4*p**5 - 7*p**4 + p**3 + p**2 + p + 1. Let s(x) = -x**5 + x**4 - x**2 + x + 1. Let i(k) = j(k) - s(k). Factor i(v).
v**2*(v - 1)**2*(5*v + 2)
Let v = -155/4 - -39. Let m(y) be the first derivative of -1/12*y**3 + v*y + 2 + 0*y**2. Suppose m(x) = 0. Calculate x.
-1, 1
Factor 16 + 10*g**2 - 5 + 6*g - 4 - 11.
2*(g + 1)*(5*g - 2)
Suppose 0 = -2*w + 4*a + 12, -1 = 2*a - 5. Suppose -f - w = 2*f + 5*s, f - 2 = s. Find b such that f*b**2 - 2*b**3 - 6*b + 0*b**2 + 6*b**2 + 2 = 0.
1
Let t(o) = 7*o**4 - 7*o**2 - 2*o. Let g(h) = -h**3. Let x(y) = 2*g(y) - t(y). Factor x(z).
-z*(z - 1)*(z + 1)*(7*z + 2)
Let b(y) be the third derivative of y**9/120960 + y**8/40320 - y**5/20 - 3*y**2. Let o(h) be the third derivative of b(h). Factor o(n).
n**2*(n + 1)/2
Let a be -1 - ((-10)/3 - -2). Factor a*s + 1/3*s**2 + 0.
s*(s + 1)/3
Factor 6*q**3 + q**2 + 21*q**4 - 18*q**4 + 2*q**2.
3*q**2*(q + 1)**2
Suppose 4*x + 6*i = 2*i - 20, 0 = 5*x - 5*i - 25. Let z = 2 - x. Factor z - 7*n + 4*n + 0*n + 0*n + n**2.
(n - 2)*(n - 1)
Let h = 5 - 2. Determine c so that h*c - c**2 - 4*c + 2*c = 0.
0, 1
Let d be (-14)/(-4) + 2/(-4). Suppose -5*f = -5*u - d*f - 8, -u = f - 4. Factor -2/9*q**3 + u + 0*q + 4/9*q**2.
-2*q**2*(q - 2)/9
Let t be 0 + (3/3 - -1). Suppose 0 = -5*q - 4*l + 4, -3*l + t - 6 = 2*q. Factor 0*k + 1 - 2*k**4 + k**q + 2*k - 2*k**3.
-(k - 1)*(k + 1)**3
Let g(y) be the first derivative of -2/65*y**5 + 4 + 0*y**3 - 1/13*y**4 + 2/13*y**2 + 2/13*y. Determine a, given that g(a) = 0.
-1, 1
Let b(f) be the third derivative of f**7/70 + f**6/40 - f**5/20 - f**4/3 + 9*f**2. Let s(d) = -1 + 1 - d. Let u(o) = b(o) - 5*s(o). Factor u(y).
3*y*(y - 1)*(y + 1)**2
Let o(r) be the first derivative of -r**4/10 - 2*r**3/15 + 2*r**2/5 - 2. Find p, given that o(p) = 0.
-2, 0, 1
Let n(c) be the second derivative of -3*c - 7/24*c**4 + 1/10*c**5 + 0 + 1/4*c**2 + 1/6*c**3. Factor n(a).
(a - 1)**2*(4*a + 1)/2
Let f = 103 + -926/9. Let o(b) be the second derivative of 0*b**3 + 0 + 2*b - 1/54*b**4 + f*b**2. Factor o(s).
-2*(s - 1)*(s + 1)/9
Let z be (-4)/16 - (-1)/2. Suppose 0*h - 10 = -5*h. Solve -z*w**h + 1/4 + 0*w = 0.
-1, 1
Let u(t) be the third derivative of -1/360*t**6 + 0*t + 0*t**3 - 1/72*t**4 + 0 - t**2 - 1/90*t**5. Factor u(q).
-q*(q + 1)**2/3
Let g(j) be the second derivative of -3*j**5/20 + j**3/2 - 4*j. Let g(a) = 0. Calculate a.
-1, 0, 1
Let d(f) = 10*f**4 + 2*f**3 - 10*f**2 - 2*f. Let a(t) = -21*t**4 - 4*t**3 + 21*t**2 + 4*t. Let h(c) = 3*a(c) + 7*d(c). Factor h(r).
r*(r - 1)*(r + 1)*(7*r + 2)
Let x = 1 + 1. Let i be (-7)/(-2) - 3/x. Factor 1/3*j**3 + 2/3*j**i + 1/3*j + 0.
j*(j + 1)**2/3
Let b(q) be the second derivative of -q**7/3 - 19*q**6/15 - 3*q**5/2 - q**4/6 + 2*q**3/3 + 6*q. Factor b(g).
