
Factor 115 + 16*t**2 + 120*t + 23*t**2 - 34*t**2.
5*(t + 1)*(t + 23)
Suppose -d + 21 = -0*d. Let c = d - 19. Factor 0 - 1 + 0*k**c - 1 - 3*k - k**2.
-(k + 1)*(k + 2)
Let v(s) be the first derivative of s**6/720 - s**5/120 + 4*s**3 - 9. Let f(o) be the third derivative of v(o). Factor f(d).
d*(d - 2)/2
Let n be ((-4)/77)/((-1230)/42 - -29). Factor -n - 1/11*u**5 + 4/11*u**4 - 4/11*u**3 - 2/11*u**2 + 5/11*u.
-(u - 2)*(u - 1)**3*(u + 1)/11
Let z = 3 - 3. Let f = -25701/2 + 12854. Factor s**2 + 0*s + z + f*s**3.
s**2*(7*s + 2)/2
Let i(j) be the second derivative of -j**6/80 - j**5/20 - j**4/24 + 3*j + 2. Let i(q) = 0. Calculate q.
-2, -2/3, 0
Let t be (14 - 12)/(1/2). Factor p**4 + 4*p**2 - 4*p**t + p**5 + 0*p**4.
p**2*(p - 2)**2*(p + 1)
Let t(a) = -a - 1. Let g(r) = r**3 - r**2 + 2. Let z(h) = -g(h) - 2*t(h). Factor z(f).
-f*(f - 2)*(f + 1)
Let d(t) be the second derivative of 0*t**3 - 1/255*t**6 - 1/51*t**4 - 3/170*t**5 - 24*t + 0*t**2 + 0. Solve d(u) = 0 for u.
-2, -1, 0
Factor -2/11*w**2 + 0 - 20/11*w.
-2*w*(w + 10)/11
Let v(a) = -a + 29. Let z be v(24). Suppose z*o - 10*o = 0. Factor 4/3*n**4 - 4/3*n**3 - 1/3*n**5 + 0*n + o + 0*n**2.
-n**3*(n - 2)**2/3
Let o(q) be the first derivative of 5*q**4/12 - 13*q**3/9 + 2*q**2/3 + 4*q/3 + 472. Find u, given that o(u) = 0.
-2/5, 1, 2
Let l be (-286)/(-78) - 2/(-6). Solve -3 - 3/4*q**l - 39/4*q**2 - 9*q - 9/2*q**3 = 0 for q.
-2, -1
Let q = 21250 + -106158/5. What is g in -2744/5 - 4/5*g**4 + q*g**3 - 756/5*g**2 + 2548/5*g = 0?
2, 7
Let d be (21/(-14))/((-3)/4). Suppose h = 2*i - 4, 3*i + 2*h = -d*h + 28. Factor 3/2*b**3 + 1/2*b**i + 3/2*b**2 + 0 + 1/2*b.
b*(b + 1)**3/2
Let a(j) = j**5 - j**3 + j**2 - 1. Let d(b) = -24*b**5 + 8*b**4 + 20*b**3 - 28*b**2 + 4*b + 20. Let i(r) = -20*a(r) - d(r). Find l, given that i(l) = 0.
-1, 0, 1
Factor -20/7*y**3 - 4*y - 52/7*y**2 + 0 + 4/7*y**4.
4*y*(y - 7)*(y + 1)**2/7
Suppose -5*n + 4*y = -8, -6*n + 2*y + 4 = -5*n. Suppose n = 9*i + 7 - 43. Factor 7/5*v**i - 23/5*v**3 + 27/5*v**2 + 2/5 - 13/5*v.
(v - 1)**3*(7*v - 2)/5
Suppose 0 = -8*i + 4*i - 16*i + 40. Find g such that -2/7*g**5 + 4/7*g**3 - 8/7*g**4 - 18/7*g + 0 + 24/7*g**i = 0.
-3, 0, 1
Let w = -122 - -86. Let g = w - -36. Suppose 1/4*m + g + 1/4*m**2 = 0. Calculate m.
-1, 0
Factor -1/6*g**3 - 3/2 + 1/6*g + 3/2*g**2.
-(g - 9)*(g - 1)*(g + 1)/6
Suppose 22*v - 68 + 1 = 131. Let -48*s**5 + 0*s**4 + 0 + 0*s - 3/2*s**2 + v*s**3 = 0. What is s?
-1/2, 0, 1/4
Let r = 5219/378 - 58/189. Factor -r + 3/2*t**2 + 27*t - 3*t**3.
-3*(t - 3)*(t + 3)*(2*t - 1)/2
Let l be 10/35 - 90/21. Let h be (-6)/l*(-48)/(-108). Factor 0*z - 4/3*z**3 - 2/3*z**4 - h*z**2 + 0.
-2*z**2*(z + 1)**2/3
Factor -24/7*k**3 - 16/7*k**4 - 4/7*k**5 + 0 - 16/7*k**2 - 4/7*k.
