120 - c**5/60 + 5*c**3/6 - 5*c. Let m(b) be the second derivative of l(b). Factor m(j).
-j*(3*j + 2)
Suppose 2/7 + 6/7*p + 2/7*p**2 - 4/7*p**4 - 6/7*p**3 = 0. Calculate p.
-1, -1/2, 1
Let c = 11 + -9. Determine i, given that 2*i**4 + i**2 - i**2 - 3*i**3 - i**3 + 2*i**c = 0.
0, 1
Let s be (-34)/8*(18 + -14). Let n = s + 35/2. Find f, given that 3/4*f**3 + n*f + 7/4*f**2 + 0 = 0.
-2, -1/3, 0
Let r(t) be the second derivative of 3/50*t**6 + 1/70*t**7 + 3/50*t**5 + 0 + 5*t + 0*t**3 + 0*t**4 + 0*t**2. Factor r(c).
3*c**3*(c + 1)*(c + 2)/5
Let c(r) = -r**3 - r**2 + 3*r + 3. Let o(t) = -3*t**3 - 2*t**2 + 10*t + 9. Let n(d) = 21*c(d) - 6*o(d). Factor n(a).
-3*(a - 1)*(a + 1)*(a + 3)
Let j be ((-2)/(-4))/((-2)/(-24)). Let k(b) be the third derivative of -3*b**2 + 1/60*b**j - 1/10*b**5 - 1/3*b**3 + 1/4*b**4 + 0 + 0*b. Factor k(u).
2*(u - 1)**3
Let f be (-2)/9 + (3825/324)/25. Let t(o) be the first derivative of -1/4*o + 3/8*o**2 - f*o**3 + 1/16*o**4 + 1. Determine y, given that t(y) = 0.
1
Let t(i) = 2*i**2 + 4*i - 2. Let v be t(-3). Factor -1/4*z**v - 5/4*z**2 + 1/2*z + 0 + z**3.
-z*(z - 2)*(z - 1)**2/4
Let t(w) be the second derivative of -w**6/10 - 3*w**5/10 - w**4/4 - w. Factor t(c).
-3*c**2*(c + 1)**2
Let w be (49/(-6))/(15/(-30)). Factor -4/3 - 28/3*g - w*g**2.
-(7*g + 2)**2/3
Factor -18/13*v**2 + 0 + 4/13*v.
-2*v*(9*v - 2)/13
Let z = 254/189 - 2/189. Factor 4/3*s**2 - z*s + 0.
4*s*(s - 1)/3
Let h be (55/275)/((-6)/(-20)). Factor 6 + 4*u + h*u**2.
2*(u + 3)**2/3
Factor 16*l**5 + 20*l**5 + 2*l**3 - 38*l**5.
-2*l**3*(l - 1)*(l + 1)
Let r(a) = a**3 + 10*a**2 + 8*a - 10. Let j be r(-9). Let o(v) = -5*v**3 - 18*v**2 - 11*v - 2. Let d(c) = c**3 - c**2. Let w(t) = j*o(t) + 2*d(t). Factor w(p).
(p + 1)**2*(7*p + 2)
Suppose -8 - 1 = -3*r. Find h, given that 2*h + h - r*h**2 - 15*h**3 - 7*h**4 - 2*h**4 = 0.
-1, 0, 1/3
Determine n, given that 9/7 + 30/7*n + 9/7*n**2 = 0.
-3, -1/3
Let h(o) be the third derivative of 3*o**2 - 1/300*o**5 + 1/30*o**4 - 2/15*o**3 + 0 + 0*o. Factor h(z).
-(z - 2)**2/5
Let m(d) = -44*d + 6. Let v be m(7). Let y be 3/5 + v/(-10). Suppose 98/5*r**4 + y*r**3 + 8/5*r + 0 + 64/5*r**2 = 0. What is r?
-1, -2/7, 0
Let v(o) be the third derivative of o**2 + 0*o**3 + 0*o + 0 + 0*o**4 + 1/100*o**5. Factor v(m).