-2*g*(g + 1)**3*(7*g - 2)
Let v(a) = -2*a**2 + 7*a. Let o be v(3). Factor 3*i + 5*i**3 - 2*i**3 - 6*i**2 - o*i**3 + 3*i**3.
3*i*(i - 1)**2
Let n(v) = 2*v + 2*v - 2*v - 3*v**2. Suppose -z + 7 = -0*f - 5*f, 2*z - 5*f - 9 = 0. Let j(s) = 4*s**2 - 2*s. Let y(r) = z*n(r) + 3*j(r). Factor y(m).
2*m*(3*m - 1)
Let p(d) be the second derivative of -d**4/4 - d**3/2 - 2*d. Factor p(a).
-3*a*(a + 1)
Let f = 64/11 - 62/11. Suppose 0 + 2/11*k + f*k**2 = 0. Calculate k.
-1, 0
Let s(a) be the third derivative of -a**6/300 + a**5/150 + 4*a**2. Solve s(h) = 0 for h.
0, 1
Let p be (-2)/6 + (-21)/(-27). Let z = 7 + -5. Factor 2/9*k**3 - 4/9 - 2/9*k + p*k**z.
2*(k - 1)*(k + 1)*(k + 2)/9
Suppose -a - 36 = 3*a. Let n = a - -13. Let 5*z**3 - 5*z**n + 2*z**4 - z**2 + 0*z - z = 0. What is z?
-1/3, 0, 1
Let d(b) be the first derivative of -b**7/2100 - 2*b**3/3 - 6. Let a(t) be the third derivative of d(t). Factor a(n).
-2*n**3/5
Let u(z) = z + 5. Let y be u(-8). Let s(a) = a**3 + 3*a. Let f(d) = d. Let i(c) = y*f(c) + s(c). Factor i(n).
n**3
Let h(z) = 10*z**4 - 37*z**3 + 30*z**2 - 3*z + 7. Let m(x) = -5*x**4 + 18*x**3 - 15*x**2 + 2*x - 3. Let w(s) = -3*h(s) - 7*m(s). Factor w(u).
5*u*(u - 1)**3
Let d(h) be the second derivative of 5/48*h**4 - 1/40*h**5 + 0 + 1/6*h**3 - h - 1/2*h**2. Let u(z) be the first derivative of d(z). Find s such that u(s) = 0.
-1/3, 2
Let l(f) = -5*f - 28. Let y be l(-6). Let w(k) be the second derivative of -1/50*k**5 + 0*k**y + 3*k - 2/15*k**3 + 0 + 1/10*k**4. Determine b so that w(b) = 0.
0, 1, 2
Let k(j) = -j**5 - j**2 + j - 1. Let m(t) = -9*t**5 - 12*t**4 - 15*t**3 - 12*t**2 + 6*t - 6. Let y(c) = 6*k(c) - m(c). Factor y(x).
3*x**2*(x + 1)**2*(x + 2)
Let o(z) = -z**3 + 8*z**2 - 8*z + 10. Let x be o(7). Let -1/2*w**2 + 3/4*w**x + 5/4*w**4 + 0 + 0*w = 0. Calculate w.
-1, 0, 2/5
Let i be (-20)/(-6)*(-36)/(-30). Suppose 0 = 3*z + 2*n + i, -4*z - 1 = n + 1. Find g, given that 1/2*g**3 + z + 0*g + 1/4*g**4 + 1/4*g**2 = 0.
-1, 0
Let r(s) = -9*s**3 - 5*s**2 + 23*s + 24. Let n(w) = 28*w**3 + 16*w**2 - 68*w - 72. Let p(y) = -5*n(y) - 16*r(y). Find m such that p(m) = 0.
-2, -1, 3
Let q = 522 - 518. Factor 2/11*g**2 - 2/11*g**q - 2/11*g**3 + 0 + 2/11*g.
-2*g*(g - 1)*(g + 1)**2/11
Let 3/2*d**2 + 0*d + 0 + 3/2*d**4 + 3*d**3 = 0. What is d?
-1, 0
Let c be (53/(-10) - -5)*2/(-3). Let m(f) be the second derivative of -1/6*f**3 - f + c*f**5 + 0 + 0*f**2 + 1/4*f**4. Let m(k) = 0. What is k?
-1, 0, 1/4
Factor 1/4*f**4 - f - 3/4 + f**3 + 1/2*f**2.
(f - 1)*(f + 1)**2*(f + 3)/4
Let q(d) = -21*d**3 - 39*d**2 + 36*d + 20. Let u(m) = -20*m**3 - 40*m**2 + 35*m + 20. Let k(o) = -5*q(o) + 4*u(o). Factor k(c).
5*(c - 1)*(c + 2)*(5*c + 2)
Let h = -16/5 - -19/5. Factor -2/5 + 1/5*t**3 + 1/5*t**4 - t - h*t**2.