-4*k*(k + 1)**4/7
Let u(k) be the third derivative of -k**7/112 - k**6/30 + k**5/20 - 7*k**3/3 - 11*k**2. Let o(g) be the first derivative of u(g). Factor o(x).
-3*x*(x + 2)*(5*x - 2)/2
Factor 49*l + 18 - 101*l + 50*l + 2*l**3 - 18*l**2.
2*(l - 9)*(l - 1)*(l + 1)
Let d(p) be the third derivative of 0*p**3 - 1/350*p**7 + 0 - 3/100*p**5 + 1/40*p**4 + 0*p + 3/200*p**6 + p**2. Let d(z) = 0. What is z?
0, 1
Suppose -5*j = 7*i - 8*i - 25, -2*i = 3*j - 2. Let w(b) be the first derivative of -4 + 0*b + 4/15*b**3 + 1/10*b**j + 1/5*b**2. Solve w(z) = 0 for z.
-1, 0
Factor -108*q - 1600 - 28*q - 4*q**2 - 24*q.
-4*(q + 20)**2
Let d be ((-942)/(-785))/(21/5). Find o such that -d*o**3 - 4/7 + 4/7*o**2 + 2/7*o = 0.
-1, 1, 2
Let m(d) = -5*d**5 - 99*d**4 - 1085*d**3 - 3995*d**2 - 2*d - 2. Let t(a) = a**5 - 2*a**3 + a**2 + a + 1. Let l(n) = m(n) + 2*t(n). Factor l(v).
-3*v**2*(v + 11)**3
Let m(a) be the first derivative of -a**5/5 - 11*a**4/2 - 77*a**3/3 - 46*a**2 - 36*a - 463. Factor m(t).
-(t + 1)**2*(t + 2)*(t + 18)
Let c(x) = -x**4 + 3*x**2 + x + 1. Let m(g) = -29*g**4 - 173*g**3 - 288*g**2 - 130*g + 2. Let s(h) = 30*c(h) + 5*m(h). Let s(t) = 0. What is t?
-2, -1, 2/35
Suppose -14*t = -16*t + 16. Suppose -2*j = t*j - 20. Factor 0 - 2/9*x**j - 2/9*x.
-2*x*(x + 1)/9
Factor 1/5*d**3 - 27/5 - 13/5*d**2 + 39/5*d.
(d - 9)*(d - 3)*(d - 1)/5
Suppose 156*t = 163*t - 49. Let s(l) be the third derivative of 0*l + 0*l**4 - 5*l**2 + 0 + 0*l**6 - 1/33*l**3 + 1/165*l**5 - 1/1155*l**t. Factor s(b).
-2*(b - 1)**2*(b + 1)**2/11
Solve 20*t**2 - 40 - 21*t**4 - 25*t**4 + 15*t**2 + 51*t**4 - 45*t + 45*t**3 = 0 for t.
-8, -1, 1
Let 352*x**3 + 35*x + 63*x**2 + 97*x - 333*x**2 - 2053*x**3 + 24 = 0. Calculate x.
-2/9, 2/7
Suppose -362/17*q + 40/17 - 688/17*q**3 + 32/17*q**4 + 978/17*q**2 = 0. Calculate q.
1/4, 1, 20
Let y(i) be the third derivative of 0*i**4 + 2/105*i**7 - 1/30*i**6 + 0*i**5 + 0 - 11*i**2 + 0*i + 0*i**3. Factor y(u).
4*u**3*(u - 1)
Let o = 6965/922 + -25/461. Factor -3/2 - 15*d**3 - 3/2*d**5 - o*d**4 - 15/2*d - 15*d**2.
-3*(d + 1)**5/2
Let y(d) be the first derivative of -d**7/63 + 2*d**6/45 + d**5/10 - 52*d + 33. Let r(b) be the first derivative of y(b). Factor r(j).
-2*j**3*(j - 3)*(j + 1)/3
Let d = 725/212 - 168/53. Factor d*k**4 + 1/4*k - 3/4*k**2 + 1/2 - 1/4*k**3.
(k - 2)*(k - 1)*(k + 1)**2/4
Suppose 16 = -n + 4*t, 1 = -2*t + 11. Let j be ((-18)/(-12))/(n/8 + 0). Factor 1/5*w**j - 1/5*w**2 + 1/5 - 1/5*w.
(w - 1)**2*(w + 1)/5
Let r be (-17 - 623/(-35))/((-84)/(-30)). Find j such that -48/7*j + r*j**2 + 288/7 = 0.
12
Let p(o) be the second derivative of 1/2*o**3 + 7*o + 0 - 3/4*o**4 + 0*o**2. Find j such that p(j) = 0.
