)*(l + 1)/5
Let r(x) = x**2 - x. Let t(c) = 8*c. Let s(n) = 2*r(n) + t(n). Factor s(p).
2*p*(p + 3)
Let w(m) be the first derivative of -m**3/3 + 7*m**2/2 - 6*m - 2. Let n be w(6). Solve n*b + 2/3*b**2 + 0 = 0 for b.
0
Let g = -17/8 + 135/56. Factor -2/7*q**3 - 2/7*q**4 + 2/7*q**5 + 0*q + g*q**2 + 0.
2*q**2*(q - 1)**2*(q + 1)/7
Find v such that 20*v**3 - 554*v**4 + 558*v**4 + 28*v - 1 + 9 + 36*v**2 = 0.
-2, -1
Let h(f) = -f**2 + f - 1. Let g(k) = 23*k**2 - 18*k + 20. Let d(s) = -8*s**2 + 6*s - 7. Let j(b) = -17*d(b) - 6*g(b). Let z(t) = 3*h(t) - j(t). Factor z(c).
-(c + 1)*(c + 2)
Find v, given that -30 + 593*v**2 - 152*v**2 + 44*v + 343*v**3 + 57 + 145*v = 0.
-3/7
Suppose 10 = -5*f - 4*o, -4 = 4*f - f + 2*o. Let s be 2/((f/2)/1). Suppose 1/3*u**s + 1/3*u - 1/3*u**3 - 1/3 = 0. Calculate u.
-1, 1
Suppose -4 - 9*p**4 - 18 - 2 - 126*p**2 - 101*p - 57*p**3 - 7*p = 0. What is p?
-2, -1/3
Factor 2*z**3 + 4*z**4 + z + 13*z**2 - 16*z**4 - z**2 - 3*z.
-2*z*(z - 1)*(z + 1)*(6*z - 1)
Let z be (-3)/1 - (-63)/15. Factor 2/5 + z*q - 8/5*q**2.
-2*(q - 1)*(4*q + 1)/5
Let a(f) be the second derivative of f**5/50 + f**4/30 - f**3/15 - f**2/5 + 7*f. Factor a(i).
2*(i - 1)*(i + 1)**2/5
Let i(f) be the second derivative of 0 + 0*f**2 + 0*f**3 - f + 3/100*f**5 + 1/20*f**4. Factor i(l).
3*l**2*(l + 1)/5
Suppose 3*t = 7*t - 28. Let v(m) be the first derivative of 2 + 16/5*m**5 - 4*m - t*m**2 - 4*m**3 + m**6 + 2*m**4. Factor v(s).
2*(s - 1)*(s + 1)**3*(3*s + 2)
Let h(u) be the third derivative of 5*u**2 + 1/210*u**5 + 0 - 1/84*u**4 + 0*u**3 + 0*u. Factor h(r).
2*r*(r - 1)/7
Factor -33 + 70 + 4*m**2 - 53.
4*(m - 2)*(m + 2)
Factor 20*h**4 + 5*h**5 + 38*h**2 - 8*h**3 + 28*h**3 - 38*h**2.
5*h**3*(h + 2)**2
Let g(x) be the first derivative of x**6/105 - x**5/210 - 5*x**2/2 + 4. Let a(w) be the second derivative of g(w). Factor a(p).
2*p**2*(4*p - 1)/7
Let x(s) be the second derivative of s**7/2100 - s**6/225 + s**5/60 - s**4/30 - s**3/3 + 5*s. Let p(t) be the second derivative of x(t). Factor p(o).
2*(o - 2)*(o - 1)**2/5
Let c(h) = -9*h**2 + 135*h + 144. Let o(y) = y**2 - 17*y - 18. Let b(v) = 4*c(v) + 33*o(v). Factor b(k).
-3*(k + 1)*(k + 6)
Let 4*h**2 - 2*h + 18*h + 18 - 6 = 0. What is h?
-3, -1
Factor -m + m + 6*m - 24*m**3 - 9*m**2 - 9*m**4.
-3*m*(m + 1)*(m + 2)*(3*m - 1)
Let x(b) = b - 4. Let l be x(5). Let q(k) be the first derivative of -2*k**3 - l + 3/2*k**4 + k**2 + 0*k - 2/5*k**5. Suppose q(p) = 0. Calculate p.
0, 1
Let o(r) = 25*r**3 + r**2 - 1. Let k be o(1). Suppose 3 = 4*w - k. What is z in -w*z - 2 + 3*z**2 - z**2 + 7*z = 0?
-1, 1
Let q(z) be the first derivative of -5*z**3/3 - 4*z**2 + 4*z + 18. Determine r, given that q(r) = 0.
-2, 2/5
Let f be ((-252)/(-24))/(2/(-4)). Let c be (-2)/(-8) + f/(-12). Factor 0 - 1/2*s**3 + 0*s**c + 0*s.
