 1, 2
Suppose 0*p = -3*n - 2*p - 2, -14 = -3*n + 2*p. Factor -5*a - 2 + 3*a + 2*a**3 - 2*a**n + 4*a**2 + 0*a.
2*(a - 1)*(a + 1)**2
Factor 0*a + 3/8 + 0*a**3 - 3/4*a**2 + 3/8*a**4.
3*(a - 1)**2*(a + 1)**2/8
Suppose 15*n - 2 = 14*n. Let o(r) be the third derivative of 1/12*r**4 - 1/6*r**3 - 1/60*r**5 + 0 + 0*r + n*r**2. Factor o(b).
-(b - 1)**2
Suppose 0 = -2*f + 3*s - 4, 2*f + 4*s - 24 = -0*f. Let l = -2 + f. Let l + t**3 - t - 1 - t**2 + 0*t**2 = 0. Calculate t.
-1, 1
Let r(t) be the first derivative of 1/4*t**4 + 0*t**2 + 2 + 0*t - 1/3*t**3. Factor r(a).
a**2*(a - 1)
Let y(p) be the second derivative of p**4/18 - 4*p**3/9 + p**2 - 4*p. Suppose y(v) = 0. Calculate v.
1, 3
Let r be -2*(3 + (-15)/6). Let d = 3 + r. Find b such that 0 + 4/9*b**d + 0*b + 22/9*b**3 + 14/9*b**5 + 32/9*b**4 = 0.
-1, -2/7, 0
Let o be 3/5 + 360/25. Let k(f) = -f**5 - 2*f**4 + 2*f**2 - 3*f + 2. Let h(q) = 3*q**5 + 4*q**4 - 4*q**2 + 7*q - 5. Let l(t) = o*k(t) + 6*h(t). Factor l(r).
3*r*(r - 1)**3*(r + 1)
Let v(k) be the third derivative of 0*k**3 + 1/25*k**6 + 0*k + k**2 - 4/75*k**5 + 0 + 1/840*k**8 + 0*k**4 - 2/175*k**7. Factor v(m).
2*m**2*(m - 2)**3/5
Let w be (0/(-3) + 1)*-27. Let q be 0/3 - 12/w. Factor -2/9*d**2 + q*d - 2/9.
-2*(d - 1)**2/9
Suppose -5/4*x + 1/4*x**2 + 3/2 = 0. What is x?
2, 3
Let k(y) be the second derivative of -y**5/60 + y**4/36 - 2*y. Let k(r) = 0. What is r?
0, 1
Let x(t) = -3*t + 9. Let i be x(6). Let a be (8/(-6))/(3/i). Factor 0*n**3 - n**3 + n**a + 2*n**3.
n**3*(n + 1)
Let u(d) = d + 2. Let t be u(2). Determine j so that -6 - 2*j**2 + j**4 - 6 - 32*j - 22*j**2 + 3*j**t = 0.
-1, 3
Let -2*k - 4*k - 5*k**2 - 2*k + 9*k**2 = 0. Calculate k.
0, 2
Let z(n) = -2*n**5 + 5*n**4 + 7*n**3 - 9*n**2 - 9*n. Let w(s) = -s**4 - s**3 + s**2 + s. Let v(m) = 18*w(m) + 2*z(m). Factor v(i).
-4*i**3*(i + 1)**2
Let k(t) be the first derivative of t**6/720 - t**5/240 - 5*t**3/3 + 3. Let w(y) be the third derivative of k(y). Suppose w(s) = 0. Calculate s.
0, 1
Solve 3/5*x**3 - 9/5 - 3/5*x**2 - 3*x = 0.
-1, 3
Suppose 2*p - 5 = 3. Let t be (-4)/6 - p/(-6). Find j such that t + 2/5*j**2 + 0*j - 2/5*j**3 = 0.
0, 1
Let z(t) be the third derivative of 1/6*t**4 + 0 + 0*t - 1/30*t**6 - 1/30*t**5 - t**2 + 1/105*t**7 + 0*t**3. Factor z(g).
2*g*(g - 2)*(g - 1)*(g + 1)
Let i(w) be the first derivative of -w**5/80 - w**4/24 + 2*w - 1. Let q(b) be the first derivative of i(b). Factor q(g).
-g**2*(g + 2)/4
Let l(a) = 2 - 2 - 1 + 0. Let m(n) = -3*n**2 + 9*n - 3. Let h(s) = -3*l(s) - m(s). Find w such that h(w) = 0.
1, 2
Let z = -116/5 - -1094/45. Let s = -4/9 + z. Suppose -4*r + 6 + s*r**2 = 0. What is r?
3
Let a(v) = -v**2 - 1. Let x(s) = -2*s**3 - 6*s**2 - 16*s - 4. Let l(c) = -4*a(c) - x(c). Suppose l(n) = 0. Calculate n.
