(y).
-2*y**3*(y + 1)
Let r(y) be the first derivative of 4*y**5/5 + 2*y**4 - 9. Factor r(p).
4*p**3*(p + 2)
Factor -8*v**2 + 17/2*v + 3 - 7/2*v**3.
-(v - 1)*(v + 3)*(7*v + 2)/2
Suppose -13*q = -11*q. Factor q*w**2 - 2/15*w**4 + 4/15*w**3 + 2/15 - 4/15*w.
-2*(w - 1)**3*(w + 1)/15
Let o(a) be the second derivative of a**4/42 - a**3/21 - 2*a**2/7 + 14*a. Factor o(u).
2*(u - 2)*(u + 1)/7
Let t = 74 - 369/5. Let d = t + 3/10. Factor 1/2*j**4 + 0*j**3 + 0*j - j**2 + d.
(j - 1)**2*(j + 1)**2/2
Let s(b) be the second derivative of -1/4*b**4 + 0*b**3 + 1/10*b**6 - 3/20*b**5 + 0 + 1/14*b**7 + 0*b**2 - b. Factor s(f).
3*f**2*(f - 1)*(f + 1)**2
Let k be (-1 - 5/(-2))*72/216. What is n in 1/2 + n + k*n**2 = 0?
-1
Let y(m) be the second derivative of m**6/285 - 3*m**5/190 + m**4/38 - m**3/57 + 22*m. Factor y(w).
2*w*(w - 1)**3/19
Suppose 1/7*x**2 + 100/7 - 20/7*x = 0. What is x?
10
Let v(s) be the first derivative of 13*s**4/4 - 11*s**3/3 + 11*s**2/2 - 9. Let j(b) = -7*b**3 + 6*b**2 - 6*b. Let t(x) = 11*j(x) + 6*v(x). Factor t(l).
l**3
Let f(z) be the third derivative of z**7/525 + z**6/150 + z**5/150 + 9*z**2. What is q in f(q) = 0?
-1, 0
Let b(g) = -16*g**2 + 12. Let l(o) = o**2 + o - 1. Let p(v) = b(v) + 12*l(v). Factor p(h).
-4*h*(h - 3)
Let a(m) be the third derivative of -5/24*m**4 + 3*m**2 - 1/3*m**3 - 1/15*m**5 + 0 - 1/120*m**6 + 0*m. Let a(o) = 0. Calculate o.
-2, -1
Suppose 23*q - 28 = -4*j + 28*q, 4 = -q. Suppose 1/2*f + 12*f**3 - 17/4*f**j + 0 - 45/4*f**4 = 0. Calculate f.
0, 1/3, 2/5
Let d(a) be the first derivative of -7*a**4/4 + 5*a**3 + 3*a + 3. Let x(g) = -g**3 + g**2 + 1. Let l(b) = d(b) - 3*x(b). Factor l(v).
-4*v**2*(v - 3)
Let f(g) = g**3 + 5*g**2 + 5*g + 5. Let k be f(-4). Suppose s = -k + 3. What is d in -1/3*d + 1/3*d**5 + 0 + 2/3*d**4 - 2/3*d**s + 0*d**3 = 0?
-1, 0, 1
What is t in 1/6*t**3 - 1/6*t - 1/2*t**2 + 1/3 + 1/6*t**4 = 0?
-2, -1, 1
Let x(a) be the first derivative of 4 - 1/2*a**6 + 0*a + a**3 + 3/4*a**4 - 3/5*a**5 + 0*a**2. Suppose x(h) = 0. What is h?
-1, 0, 1
Let u = -1 + 0. Let q be (-1)/3*-3 - u. Factor 6*t + t**q - 6*t - t**3 - t**4 + t**5.
t**2*(t - 1)**2*(t + 1)
Let g(d) = -17*d**4 - 17*d**3 + 29*d**2 + 30*d + 23. Let j(i) = 9*i**4 + 9*i**3 - 15*i**2 - 15*i - 12. Let a(w) = 6*g(w) + 11*j(w). Let a(t) = 0. Calculate t.
-1, 2
Let f = -9 - -15. Let d(z) be the second derivative of -1/135*z**f + 0*z**4 + 0 - 1/45*z**5 + 3*z + 1/9*z**2 + 2/27*z**3. Factor d(c).
-2*(c - 1)*(c + 1)**3/9
Let x(q) be the second derivative of -q**5/70 - 5*q**4/14 - 3*q**3 - 7*q**2 + 17*q + 1. Solve x(v) = 0.
-7, -1
Factor -a - 9*a - 45*a**3 - 35*a**2 + 30*a**3.
-5*a*(a + 2)*(3*a + 1)
Let d(b) be the third derivative of -1/2*b**3 + 0 + 0*b + 1/4*b**4 - 1/20*b**6 - 3*b**2 + 0*b**5 + 1/70*b**7. Factor d(u).