-s**3/2
Let i(g) be the second derivative of -3*g**5/40 + 3*g**3/4 + 3*g**2/2 + 14*g. Factor i(r).
-3*(r - 2)*(r + 1)**2/2
Let x = -61 + 245/4. Factor 1/2 + 3/4*k + x*k**2.
(k + 1)*(k + 2)/4
Let z(f) be the first derivative of -5*f**3/3 + 11*f**2 - 8*f + 21. Factor z(c).
-(c - 4)*(5*c - 2)
Let u(z) be the second derivative of -z**4/16 + 9*z**3/8 + 14*z. Factor u(f).
-3*f*(f - 9)/4
Let t = -518 + 1558/3. Factor -52/3*l - t - 169/3*l**2.
-(13*l + 2)**2/3
Let b = 6 + -2. Let p be b/14 + 72/42. Factor 0*i + 0 + 1/3*i**p.
i**2/3
Let o(h) = 25*h + 17*h**3 + 10*h - 36*h**2 + 12*h**2 + 11. Let x(s) = 6*s**3 - 8*s**2 + 12*s + 4. Let l be 18/5 + 2/5. Let v(p) = l*o(p) - 11*x(p). Factor v(k).
2*k*(k - 2)**2
Let g(y) = 6*y**2 + 4*y - 12. Let m(b) = -2*b**2 - b + 4. Suppose -25 = -5*t - 75. Let j(d) = t*m(d) - 3*g(d). Factor j(p).
2*(p - 2)*(p + 1)
Let x(y) = 2*y**3 + 3*y**2 - 1. Let f(r) = -3*r**3 - 4*r**2 + r + 2. Let p(b) = -3*f(b) - 4*x(b). Factor p(h).
(h - 2)*(h + 1)**2
Let n = -19 + 11. Let b be -4*((-2)/n + -1). Suppose -20*s**2 - 16/7 - 104/7*s + 14*s**b = 0. Calculate s.
-2/7, 2
Let n = 60 - 85. Let p = n - -177/7. Determine y so that -2/7*y**3 - 4/7*y**2 - p*y + 0 = 0.
-1, 0
Let z(n) be the first derivative of -4*n**5/25 - 2*n**4/5 + 4*n**3/15 + 4*n**2/5 + 7. What is g in z(g) = 0?
-2, -1, 0, 1
Let n(y) = 20*y**4 + 18*y**3 + 4*y**2 - y. Let b(q) = -q. Suppose -2*o - 2*o = -4. Let x(s) = o*n(s) - b(s). Factor x(l).
2*l**2*(2*l + 1)*(5*l + 2)
Suppose 6 = a - j + 4, j = 2*a - 4. Factor -1/4*z**a + 1/4 + 0*z.
-(z - 1)*(z + 1)/4
Let l = -364 - -1100/3. Factor -2/3*m**3 - 2/3*m**5 + 8/3*m + 16/3 + l*m**4 - 20/3*m**2.
-2*(m - 2)**3*(m + 1)**2/3
Let 76*m + 66*m**3 - 20*m**2 - 80*m**4 + 0 + 32*m**5 + 0 - 74*m = 0. Calculate m.
0, 1/4, 1
Suppose -4*k + 5*f + 21 = 3, k + 2*f + 2 = 0. Determine z so that -4/7*z + 2/7*z**4 - 6/7*z**k + 0*z**3 + 0 = 0.
-1, 0, 2
Let g(a) be the third derivative of 1/24*a**3 + 6*a**2 + 0 - 1/120*a**6 + 0*a + 1/40*a**5 + 1/840*a**7 - 1/24*a**4. Factor g(c).
(c - 1)**4/4
Determine v so that -2/11*v**2 + 2/11*v**3 + 0*v + 0 = 0.
0, 1
Let b(k) = -k**4 + k**3 - k + 1. Let m(n) = n**4 + 3*n**3 - 2*n**2 - 3*n + 1. Let z(h) = 2*b(h) - 2*m(h). What is u in z(u) = 0?
-1, 0, 1
Let l(w) be the third derivative of -1/48*w**4 - 1/6*w**3 + 0*w + 2*w**2 - 1/160*w**5 + 0 - 1/1440*w**6. Let g(m) be the first derivative of l(m). Factor g(b).
-(b + 1)*(b + 2)/4
Suppose 5*y = 2*y + 36. Suppose 3*f + y = 0, 3*s + f + 0 = 2. Factor -s - 1 + 1 + 2*n**2.
2*(n - 1)*(n + 1)
Let i be (0 - 0) + 3/4. Let d = -27/2 + 14. Suppose -i*r**2 - d*r + 1/4 = 0. What is r?