-2, -1
Let j(d) be the second derivative of -4/5*d**6 + 0*d**2 - 12/5*d**5 - 2*d**3 + 0 - 10/3*d**4 + 6*d - 2/21*d**7. Factor j(z).
-4*z*(z + 1)**3*(z + 3)
Let h(v) be the third derivative of 3*v**6/80 - v**5/20 - 5*v**4/12 - 2*v**3/3 - 9*v**2. Suppose h(n) = 0. What is n?
-2/3, 2
Let w(k) be the first derivative of -7*k**4/36 - k**3/9 + 4*k - 3. Let c(f) be the first derivative of w(f). Factor c(o).
-o*(7*o + 2)/3
Let o be (-3)/(-2) - (-253)/(-198). Solve -o*a**2 - 2/3*a - 4/9 = 0 for a.
-2, -1
Let b(t) = 3*t**2 + 77*t + 64. Let i(c) = 20*c**2 + 500*c + 416. Let k(m) = 32*b(m) - 5*i(m). Find v, given that k(v) = 0.
-8, -1
Let r(k) be the first derivative of -k**4/12 + k**3/3 - k - 4. Let u(x) be the first derivative of r(x). Factor u(j).
-j*(j - 2)
Let c be 16/136 + (-237)/(-153). Factor c*k**2 + 4/3 + 4*k.
(k + 2)*(5*k + 2)/3
Suppose 17 = -2*m + 4*t + t, 0 = 3*m - t - 7. Suppose 4*g + 2*r = 5*r - 7, -m*g - 12 = -4*r. Factor -2*w**2 + 2*w**4 - w**4 + 0*w**4 + g*w**3 - w + 1 - w**5.
-(w - 1)**3*(w + 1)**2
Suppose -3*j = -j - 4. Suppose -3*k = -j*k - 3. Factor -1/2*r**k + 0 - 1/2*r + r**2.
-r*(r - 1)**2/2
Let x(q) = -q**2 - 12*q - 8. Let k(p) = p. Let t(v) = k(v) + x(v). Let g be t(-10). Factor -1/2*d**3 + 1/2*d - 1/2 + 1/2*d**g.
-(d - 1)**2*(d + 1)/2
Let r(y) = -12*y**4 - 9*y**3 + 6*y**2 + 3*y - 3. Let t(f) = -37*f**4 - 27*f**3 + 18*f**2 + 8*f - 8. Let x(j) = 8*r(j) - 3*t(j). Factor x(h).
3*h**2*(h + 1)*(5*h - 2)
Let a(c) = 20*c**2 + 44*c + 8. Let y(o) = 29*o + 20*o + 5 + 13*o**2 - 20*o. Let f(r) = -5*a(r) + 8*y(r). Let f(j) = 0. What is j?
-3, 0
Let j(m) = m - 3. Let n be j(4). Let p be (2 - (-12)/(-9))*n. Factor 4/3*t - 2/3 - p*t**2.
-2*(t - 1)**2/3
Factor 0*n - 2/5 + 2/5*n**2.
2*(n - 1)*(n + 1)/5
Let t(l) be the second derivative of l + 1/10*l**5 + l**2 + 0 - 1/6*l**4 - 1/3*l**3. Factor t(f).
2*(f - 1)**2*(f + 1)
Let r(n) = n**3 + 7*n**2 + 5*n - 6. Let p be r(-6). Let h(v) be the third derivative of -2/3*v**3 - 1/60*v**5 + 1/6*v**4 + 0 - 3*v**2 + p*v. Factor h(b).
-(b - 2)**2
Let w(y) = y**2 + y. Let t = 4 + -3. Let v(j) = -8*j**2 - 10*j - 2. Let o(q) = t*v(q) + 6*w(q). Determine b so that o(b) = 0.
-1
Let w be (-18)/(-6) + -8*1. Let l(x) = -4*x**3 + 4*x**2 - 2*x - 1. Let i(m) = -7*m**3 + 7*m**2 - 3*m - 2. Let d(p) = w*l(p) + 3*i(p). Factor d(z).
-(z - 1)**2*(z + 1)
Let a(y) = 23*y + 94. Let s be a(-4). Let 0 + 2/9*c - 2/9*c**s = 0. Calculate c.
0, 1
Let j(f) = -f**3 + 13*f**2 - f + 17. Let r be j(13). What is p in -8*p + 1 + p**3 + 5*p**2 - 2*p**2 - r*p**2 + 7*p = 0?
-1, 1
Let y be (-3 - 1)*(-18)/8. Let x be 6/8 - y/12. Solve 1/2*r**2 + x - r = 0.
0, 2
Determine q, given that 16*q**3 - 20/3*q + 76/9*q**2 + 8/9 = 0.
-1, 2/9, 1/4
Factor 11*f + 33*f**2 - 38*f**2 - f.