(t - 2)*(t + 1)**3/5
Let i(a) be the second derivative of a**5/10 + a**4/2 + 2*a**3/3 + 35*a. Solve i(v) = 0.
-2, -1, 0
Suppose x + h = -0*h - 12, 13 = -4*x + 3*h. Let b(f) = -2*f**3 - 2*f**2 - 5*f - 5. Let m(q) = q**3 + q**2 + 2*q + 2. Let l(z) = x*m(z) - 3*b(z). Factor l(u).
-(u - 1)*(u + 1)**2
Let x(r) be the first derivative of r**6/18 - r**4/6 + r**2/6 + 41. Solve x(n) = 0.
-1, 0, 1
Let j(y) be the first derivative of 3*y**4/4 - y**3/3 + y**2 - y + 2. Let s be j(1). Factor 2 - 10*h + 4*h + 0*h**4 + 8*h**4 - 10*h**2 + 6*h**s.
2*(h - 1)*(h + 1)**2*(4*h - 1)
Suppose 4 = 3*r - 11. Let w(t) be the third derivative of 2*t**2 + 0*t**3 - 4/945*t**7 + 0 + 0*t + 0*t**r + 1/540*t**6 + 0*t**4. Factor w(c).
-2*c**3*(4*c - 1)/9
Factor -4 - 2605*n + 2605*n + 4*n**2.
4*(n - 1)*(n + 1)
Let q(z) be the first derivative of z**5/20 + 2*z + 3. Let t(f) be the first derivative of q(f). Suppose t(c) = 0. Calculate c.
0
Let j(n) be the first derivative of -1/180*n**6 + 1/36*n**4 - 1/9*n**3 + 0*n - 1 - n**2 + 1/90*n**5. Let r(x) be the second derivative of j(x). Factor r(i).
-2*(i - 1)**2*(i + 1)/3
Let g(i) = i**3 - i**2 - 1. Let t(z) = 39*z**2 - 147*z - 3. Let y(a) = 3*g(a) - t(a). Suppose y(w) = 0. What is w?
0, 7
Let y(u) = u**3 + 4*u**2 - u - 1. Let v be y(-4). Let n be (-12)/(-15) + v/(-10). Solve n*f**2 + 1/2*f + 0 - 1/2*f**3 - 1/2*f**4 = 0.
-1, 0, 1
Suppose -38 = 4*y - 46. Let 2/3*r**y + 32/3 - 16/3*r = 0. Calculate r.
4
Let i(n) be the third derivative of 1/180*n**5 - 1/36*n**4 - 2*n**2 + 0 + 0*n + 1/18*n**3. What is p in i(p) = 0?
1
Let j(s) be the second derivative of 0*s**3 + 3*s**2 - 3*s + 0 + 3/40*s**5 - 3/8*s**4. Suppose j(k) = 0. Calculate k.
-1, 2
Let c(b) be the second derivative of -1/4*b**4 - 2*b + 3/2*b**3 + 0 - 3*b**2. Factor c(n).
-3*(n - 2)*(n - 1)
Let n = -301 - -162541/540. Let i(k) be the third derivative of -n*k**6 + 0 + 0*k**3 + 1/135*k**5 + 2*k**2 + 0*k - 1/108*k**4. Factor i(b).
-2*b*(b - 1)**2/9
Factor -4*k**3 - 3*k + 25*k - 22*k.
-4*k**3
Let t(a) be the third derivative of 1/168*a**8 + 0 - 3*a**2 + 0*a**5 + 0*a**7 - 1/60*a**6 + 0*a + 0*a**3 + 0*a**4. Factor t(z).
2*z**3*(z - 1)*(z + 1)
Let f(x) be the third derivative of x**8/5040 - x**6/360 + x**5/180 + x**3 - 3*x**2. Let q(n) be the first derivative of f(n). Let q(k) = 0. What is k?
-2, 0, 1
Suppose 2/3*u**2 + 10/3 - 4*u = 0. Calculate u.
1, 5
Let k(j) be the first derivative of -3/4*j**4 + 0*j + 4 + j**3 + 3*j**2. Factor k(a).
-3*a*(a - 2)*(a + 1)
Suppose -1/2*d**4 - 1/2 - 1/2*d**5 + d**3 + d**2 - 1/2*d = 0. What is d?
-1, 1
Let x(t) = t**3 + 6*t**2 + 4*t. Let w be x(-5). Let f = -3 + w. Factor -4*r - 5 - r**3 + 1 + 4 + 4*r**f.
-r*(r - 2)**2
Let m = -13 + 18. Suppose 0 = m*o - 11 - 9. Let -k**2 - 3*k**2 + 6*k**3 + 6*k**o + 4*k**4 = 0. What is k?
-1