3*(u - 1)**3*(u + 1)
Let h(s) = -6*s**4 + 47*s**3 - 178*s**2 + 98*s + 3. Let k(f) = -f**4 + f**3 - f**2 + 1. Let z(b) = h(b) - 3*k(b). Factor z(v).
-v*(v - 7)**2*(3*v - 2)
Let s(w) be the first derivative of w**4/4 - w**3 + 3*w**2/2 - w - 23. Factor s(y).
(y - 1)**3
Let u(n) = -n**3 - 12*n**2 - 2*n + 1. Let x be u(-12). Suppose -3*b + 8*b - x = 0. Let 1/2*v**3 + v**2 - 3/4*v**4 - 1/2*v**b - 1/4 + 0*v = 0. What is v?
-1, 1/2, 1
Let d(r) be the second derivative of -r**9/68040 + r**8/15120 - r**6/1620 + r**5/540 + r**4/12 - 3*r. Let c(j) be the third derivative of d(j). Factor c(f).
-2*(f - 1)**3*(f + 1)/9
Suppose 0 = 7*f - 0*f - 21. Let t be (0 - f/9)*-2. Factor -2/3 + 4/3*x**3 + 4/3*x**2 - t*x - 2/3*x**5 - 2/3*x**4.
-2*(x - 1)**2*(x + 1)**3/3
Suppose 0 = r - 2*r + 2. Let c(q) be the first derivative of 2 - 2/15*q**3 + 3/10*q**4 + 0*q - 6/25*q**5 + 1/15*q**6 + 0*q**r. Find f such that c(f) = 0.
0, 1
Let r(o) be the second derivative of o**7/357 - o**6/255 - 7*o**5/170 + 13*o**4/102 - 2*o**3/17 + 8*o. What is t in r(t) = 0?
-3, 0, 1, 2
Let t(u) = 1 + 7*u - 4*u - 2*u - 5. Let g be t(6). Factor 0 + 0*a**g - 1/4*a**3 + 1/4*a.
-a*(a - 1)*(a + 1)/4
Let u(n) be the first derivative of -27*n**5/20 + 21*n**4/4 - 8*n**3 + 6*n**2 - 2*n - 2. Let c(h) be the first derivative of u(h). Factor c(v).
-3*(v - 1)*(3*v - 2)**2
What is a in -1 - 4*a**3 + 9*a**2 - 1 + 8*a**3 - 3*a**2 = 0?
-1, 1/2
Suppose 8*u - 3*u + 20 = 0. Let s(v) = 7*v**4 + 4*v**3 + 4*v**2. Let j(f) = 48*f**4 + 27*f**3 + 27*f**2. Let h(n) = u*j(n) + 27*s(n). Factor h(y).
-3*y**4
Determine c so that 9*c**2 - 18*c**2 - 3*c**4 + 3*c**2 + 9*c**2 = 0.
-1, 0, 1
Let i be 4/(3/9*1). Let x(p) = i*p**3 - p**2 + 3*p**2 + 2*p**2 - 2*p**2. Let h(t) = t**3. Let y(z) = -10*h(z) + x(z). Factor y(c).
2*c**2*(c + 1)
Let y(m) be the first derivative of 3*m**5/25 + 3*m**4/20 - 10. Factor y(s).
3*s**3*(s + 1)/5
Factor 15/4*t - 5/4*t**3 + 5*t**2 - 45/2.
-5*(t - 3)**2*(t + 2)/4
Let o = -4 - -6. Suppose x - 2*x = -o. Find y such that y**2 - 2*y**2 - 3*y**3 + 0*y**3 + x*y**3 = 0.
-1, 0
Let x(n) = -n**2 + 2*n. Let s be x(3). Let b = 9 + s. Determine k so that 3*k**5 - 2*k**3 + 8*k**3 - k**5 - b*k**4 - 2*k**2 = 0.
0, 1
Find t, given that -28/3*t - 32/9 - 2/3*t**3 - 58/9*t**2 = 0.
-8, -1, -2/3
Let h(z) be the third derivative of -z**7/3360 - z**6/240 - z**5/40 - z**4/6 + 3*z**2. Let o(f) be the second derivative of h(f). What is r in o(r) = 0?
-2
Let a(n) = 9*n**2 + 12*n - 21. Let m(h) = -4*h**2 - 6*h + 10. Let v(p) = -2*a(p) - 5*m(p). Solve v(s) = 0 for s.
-4, 1
Suppose 0*m + 2*m = 8. Factor -6*x + 4*x**3 + 2 + 4*x**5 - 2*x**5 + 0*x**m + 4*x**2 + 0*x**5 - 6*x**4.
