s**5/5 + 1495*s**4/3 - 544*s**3/9 + 8*s**2/3 + 60*s. Factor n(m).
4*(m + 1)*(69*m - 2)**2/3
Let g = -1822/155 + 662/31. Determine n, given that -g*n + 64/5 - 1/5*n**3 + 12/5*n**2 = 0.
4
Suppose -5 - 10 = -3*v. Let t(u) = u**3 - 5*u**2 + 2*u - 8. Let x be t(v). Factor 2*r**3 + 5*r**2 - 3*r**x + r**4 + r**3.
r**2*(r + 1)*(r + 2)
Let j = -411 + 411. Factor j*b + 0 - 2/11*b**3 + 0*b**2.
-2*b**3/11
Let c = -2 - -4. Let k be (-4)/(-14) - (-114)/42. Solve -4/5*b - 2/5*b**4 + 0*b**k + 6/5*b**c + 0 = 0 for b.
-2, 0, 1
Let x = -10 - -20. Factor 5*h**2 + 2*h**4 + x*h**3 + 99 - 95 + 13*h**2 + 14*h.
2*(h + 1)**3*(h + 2)
Let p(h) be the first derivative of -8*h**5/5 - 3*h**4/2 + 6*h**3 - 2*h**2 - 594. Factor p(o).
-2*o*(o - 1)*(o + 2)*(4*o - 1)
Suppose 0 = 8*o + 6557 - 6589. Solve 0 + 0*u - 2/3*u**o + 0*u**2 + 4/3*u**3 = 0 for u.
0, 2
Let u(a) be the third derivative of -4*a**6/105 - 4*a**5/35 + 5*a**4/28 + 25*a**3/21 - 711*a**2. Suppose u(d) = 0. Calculate d.
-5/4, 1
Let f(r) = -4 + 4*r**2 - r**3 + 2*r + 5*r**2 - 3*r**2. Let t be f(6). Suppose 14*l - 4*l + 3*l**3 + 4 + t*l**2 - l**3 = 0. What is l?
-2, -1
Let k be 3/(10/(60/18)). Suppose -13*v - k = -1. Factor -1/6*t**3 + v*t + 1/6*t**2 + 0.
-t**2*(t - 1)/6
Let b be -1*(2 + -5 + -1). Suppose 2 = -0*g + 5*g - b*i, -4*g + 10 = i. Solve g*r**2 - 5*r**2 - 12*r + 5*r**2 + 18 = 0 for r.
3
Let z(v) be the second derivative of 5/4*v**4 + 0*v**2 + 0 - 5/3*v**3 + 14*v - 1/4*v**5. Factor z(q).
-5*q*(q - 2)*(q - 1)
Let v(y) be the second derivative of -2*y**4/63 + 11*y**3/63 + y**2/7 - y + 3. Factor v(d).
-2*(d - 3)*(4*d + 1)/21
Let v = 17 - 14. What is z in 2*z**3 - v*z**2 - 2*z**5 - 4*z**4 + 0*z**4 + 7*z**2 = 0?
-2, -1, 0, 1
Let k(q) be the second derivative of -q**6/135 - 7*q**5/90 - q**4/6 + q**3 + 6*q**2 + 4*q + 5. Determine p so that k(p) = 0.
-3, 2
Find z, given that 4*z - 3*z**2 + 1/4*z**4 + 0*z**3 + 0 = 0.
-4, 0, 2
Let o be -22 - ((-588)/15 + 16). Find z, given that -3/5*z**2 - o*z - 3/5 = 0.
-1
Let j = 87305/2 - 43652. Factor -6*l - j*l**3 - 4 - 3*l**2.
-(l + 2)**3/2
Let x = -39/19 + 135/38. Let v(l) be the second derivative of 7/6*l**3 - 1/3*l**4 + 6*l + 0 - x*l**2. Factor v(c).
-(c - 1)*(4*c - 3)
Let g be (168/1680)/(0 + 1/2). Let v(j) = j**3 + j**2 - j - 1. Let p be v(-1). Factor g*x + p + 1/5*x**2.
x*(x + 1)/5
Determine b so that 44/7*b**2 + 0*b + 36/7*b**3 - 16/7 + 8/7*b**4 = 0.
-2, -1, 1/2
Let b be 805/700 - (-2)/20. Factor 5/2*t**3 - b*t**4 + 0 - 5/4*t**2 + 0*t.
-5*t**2*(t - 1)**2/4
Let u be (-56)/(-25)*(-13 + 1425/100). Factor -12/5 - u*j - 2/5*j**2.
-2*(j + 1)*(j + 6)/5
Let l(y) = y**2 - 8*y + 3. Let z be l(8). Suppose 8 + 6 = 4*m + z*b, 2*m + b = 6. Find u, given that -2/3 + 2/3*u**3 + m*u - 2*u**2 = 0.