-5*f*(f - 2)
Let a(r) = -r**3 + 2*r**2 + 4*r - 1. Let u be a(3). Solve 0*p**3 + 0*p**3 - 3*p**u - 3*p**3 = 0.
-1, 0
Let g be (-1 + 4)/(6/8). Let h(w) = 4*w**3 + 2*w**2 - 2*w + 1. Let i be h(1). Factor -i*p**2 + 4*p**2 + 3*p**5 + p**g - 2*p - 5*p**3 + 4*p.
p*(p - 1)*(p + 1)**2*(3*p - 2)
Let u(y) be the second derivative of y**5/180 - y**4/36 + 3*y**2/2 - 5*y. Let q(v) be the first derivative of u(v). Suppose q(p) = 0. What is p?
0, 2
Let l = -968/3 - -323. Factor 0*w + l*w**2 + 7/3*w**3 + 0 + 4*w**4.
w**2*(3*w + 1)*(4*w + 1)/3
Suppose -s = -3*s. Suppose s*j = 3*j. Factor 1/2*l**2 - 1/2*l**4 + 0*l + 0 + j*l**3.
-l**2*(l - 1)*(l + 1)/2
Factor 2/11*y + 2/11*y**2 - 2/11 - 2/11*y**3.
-2*(y - 1)**2*(y + 1)/11
Let p(s) = -s**3 - 8*s**2 - 3*s + 4. Let d(a) = a - 8. Let k be d(7). Let c(h) = -h**2 + 1. Let n(t) = k*p(t) + 5*c(t). Find u, given that n(u) = 0.
-1
Suppose -5*k = -14*k + 18. Determine u, given that -2/13*u**k + 16/13*u - 32/13 = 0.
4
Factor 2/15 + 2/15*d - 2/15*d**3 - 2/15*d**2.
-2*(d - 1)*(d + 1)**2/15
Let r(p) be the first derivative of p**6/54 + p**5/45 - p**4/18 - 2*p**3/27 + p**2/18 + p/9 - 2. Let r(a) = 0. What is a?
-1, 1
Let q(l) be the third derivative of l**5/30 - 7*l**4/12 + 2*l**3 + 3*l**2. Let q(v) = 0. Calculate v.
1, 6
Suppose -13*t + 7 = -45. Let f(w) be the second derivative of -1/5*w**5 + 0*w**2 - t*w - 1/15*w**6 + 0 - 1/6*w**4 + 0*w**3. Factor f(m).
-2*m**2*(m + 1)**2
Let z(t) be the first derivative of 2*t**5/35 - 3*t**4/14 - 4*t**3/21 + 12*t**2/7 - 16*t/7 + 29. Factor z(l).
2*(l - 2)**2*(l - 1)*(l + 2)/7
Let n(t) = 9*t + 189. Let d be n(-21). Let d*h**2 - 4/9*h**3 + 0 + 0*h + 2/9*h**5 - 2/9*h**4 = 0. Calculate h.
-1, 0, 2
Let h be (-20)/(-15) - 11/(-3). Factor 2/5*f**h + 0*f + 2/5*f**2 - 2/5*f**4 + 0 - 2/5*f**3.
2*f**2*(f - 1)**2*(f + 1)/5
Let h(v) be the second derivative of 3*v**5/40 - v**3/4 - 7*v. Suppose h(i) = 0. Calculate i.
-1, 0, 1
Let y = -3/3847 + 96328/196197. Let p = 3/17 + y. Factor 2*z**2 + 0 - p*z.
2*z*(3*z - 1)/3
Let y(u) be the first derivative of -u**6/240 - u**5/120 + u**2/2 - 3. Let o(l) be the second derivative of y(l). Solve o(w) = 0 for w.
-1, 0
Let o = -4/79 - -266/2133. Let z = o - -19/108. Suppose 1/2*m - z - 1/4*m**2 = 0. What is m?
1
Suppose -f - 2*f + 12 = 0. Let k = f + 0. Factor 1/4*j**3 - 1/4*j - 3/4*j**2 + 0 + 3/4*j**k.
j*(j - 1)*(j + 1)*(3*j + 1)/4
Let m(f) be the second derivative of 2*f**7/147 - f**6/21 + 2*f**5/35 - f**4/42 + 21*f. Factor m(o).
2*o**2*(o - 1)**2*(2*o - 1)/7
Factor 39/4*q - 9/2 + 15/4*q**2.
3*(q + 3)*(5*q - 2)/4
Let c(r) be the third derivative of 1/3*r**3 - 1/6*r**4 + 0 + 0*r**5 - 1/105*r**7 + 0*r - 7*r**2 + 1/30*r**6. Find g such that c(g) = 0.
-1, 1
Factor 20*u + 4*u**3 + 13 + 0 + 16*u**2 - 5.
4*(u + 1)**2*(u + 2