*2*(b + 1)**2
Let s = 16 + -7. Let v be (1 - -2)/(s/6). Factor -x**2 - x**2 + x + 3*x**v.
x*(x + 1)
Let g = -13 + 15. Let d(r) be the second derivative of r - 1/3*r**g + 0 - 1/18*r**4 - 2/9*r**3. Solve d(k) = 0 for k.
-1
Factor -2*j**2 + 34*j + 4 + 2*j**2 - 28*j + 2*j**2.
2*(j + 1)*(j + 2)
Suppose 682 = -8*u - 758. Let c = 1262/7 + u. Factor -12/7*b - c*b**2 - 18/7.
-2*(b + 3)**2/7
Let u(q) be the first derivative of -2*q**5/75 - q**4/30 + 2*q**3/15 + q**2/3 + 4*q/15 - 7. Factor u(p).
-2*(p - 2)*(p + 1)**3/15
Let y(j) be the second derivative of -j**5/180 - j**4/54 - 9*j. Solve y(n) = 0 for n.
-2, 0
Let u(z) be the third derivative of -7*z**2 + 0*z + 0 + 1/24*z**4 + 1/18*z**3 + 1/90*z**5. What is q in u(q) = 0?
-1, -1/2
Let h(i) be the second derivative of i**7/14 - 4*i**6/5 + 33*i**5/10 - 6*i**4 + 9*i**3/2 + 18*i. Factor h(r).
3*r*(r - 3)**2*(r - 1)**2
Factor -2*h**2 - 14*h + 2*h**2 - 6 - 10*h**2 + 2*h**3 - 4*h**3.
-2*(h + 1)**2*(h + 3)
Suppose -d + 6 = -2*i + 3, 3 = i + d. Let z(b) be the third derivative of 0 + 0*b**4 + 0*b + 0*b**5 + i*b**3 + 1/420*b**6 + 2*b**2. Factor z(t).
2*t**3/7
Let s(t) be the first derivative of -15*t**4/4 - 42*t**3 - 144*t**2 - 96*t + 51. Solve s(y) = 0 for y.
-4, -2/5
Let g(q) be the third derivative of -q**5/390 + q**4/78 - q**3/39 - 18*q**2. Solve g(z) = 0 for z.
1
Let t(p) = 2*p + 7. Let g be t(-6). Let m = 7 + g. Suppose 10*f**m - 4*f**5 + 5*f**4 - 5*f - 2 + 3*f**5 + 3 - 10*f**3 = 0. What is f?
1
Let a(c) be the second derivative of -c**5/210 - 4*c. Determine q, given that a(q) = 0.
0
Let a(x) = x**3 - 4*x**2 - x + 4. Let h(j) = -2*j**3 + 9*j**2 + 2*j - 9. Let p(l) = 15*a(l) + 6*h(l). Factor p(r).
3*(r - 2)*(r - 1)*(r + 1)
Let o = -50 - -251/5. Let z(d) be the first derivative of 0*d**2 + o*d**6 - 2 + 0*d**3 + 8/25*d**5 + 0*d - 2/5*d**4. Determine c so that z(c) = 0.
-2, 0, 2/3
Let x(b) = -11*b + 1. Let l(p) = 5*p. Let i(n) = -9*l(n) - 4*x(n). Let y be i(-4). Factor -2/3*h**4 + 0 + y*h + 4/3*h**3 - 2/3*h**2.
-2*h**2*(h - 1)**2/3
Let n(t) be the third derivative of 4*t**5/15 + t**4/2 - 2*t**3/3 - 37*t**2. Factor n(g).
4*(g + 1)*(4*g - 1)
Let j(p) be the first derivative of p**4/54 - p**2/9 - p + 3. Let t(q) be the first derivative of j(q). Let t(l) = 0. What is l?
-1, 1
Factor 1/4*g**2 - 1/4 + 0*g.
(g - 1)*(g + 1)/4
Factor -64 - 26*a**3 - 5*a**2 + 64*a + 5*a**2 + 10*a**3 + 4*a**4.
4*(a - 2)**3*(a + 2)
Let l(y) be the first derivative of 5 + 2/21*y**3 - 2/35*y**5 + 0*y + 1/14*y**4 - 1/7*y**2. Suppose l(t) = 0. Calculate t.
-1, 0, 1
Let y(i) be the first derivative of 2*i**6 + 4/5*i**5 + 0*i**3 + 0*i + 0*i**2 + 2 - 2*i**4. Suppose y(p) = 0. Calculate p.
-1, 0, 2/3
Suppose 6*s - 3*y - 51 = 3*s, 77 = 5*s - y. Suppose 0 = 5*t - s - 5. Factor -1/3*r**t - 1/6*r + 1/3*r**2 + 0 + 1/6*r**3.