1
Let f be 234 + (6/(-15))/((-4)/(-20)). Let j = f + -232. Suppose 0 + 0*a**2 + 2/9*a**5 - 2/9*a**4 + j*a**3 + 0*a = 0. What is a?
0, 1
Let g(o) = o**3 - 21*o**2 + 24*o - 78. Let q be g(20). Suppose -2*c = 2*c - 8. Solve -12*h**2 + 16*h**q + 2*h + 4*h + 17*h**c = 0 for h.
-2/7, 0
Let o be (6 - (7 - 0))*(2 + -1). Let x(d) = 199*d**2 + 39*d + 2. Let n(g) = -g**2 - g. Let w(c) = o*n(c) + x(c). Factor w(t).
2*(10*t + 1)**2
Suppose 0*y - 10 = -10*y. Let l(c) = 2*c**3 + c**2 + 2*c - 2. Let a be l(y). Let 1/3*h**5 + 0 + 0*h - h**a + 2/3*h**2 + 0*h**4 = 0. Calculate h.
-2, 0, 1
Factor -2025/4*h**2 - 45/2*h**3 - 151875/8 - 3/8*h**4 - 10125/2*h.
-3*(h + 15)**4/8
Let x(i) be the first derivative of 2*i**3/3 - 29*i**2/2 - 15*i + 831. Let x(l) = 0. Calculate l.
-1/2, 15
Let c(x) = x**2 + 13*x. Let p be c(-9). Let d be (p/675)/(1 - 14/10). Determine j so that -d*j**2 + 2/15*j**4 + 4/15*j - 4/15*j**3 + 0 = 0.
-1, 0, 1, 2
Let b(s) be the third derivative of 0*s - 1/210*s**6 - 17*s**2 + 0*s**3 - 2/105*s**5 - 1/42*s**4 + 0. Factor b(k).
-4*k*(k + 1)**2/7
Suppose 30/7*i - i**2 - 8/7 = 0. Calculate i.
2/7, 4
Suppose 0 = 20*d - 292 - 68. Suppose -d = -5*y + 7*w - 5*w, 0 = -2*y - w. Factor 2/7*x**y + 2/7 + 4/7*x.
2*(x + 1)**2/7
Let v(j) be the third derivative of 0 + 0*j + 1/3*j**3 + 0*j**4 + 0*j**5 + 5*j**2 + 1/900*j**6. Let y(c) be the first derivative of v(c). Factor y(s).
2*s**2/5
Let k be (7 - 2)/(-5) - 12/(-9). Solve 0 + k*o**4 - 1/3*o**3 - 1/3*o**2 + 1/3*o**5 + 0*o = 0.
-1, 0, 1
Let m(h) be the third derivative of -1/240*h**6 + 0 + 0*h + 1/40*h**5 - 10*h**2 - 1/16*h**4 + 1/12*h**3. Factor m(o).
-(o - 1)**3/2
Let f(z) = -z - 24. Let u be f(-20). Let h be (11 - 4)*u/(-14) - 0. Let 2/3 + 8/9*a + 2/9*a**h = 0. Calculate a.
-3, -1
Suppose 1/3*o**3 + 1/3 + o + o**2 = 0. Calculate o.
-1
Suppose -3*g = -2*f - 8, 2*f = 31*g - 30*g. Factor 44/7*c + 24/7*c**f + 4/7*c**3 + 24/7.
4*(c + 1)*(c + 2)*(c + 3)/7
Let g = -8 - 16. Let f = g + 24. Find s such that 2/7*s + f + 2/7*s**2 = 0.
-1, 0
Let a(m) = 4*m**2 + 26*m. Let p(w) = 5*w**2 + 25*w. Let v(d) = 3*a(d) - 2*p(d). Suppose v(r) = 0. What is r?
-14, 0
Let g(a) be the third derivative of -a**5/210 - 9*a**4/14 - 243*a**3/7 - 63*a**2. Find f, given that g(f) = 0.
-27
Let l = 147 + -144. Solve -9*b**4 + 3*b**2 + 63*b - 8 - 15*b**l - 46 + 27*b**4 - 15*b**4 = 0.
-2, 1, 3
Let a(s) be the first derivative of 2/11*s**3 - 13 - 6/11*s + 0*s**2. Let a(g) = 0. Calculate g.
-1, 1
Let g = 719/1086 + 5/1086. Factor g*l**2 + 0 + 0*l.
2*l**2/3
Let z(b) = b**3 + 14*b**2 - 63*b - 56. Let s(y) = -y**3 - 29*y**2 + 128*y + 111. Let o(r) = -4*s(r) - 9*z(r). Factor o(v).
-5*(v - 3)*(v + 1)*(v + 4)
Let t(l) be the second derivative of 81*l**5/5 - 228*l**4 + 584*l**3/3 - 64*l**2 - 7*l. Find d such that t(d) = 0.
