5. Let m(r) = -r**5 + r**4 + r**2 + r - 1. Let w(o) = -3*m(o) + s(o). Factor w(v).
-2*(v - 1)**4*(v + 1)
Let f(w) be the third derivative of 2*w**7/315 - 13*w**6/360 + w**5/12 - 7*w**4/72 + w**3/18 - 4*w**2. Let f(a) = 0. What is a?
1/4, 1
Find w such that -8*w - 8*w**2 - 9*w + w - w**5 + 32*w + 16 - 7*w**4 - 16*w**3 = 0.
-2, 1
Let b(h) = -6*h**3 - h**2 + 1. Let f be b(1). Let n(g) = g**2 + 7*g + 6. Let p be n(f). Factor 3*a**3 + p*a - a**3 - 2*a.
2*a*(a - 1)*(a + 1)
Let x(s) = -s**4 + s**3 + s**2 + 1. Let t(f) = -5*f**4 + 7*f**3 + 3*f**2 - f + 8. Let p(g) = t(g) - 6*x(g). Determine z so that p(z) = 0.
-2, -1, 1
Let t(p) = p**3 - 3*p**2 + 4*p - 2. Let y = 5 - 3. Let o be t(y). Factor 4 - 4 + o*x**2 - 2*x.
2*x*(x - 1)
Suppose 3*y + 49 = 2*o, -5*o = -3*y - 3