3*m**2/5
Factor -4*b + 2*b**4 + 112 - 112 - 2*b**2 + 4*b**3.
2*b*(b - 1)*(b + 1)*(b + 2)
Let q(k) be the second derivative of k**6/105 + 3*k**5/70 - k**4/42 - k**3/7 + 45*k. Determine y, given that q(y) = 0.
-3, -1, 0, 1
Let k(w) be the first derivative of 1/4*w**3 - 1/4*w**2 + 1/16*w**4 + 0*w + 1/24*w**6 - 2 - 3/20*w**5. Let k(g) = 0. Calculate g.
-1, 0, 1, 2
Let g(t) be the first derivative of 1/2*t**2 + 2/3*t**3 + 0*t - 2/5*t**5 - 1/4*t**4 + 3. Find u, given that g(u) = 0.
-1, -1/2, 0, 1
Let b(q) be the first derivative of 3*q**4/4 + 2*q**3 - 3*q**2/2 - 6*q + 1. Find m such that b(m) = 0.
-2, -1, 1
Let s(c) = -14*c + 129. Let k be s(9). Suppose -3/2*l + 1 - 7/2*l**k - 6*l**2 = 0. Calculate l.
-1, 2/7
Let w be (-60)/(-18) - (-3 - (3 + -8)). Factor -w*f**2 + 2/3 + 2/3*f + 2/3*f**5 - 4/3*f**3 + 2/3*f**4.
2*(f - 1)**2*(f + 1)**3/3
Let p be (4 + 1/1)/1. Suppose 0 = -3*s + p + 1. Solve -2*o**2 - o**4 + s*o**3 + 3*o**2 - o**5 - o**3 = 0 for o.
-1, 0, 1
Let a(j) = -13*j**3 + 31*j**2 - 23*j + 5. Let b(s) = 4*s**3 - 10*s**2 + 8*s - 2. Suppose 3*d + 20 = -1. Let w(m) = d*b(m) - 2*a(m). Suppose w(i) = 0. What is i?
1, 2
Factor -16*z + 96/7 + 12/7*z**3 - 4/7*z**4 + 24/7*z**2.
-4*(z - 2)**3*(z + 3)/7
Let q be (-102)/18*(-1 + 4). Let a = 21 + q. Factor 1/2*o**a + 0*o + 1/2*o**3 + 0 - 1/2*o**2 - 1/2*o**5.
-o**2*(o - 1)**2*(o + 1)/2
Suppose c = 2*c + 3*z - 18, 4*c - z = 7. Let k be ((-6)/15)/(c/(-15)). Factor 2*f**4 - 3*f**4 - 2*f**3 + f**2 + 2*f**4 + 0*f**k.
f**2*(f - 1)**2
Suppose 4*w = s + 2*s - 20, 5*w = -25. Let p(y) be the first derivative of 0*y**5 + 0*y**3 + 1/2*y**4 + s*y - 1/2*y**2 - 1/6*y**6 + 2. Factor p(q).
-q*(q - 1)**2*(q + 1)**2
Let f(r) = -2*r**3 + r**4 + 5*r + 10*r**3 - 3 - 2. Let s(d) = -8*d**3 - 4*d + 4. Let x(w) = -4*f(w) - 5*s(w). Factor x(c).
-4*c**3*(c - 2)
Suppose 7 = y + 5. Solve -21*m**y + 2*m - 6*m + 23*m**2 = 0.
0, 2
Let m(k) = 4*k - 5 + 0 - 3*k. Let o be m(5). Solve 0*y - 5*y**3 + y + 3*y**3 + y**5 + o*y = 0 for y.
-1, 0, 1
Let x(c) = c**3 - 2*c**2 - 6*c + 7. Let f be x(6). Determine y, given that -13*y + 132*y**2 - 75*y**5 + 23*y**4 + 83*y**3 - 8*y**4 + f*y**3 + 37*y = 0.