2/9, 8
Factor 633*j - 593*j + 0*j**2 - 2*j**2.
-2*j*(j - 20)
Factor -100*z**4 + 130*z**4 - 2*z**5 + 7*z**5 + 10*z**2 - 60*z - 40 + 55*z**3.
5*(z - 1)*(z + 1)*(z + 2)**3
Let f(x) be the third derivative of 1/60*x**6 + 0 + 0*x - 1/12*x**4 - 2*x**2 - 1/105*x**7 + 0*x**3 + 1/30*x**5. Let f(w) = 0. Calculate w.
-1, 0, 1
Determine q so that -2/7*q**4 - 10/7*q**3 + 0 + 10/7*q + 2/7*q**2 = 0.
-5, -1, 0, 1
Let r(y) be the first derivative of y**3/9 - y**2/2 - 18*y + 215. Factor r(c).
(c - 9)*(c + 6)/3
Suppose 0 = -5*b + 4*m - m + 34, -2*m = 5*b - 19. Suppose 0 = -5*z - b*v - 5, -4*z - 4 = -5*z + 4*v. Let -2*k + z*k - 7*k - 6 - 3*k**2 = 0. Calculate k.
-2, -1
Let z(p) be the second derivative of 0*p**3 + 0 - 1/18*p**4 - 13*p + 0*p**2 - 1/90*p**5. Factor z(d).
-2*d**2*(d + 3)/9
Suppose 0*w**3 + 0*w + 8 + 1/2*w**4 - 4*w**2 = 0. Calculate w.
-2, 2
Let s = 23 - 35. Let i be s/9*(-9)/6. Determine j so that 0*j - 2*j**2 - 5*j - 13*j**i - 5*j**3 - 5*j = 0.
-2, -1, 0
Let x be 100/(-112)*(-240)/50 + -4. Solve 0*i - x*i**4 + 0 - 4/7*i**2 - 6/7*i**3 = 0.
-2, -1, 0
Let t(y) = -y + 3. Let i be t(-2). Let c(u) be the third derivative of -1/8*u**4 + 0*u + 1/60*u**i - 3*u**2 + 0 + 1/3*u**3. Determine m so that c(m) = 0.
1, 2
Determine r so that 17 + 11/2*r**2 + 89/4*r + 1/4*r**3 = 0.
-17, -4, -1
Let v(i) be the second derivative of 1/36*i**4 + 0*i**2 + 0 - 1/45*i**5 + 7/2160*i**6 + i**3 + 3*i. Let c(q) be the second derivative of v(q). Factor c(p).
(p - 2)*(7*p - 2)/6
Let k = 55 - 52. Let q = 16 - 16. Determine d, given that 38*d**3 - 10*d + q*d**4 - 18*d**k - 5*d**4 + 5 - 10*d**3 = 0.
-1, 1
Let w(p) = -3 - 252*p - 2*p**2 + 255*p + 0*p**2. Let r be 4/(-10) - 17/(-5). Let h(d) = 3*d**2 - 4*d + 4. Let k(a) = r*h(a) + 4*w(a). Let k(m) = 0. Calculate m.
0
Suppose 115/3*t**2 + 5/3*t**5 + 40*t - 60 - 15*t**3 - 5*t**4 = 0. Calculate t.
-2, 1, 3
Let z(c) = 9*c**2 + 74*c + 18. Let t be z(-8). Solve -4/3*p**3 + 0 - 4/3*p + 8/3*p**t = 0 for p.
0, 1
Let t(l) be the first derivative of -l**6/12 - l**5/5 - l**4/8 - 86. Find o such that t(o) = 0.
-1, 0
Let c be 75/21 + -2 - (-21)/(-14). Let m(p) be the second derivative of 4/21*p**3 - p - 2/35*p**5 + 0 + c*p**4 + 1/105*p**6 - 4/7*p**2. Solve m(x) = 0 for x.
-1, 1, 2
Suppose 43*j = 30*j. Let s(m) be the second derivative of j*m**2 + 1/48*m**4 - 1/12*m**3 + 2*m + 1/80*m**5 + 0. Determine c so that s(c) = 0.
-2, 0, 1
Let t(s) = -s**2 - 23*s. Let m(v) = -15*v. Let j(h) = -8*m(h) + 5*t(h). Factor j(z).
-5*z*(z - 1)
Suppose 4*t - 5*b + b = 0, 0 = -2*t + 5*b + 12. Let w be t/30 + 12/15. Factor 2*n**2 + 2*n + w*n**3 + 2/3.
2*(n + 1)**3/3
Let b = -34029 + 136119/4. Factor 0*v + b*v**5 - 3*v**2 + 0*v**3 + 0 + 9/4*v**4.
3*v**2*(v - 1)*(v + 2)**2/4
Let l(q) be the third derivative of -q**8/11