-1, 1/3
Let l(n) be the second derivative of 0 + 1/48*n**4 + 0*n**2 + 0*n**3 - n. Factor l(s).
s**2/4
Let x = 3/20 - -11/60. Factor 0 + 13/3*z**3 - 4*z**2 + 4/3*z + x*z**5 - 2*z**4.
z*(z - 2)**2*(z - 1)**2/3
Let a be -3*(-6)/81*12. Let -2/3*t**3 + 7/3*t**4 - 2/3*t + 4/3*t**5 - a*t**2 + 1/3 = 0. Calculate t.
-1, 1/4, 1
Suppose 2/3*t + 0 + 7/3*t**3 + 3*t**2 = 0. Calculate t.
-1, -2/7, 0
Let b(z) = z**5 - 7*z**4 - 13*z**3 + 48*z**2 - 29*z + 5. Let p(w) = 3*w**4 + 6*w**3 - 24*w**2 + 15*w - 3. Let d(q) = 3*b(q) + 5*p(q). Factor d(s).
3*s*(s - 2)*(s - 1)**2*(s + 2)
Let f(s) be the first derivative of -s**4/5 + 4*s**3/15 + 11. Solve f(q) = 0.
0, 1
Let v(r) be the third derivative of r**6/900 + r**5/225 - r**4/180 - 2*r**3/45 - r**2. Factor v(d).
2*(d - 1)*(d + 1)*(d + 2)/15
Let c(l) be the first derivative of 3*l**4/10 + 8*l**3/15 + l**2/5 - 1. Find p such that c(p) = 0.
-1, -1/3, 0
Let -4*d**2 - 3*d + 4 - 3*d + 4*d + 11*d**3 - 9*d**3 = 0. Calculate d.
-1, 1, 2
Let y(g) = -7*g**2 - 10*g + 5. Let t(w) = 2*w**2 + w. Let z(u) = -12*t(u) - 3*y(u). Factor z(v).
-3*(v - 5)*(v - 1)
Let r(i) be the third derivative of 0*i + 0*i**3 - 2/15*i**5 - 5*i**2 - 1/30*i**6 - 1/6*i**4 + 0. Factor r(k).
-4*k*(k + 1)**2
Let j(w) = w**2 - 6*w - 51. Let n be j(11). Factor -1/4*k**n + 1/4*k**2 + 0 - 1/4*k**3 + 1/4*k.
-k*(k - 1)*(k + 1)**2/4
Let b(a) = -a**3 + 13*a**2. Let z(s) = s**2 - 13*s - 1. Let y be z(14). Let v be b(y). Determine p so that 1/2*p**2 + 1/2*p + v = 0.
-1, 0
Let a(p) be the third derivative of p**8/2240 + p**7/3360 + p**3/2 - p**2. Let n(r) be the first derivative of a(r). What is c in n(c) = 0?
-1/3, 0
Let i(w) be the first derivative of w**7/3780 + w**6/810 - w**5/180 - w**3/3 + 5. Let n(k) be the third derivative of i(k). Factor n(x).
2*x*(x - 1)*(x + 3)/9
Let m be (12/45 - 0)*99/88. Let v(g) be the second derivative of 0*g**3 + 1/10*g**6 + 0*g**2 + 0 + m*g**5 - 2*g + 0*g**4. Solve v(i) = 0 for i.
-2, 0
Let o(c) be the second derivative of c**7/105 + c**6/75 - 10*c. Factor o(n).
2*n**4*(n + 1)/5
Let v(n) = -n**2 - 4*n. Let t be v(-3). Let u(f) be the second derivative of -1/135*f**6 + 1/45*f**5 - 1/54*f**4 + 0*f**2 + 0*f**t - 2*f + 0. Factor u(d).
-2*d**2*(d - 1)**2/9
Let o(y) be the first derivative of y**4/18 - y**2/3 + 8*y + 1. Let j(h) be the first derivative of o(h). Suppose j(i) = 0. What is i?
-1, 1
Let p = -18 + 23. Let c(i) be the second derivative of -1/6*i**4 + 0 - 1/10*i**p + 0*i**2 + 1/15*i**6 + 1/3*i**3 + 2*i. Determine w so that c(w) = 0.
-1, 0, 1
Let o be 1 + (-3)/((-63)/(-14)). Factor 2/3*n - 1/3*n**2 + 0 - o*n**3.
-n*(n - 1)*(n + 2)/3
Let w be -9*(22/(-3) - 0). Suppose 18 = 2*s - 4*i, 3*s + 33 = 8*s - 4*i. Solve 6*q + 9*q**4 - 9*q**2 + 33*q**5 + 23*q**s - w*q**3 + 4*q**5 = 0 for q.
-1, -2/5, 0, 1/4, 1
Let z(i) = -2*i**2 + 10*i - 5. Let w be z(4). Let s be w - (-3 + 4 