-r*(r - 1)*(r + 1)*(2*r - 1)/6
Let v = 4/151 - 41/7248. Let o(h) be the third derivative of 0*h - 3*h**2 - 1/840*h**7 + v*h**4 + 0 + 0*h**3 + 0*h**6 + 1/80*h**5. Factor o(i).
-i*(i - 2)*(i + 1)**2/4
Let 9*n**4 - 9*n**3 - n**5 - 2*n**2 + n**5 + 5*n**2 - 3*n**5 = 0. Calculate n.
0, 1
Suppose -9 + 8*v**5 + 0*v**4 + 9 + 6*v**4 - 2*v**3 = 0. Calculate v.
-1, 0, 1/4
Factor 74*r - 12 + 3*r**2 - 74*r.
3*(r - 2)*(r + 2)
Suppose 3*f = -2*f + 15. Suppose 9*j**2 - 6*j**4 - 9*j**4 + 6*j**f + 12*j**4 = 0. Calculate j.
-1, 0, 3
Let w = -485/6 + 81. Let v(a) be the first derivative of 0*a**2 - 1/15*a**5 + 0*a - 1/9*a**3 - w*a**4 + 1. Find l such that v(l) = 0.
-1, 0
Let g(y) be the second derivative of y**8/26880 - y**6/2880 + y**4/3 - 4*y. Let v(o) be the third derivative of g(o). Factor v(i).
i*(i - 1)*(i + 1)/4
Suppose -3*s = -o - 3, 0 = -s - s. Let z(p) = -p**3 + p**2. Let f(l) = 7*l**3 - 13*l**2 - 3*l + 9. Let i(j) = o*f(j) - 24*z(j). Factor i(a).
3*(a - 1)*(a + 3)**2
Let m be -3 - (-5)/(15/9). Suppose 5*k - 5 = 5*s, -k + 11 = -2*s + 4*k. Factor -6/5*j**s + 6/5*j**3 - 2/5*j**4 + 2/5*j + m.
-2*j*(j - 1)**3/5
Suppose 2*t + 12/5 + 2/5*t**2 = 0. Calculate t.
-3, -2
Let 6/7*g**3 - 2/7*g**4 - 2/7*g**2 - 6/7*g + 4/7 = 0. What is g?
-1, 1, 2
Let x(o) be the second derivative of 0 + 4/105*o**7 + 0*o**2 + 5*o + 0*o**3 + 1/75*o**6 + 1/60*o**4 - 1/20*o**5. Determine t, given that x(t) = 0.
-1, 0, 1/4, 1/2
Let t(q) be the third derivative of -q**8/1344 + q**7/140 - q**6/60 - q**5/15 + q**4/2 - 4*q**3/3 + 22*q**2. Determine p, given that t(p) = 0.
-2, 2
Let k(t) be the second derivative of t**2 - 1/300*t**5 + 0*t**3 + 0 - 1/120*t**4 + 4*t. Let p(h) be the first derivative of k(h). Let p(m) = 0. What is m?
-1, 0
Let o = 169/95 + -30/19. Factor 0 - o*i**2 - 2/5*i.
-i*(i + 2)/5
Let k(j) = j**2 + j - 1. Let t(z) = 10*z**2 - 5. Let w(r) = 5*k(r) - t(r). Determine i, given that w(i) = 0.
0, 1
Let o = -59/20 - 503/60. Let q = o + 12. Let q*t**2 + 4/9*t + 0 = 0. Calculate t.
-2/3, 0
Factor 2/3*a + 2/3*a**2 - 2/3*a**3 - 2/3*a**4 + 0.
-2*a*(a - 1)*(a + 1)**2/3
Let m be ((-5)/3)/((-5)/15). Find k such that -2/3*k**3 + 4/3*k**m - 2/3*k + 8/3*k**2 - 7/3*k**4 - 1/3 = 0.
-1, -1/4, 1
Let y(w) be the third derivative of -w**11/73920 + w**10/14400 - w**9/7560 + w**8/10080 - w**5/30 + w**2. Let r(j) be the third derivative of y(j). Factor r(u).
-u**2*(u - 1)*(3*u - 2)**2/2
Let j(u) be the third derivative of u**10/105840 + u**9/26460 - u**4/8 + 2*u**2. Let a(q) be the second derivative of j(q). Solve a(r) = 0.
-2, 0
Let k = 51 + -49. Let q(u) be the first derivative of 1/5*u**5 - 1/2*u**4 + 0*u**2 + 0*u + k + 0*u**3. Solve q(j) = 0 for j.
0, 2
Factor -6*f + 9/2 + 3/2*f**2.