0, 1/3
Let n(p) = 5*p**3 + 48*p**2 - 47*p - 3. Let z(y) = -10*y**3 - 95*y**2 + 95*y + 5. Let w be (4 - 4) + 3 - 6. Let v(g) = w*z(g) - 5*n(g). Factor v(j).
5*j*(j - 1)*(j + 10)
Let l(z) be the second derivative of z**7/168 - z**6/24 - z**5/40 + 7*z**4/8 - 21*z**3/8 + 27*z**2/8 + 27*z. Let l(x) = 0. Calculate x.
-3, 1, 3
Suppose 0 = 7*z - 46 - 52. Suppose 0 = 4*r - 26 + z. Solve i**2 - 1/2*i**r - 1/2*i + 0 = 0.
0, 1
Suppose -3 = z + 3*c, -3*c + 7 - 16 = 0. Let w(d) be the third derivative of -6*d**2 + 0 + 0*d**4 + 1/6*d**5 + 0*d + 0*d**z - 5/6*d**3 - 1/42*d**7. Factor w(r).
-5*(r - 1)**2*(r + 1)**2
Let a(l) = l**4 - 5*l**3 - 3*l**2 + 3*l + 2. Let k(j) = -j**2 - j + 1. Let o(f) = a(f) - 2*k(f). Find v, given that o(v) = 0.
-1, 0, 1, 5
Let p be ((-134)/8)/(3/(-12)). Factor 25 + p - h**2 + 8 + 40*h + 5*h**2.
4*(h + 5)**2
Let r(k) be the third derivative of 7*k**5/270 - 31*k**4/108 - 20*k**3/27 + 30*k**2 + 4. Factor r(n).
2*(n - 5)*(7*n + 4)/9
Let s = 121/262 + 5/131. Let k(l) be the second derivative of 0*l**5 + 0 + l + 1/2*l**3 - 1/5*l**6 + 0*l**2 + s*l**4 - 1/14*l**7. Determine b so that k(b) = 0.
-1, 0, 1
Let c(x) = x**3 - 7*x**2 - 9*x - 7. Let t be c(8). Let z = 53 + t. Factor -8*s**2 - 16*s**3 - 18*s**3 + 4*s**4 + z*s**3.
4*s**2*(s - 1)*(s + 2)
Let u be -2*5/(-6) - 8/8. Factor -2/3*l + u*l**4 - 2*l**3 + 2*l**2 + 0.
2*l*(l - 1)**3/3
Factor -2/5*t**2 + 12 - 58/5*t.
-2*(t - 1)*(t + 30)/5
Let n(g) be the second derivative of 0 + 12*g + 7/3*g**3 + 2*g**2 - 7/10*g**5 - 1/3*g**4. Find b such that n(b) = 0.
-1, -2/7, 1
Factor -8 + 2*v**2 - 33*v + 18*v + 15*v.
2*(v - 2)*(v + 2)
Let h(l) be the third derivative of -l**8/84 + 8*l**7/105 - 2*l**6/15 - 20*l**2. Find v, given that h(v) = 0.
0, 2
Let o(l) be the third derivative of l**6/270 - 13*l**5/360 + l**4/24 + 2*l**3 - 10*l**2. Let n(q) be the first derivative of o(q). Factor n(d).
(d - 3)*(4*d - 1)/3
Find r such that -3*r + 0 + 10 - 4*r**2 - 2 - r = 0.
-2, 1
Let a(m) be the first derivative of -m**4/24 + m**3/9 + 95. Solve a(h) = 0.
0, 2
Let h be 9/3 - (-2)/(-2)*-11. Let r = h - 92/7. Factor -r*j - 2/7*j**2 + 8/7.
-2*(j - 1)*(j + 4)/7
Solve -2*y**5 - 4/9*y + 0 - 10/9*y**2 + 2*y**4 + 14/9*y**3 = 0 for y.
-2/3, -1/3, 0, 1
Suppose -4*y = u + 9, -4*u = -3*y - 9 + 26. Let t be 16*(-1)/u + 108/(-36). Solve -1/5*s**3 - t*s**2 + 1/5 + 1/5*s = 0 for s.
-1, 1
Let q be (-243)/162 - (-2 - (-1)/6). Factor -5/3*y**2 - q*y + 0.
-y*(5*y + 1)/3
Let m(l) = l**2 - 5*l + 2. Let j be m(3). Let k be (2/j)/((-36)/24). Factor 0 + k*p**2 - 2/3*p.
p*(p - 2)/3
Suppose 3*q + 3*x - 2 = 4, -4*q - 3*x = -6. Let j(o) be the second derivative of -1/12*o**4 + q + o**2 - 1/6*o**3 - 5*o. Determine v, given that j(v) = 0.
-2, 1
Let b(a) be the first derivative of 3 - 8/3*a - 2*a**2 + 16/3*a**3 - 7/3*a**4. Factor b(n).
-4*(n - 1)**2*(7*n + 2)/3
Let n(r) be the third derivative of r*