2*(x - 1)**4*(x + 1)
Suppose -2*g - 10 = -7*g. Let 4*j**g + 0*j + 0*j - 5*j**3 - 2*j + 3*j**3 = 0. What is j?
0, 1
Let d(j) be the first derivative of -j**4/20 - j**3/15 + j**2/2 - 3*j/5 + 7. Factor d(w).
-(w - 1)**2*(w + 3)/5
Factor -13*w**4 - 6*w**2 + 9*w**4 + 10*w + 6*w**4 - 2*w**3 - 4.
2*(w - 1)**3*(w + 2)
Suppose 4*h - 20 = 0, -3*h + 8 = -c - 4. Let z(l) be the second derivative of 1/8*l**4 + 0 + 1/40*l**5 - 3*l + 1/4*l**2 + 1/4*l**c. Factor z(m).
(m + 1)**3/2
Let s be (-21)/14*(-8)/6. Find n such that 4*n**2 - n**3 + n - 2*n + 0*n**2 - 2*n**s = 0.
0, 1
Let z be (-8)/(-2)*1 - (-40 + 42). Factor -2/3*j + 1/3 + 1/3*j**z.
(j - 1)**2/3
Let m(d) be the third derivative of d**10/90720 + d**9/22680 - d**7/3780 - d**6/2160 - d**4/8 - 2*d**2. Let k(q) be the second derivative of m(q). Factor k(i).
i*(i - 1)*(i + 1)**3/3
Suppose 0*h + 5*h = 5. Suppose -5*l - 5*f = -h + 6, -2*l + 4 = -4*f. Find g, given that g**2 + g**4 - g**3 + 3*g**3 + l*g**4 = 0.
-1, 0
Factor 5/4*l**2 + 0 + 5/2*l - 5/4*l**3.
-5*l*(l - 2)*(l + 1)/4
Let a(b) be the second derivative of -b**5/180 - 5*b**2/2 + b. Let v(c) be the first derivative of a(c). Determine k so that v(k) = 0.
0
Suppose -5*t = 3*a - 2*a, -4*a + 5*t = 0. Let u(f) be the second derivative of -1/30*f**4 - 1/50*f**5 - 2*f + 1/15*f**3 + 0 + 1/75*f**6 + a*f**2. Factor u(n).
2*n*(n - 1)**2*(n + 1)/5
Let m(t) be the first derivative of t**6/140 - t**5/42 + t**4/84 + t**3/21 - t**2/2 - 2. Let p(r) be the second derivative of m(r). Let p(b) = 0. Calculate b.
-1/3, 1
Suppose 5*o + 3*k + 2 = 0, 3*o - 4*k = 13 + 9. Suppose -2 = -o*n - 2*r - 4, -22 = -5*n + 4*r. Factor 8*g - g + g**n - 5*g + 1.
(g + 1)**2
Let n(z) be the third derivative of 0*z + 0*z**3 + 2/55*z**5 + 1/132*z**6 + 0 + z**2 + 1/33*z**4. Suppose n(j) = 0. Calculate j.
-2, -2/5, 0
Let p(g) = 2*g - 14. Let t be p(7). Suppose -3*r + 6 = q, -5*r - 3*q - q + 3 = t. Determine y, given that 8/7*y**2 + 8/7*y + 2/7*y**r + 0 = 0.
-2, 0
Let c(d) be the second derivative of -2/11*d**2 + 3*d + 1/66*d**4 + 0 + 1/33*d**3. Determine u, given that c(u) = 0.
-2, 1
Let z(o) be the first derivative of 1/36*o**4 + 0*o**3 + 0*o - 3/2*o**2 + 1/90*o**5 + 3. Let a(k) be the second derivative of z(k). Factor a(v).
2*v*(v + 1)/3
Suppose 5*q = -r + 6*r - 5, r - 3 = 0. Suppose -4*k - 2*z + 2 = 0, -3*k + q = -3*z + 5*z. Factor k*d + 2/3*d**2 - 1/3 + 0*d**3 - 1/3*d**4.
-(d - 1)**2*(d + 1)**2/3
Let n(c) be the first derivative of -c**5/110 - 5*c**4/132 - 2*c**3/33 + c**2 + 2. Let z(i) be the second derivative of n(i). Let z(h) = 0. Calculate h.
-1, -2/3
Factor -2/5*r + 0 + 7/5*r**2.
r*(7*r - 2)/5
Factor 2/3*g - 2/3*g**5 + 4/3*g**4 - 4/3*g**2 + 0 + 0*g**3.
-2*g*(g - 1)**3*(g + 1)/3
Let a(b) be the third derivative of -5*b**8/672 - b**7/42 - b**6/48 - 15*b**2. Factor a(o).
-5*o**3*(o + 1)**2/2
Let c = 240 + -4