3*(f - 3)*(f - 1)/2
Factor 1/3*z**5 + 0*z**3 - 2/3*z**2 + 2/3*z**4 - 1/3*z + 0.
z*(z - 1)*(z + 1)**3/3
Let x(p) = 2*p**2 + 1. Let m be x(1). Factor -m*k**2 - 2*k - k**3 + 3*k**3 + k**2 + 2*k**4.
2*k*(k - 1)*(k + 1)**2
Let k = -391 + 2743/7. Factor 6/7*p**2 + 2/7*p**3 + 2/7 + k*p.
2*(p + 1)**3/7
Let u(s) be the third derivative of -s**9/60480 + s**8/13440 + 7*s**4/24 - s**2. Let h(c) be the second derivative of u(c). Factor h(b).
-b**3*(b - 2)/4
Suppose 3*p + 11/4 + 1/4*p**2 = 0. Calculate p.
-11, -1
Suppose -4*g = 3*x - 11, 2*x - x = 4*g - 7. Let l(s) be the first derivative of -s**4 + s + 3*s**3 - 5 - 4*s**3 - 3*s**g + 2 + 4*s**3. Factor l(a).
-(a - 1)**2*(4*a - 1)
Let m(l) = -l - 2. Suppose s = -2*s - 6. Let a be m(s). What is d in 0*d**2 - 2/5*d**5 + a*d**3 - 2/5*d**4 + 0*d + 0 = 0?
-1, 0
Factor 8/11*p**4 + 0 + 2/11*p**3 + 6/11*p**5 + 0*p**2 + 0*p.
2*p**3*(p + 1)*(3*p + 1)/11
Factor 6/7*i + 0 + 2/7*i**2.
2*i*(i + 3)/7
Suppose x + 4*j - 20 = 0, 5*x - 4*j = 36 + 64. Suppose 0 = b - 6*b + x. Determine y so that 4*y**4 - 6*y**2 - b*y**3 + 4 + 2*y - 8*y**5 + 10*y**5 - 2*y**2 = 0.
-2, -1, 1
Let c be (-1 + 1)/(1*-3). Suppose -3*n - y + 10 = 0, -3*y = n - c*y + 10. Find v such that 2*v**2 + n + 1 - 6 = 0.
0
Let n(a) = a + 11. Let o be n(-14). Let h be 2*(-1 - 4/o). Factor 1/3 + 0*m + 1/3*m**4 + 0*m**3 - h*m**2.
(m - 1)**2*(m + 1)**2/3
Suppose -4*p - 219 = 341. Let s be p/(-225) - 2/5. Suppose -s*f**2 + 2/9*f + 4/9 = 0. What is f?
-1, 2
Let k(y) = 2*y**4 + 4*y**2 + 20*y - 4. Let o(q) = -3*q**4 - q**3 - 3*q**2 - 21*q + 5. Let w(b) = 5*k(b) + 4*o(b). Let w(j) = 0. What is j?
-2, 0, 2
Solve -3 + 9*y + 3/4*y**2 - 9/4*y**3 = 0 for y.
-2, 1/3, 2
Let k(w) be the first derivative of 2*w**5/15 - 5*w**4/18 + 2*w**3/27 + w**2/9 + 34. Factor k(g).
2*g*(g - 1)**2*(3*g + 1)/9
Let x(t) be the third derivative of -t**5/270 + t**4/54 - t**3/27 - t**2. Solve x(q) = 0 for q.
1
Suppose y + 2*d + 39 = -0*d, 0 = -2*y + 2*d - 60. Let h be (-6)/6 - y/27. Suppose 0*x + 0*x**2 + 0 + 8/9*x**5 + h*x**3 - 10/9*x**4 = 0. Calculate x.
0, 1/4, 1
Let b(m) be the second derivative of m**5/50 - m**4/5 - 7*m**3/15 + 24*m. Find r such that b(r) = 0.
-1, 0, 7
Let g = 382957/4 + -95025. Let j = g - 708. Solve 1 - j*a**4 + 5*a**3 - 5*a + 21/4*a**2 = 0 for a.
-1, 2/5, 1
Let r(g) be the second derivative of 1/15*g**3 + g - 1/30*g**4 + 0 + 0*g**2 + 1/75*g**6 - 1/50*g**5. Factor r(d).
2*d*(d - 1)**2*(d + 1)/5
Let o(n) = n**2 - 6*n - 5. Let w be o(7). Solve 7*y**3 + 5*y**2 - 2*y - w*y + 2*y = 0 for y.
-1, 0, 2/7
Let n(t) = -t**3 - t**2 - t - 1. Let w(u) = -49*u**3 - 29*u**2 + 19*u - 1. Let v(p) = -n(p) - w(p). Solve v(s) = 0 for s.
-1, 1/5
Let v(z) be the first derivative of -11/8*z**4 - 5/2*z**2 + z - 4 + 11/4*z**3 + 1/4*z**5. Find t, given that v(t) =