-1, -2/5, 0, 2
Suppose 8*p - 5*p - 6 = 0. Let c(t) be the second derivative of -1/48*t**4 + 0 - 1/8*t**p + 1/12*t**3 - 2*t. Factor c(j).
-(j - 1)**2/4
Let f(p) be the first derivative of -p**7/2520 + p**6/1080 + p**5/180 + 7*p**3/3 + 5. Let c(s) be the third derivative of f(s). Factor c(g).
-g*(g - 2)*(g + 1)/3
Let z(i) be the third derivative of -i**8/11200 + i**7/4200 - i**4/8 - 2*i**2. Let g(w) be the second derivative of z(w). Let g(a) = 0. What is a?
0, 1
Let o(k) be the second derivative of k**7/42 + k**6/30 - k**5/10 - k**4/6 + k**3/6 + k**2/2 + 6*k. Suppose o(j) = 0. What is j?
-1, 1
Let r = -312 + 937/3. Let b = -128/3 - -43. Factor -2/3*h + r + b*h**2.
(h - 1)**2/3
Let -9*z**2 + 3*z - 3*z**4 - 18 + 18 + 3*z**3 + 6*z**3 = 0. What is z?
0, 1
What is i in -4/11*i**2 - 2/11*i**3 + 0*i + 0 = 0?
-2, 0
Let a be 33/11*4/6. Let f(o) be the second derivative of -2*o - 1/30*o**4 - 1/50*o**5 + 0 + 1/15*o**3 + 1/5*o**a. What is r in f(r) = 0?
-1, 1
Let g(j) be the first derivative of 0*j + 4/21*j**3 + 0*j**2 - 1 - 5/14*j**4. Find l, given that g(l) = 0.
0, 2/5
Let c(s) be the third derivative of -s**5/12 - 5*s**4 - 120*s**3 + 65*s**2. Factor c(o).
-5*(o + 12)**2
Let s(g) = g**2 + 11*g - 6. Let a be s(-12). Suppose -3*i = -r + a - 0, 4*i - 2 = -2*r. Factor -2*q**r + 4/5*q**2 + 2*q - 4/5.
-2*(q - 1)*(q + 1)*(5*q - 2)/5
Let a(f) be the third derivative of f**8/168 - f**7/15 + 3*f**6/10 - 11*f**5/15 + 13*f**4/12 - f**3 - 25*f**2. Factor a(z).
2*(z - 3)*(z - 1)**4
Let u(v) be the first derivative of v**6/90 - v**5/30 + 7*v**3/3 + 1. Let o(q) be the third derivative of u(q). Factor o(s).
4*s*(s - 1)
Let d(q) = -q**2 - 7*q - 6. Let p be d(-6). Let t(x) be the first derivative of 0*x + 2 - 1/16*x**4 + p*x**3 + 1/8*x**2. Factor t(i).
-i*(i - 1)*(i + 1)/4
Factor 1/2*s**2 + 1/4*s**3 + 0 + 1/4*s.
s*(s + 1)**2/4
Let y(b) be the third derivative of -b**6/840 + b**5/420 + b**4/168 - b**3/42 + 9*b**2. Solve y(u) = 0.
-1, 1
Let m(z) = -z**2 + z. Let a(o) = -2*o**2 + 4*o - 8. Let t(d) = a(d) - 4*m(d). Factor t(r).
2*(r - 2)*(r + 2)
Solve 4/7*u**3 - 2/7*u**4 + 0*u - 2/7*u**2 + 0 = 0.
0, 1
Let z be 12/(-16) + (-38)/(-8). Factor -2*f**3 + 0*f**z + f**5 + f**4 + 0*f**4.
f**3*(f - 1)*(f + 2)
Let b(m) = -6*m**3 + 6*m**2 + 3*m + 3. Suppose t = 5*v - 8, -5*t + 1 = -v + 17. Let l(x) = 17*x**3 - 17*x**2 - 8*x - 8. Let q(g) = t*l(g) - 8*b(g). Factor q(s).
-3*s**2*(s - 1)
Let d = -47/3 - -63/4. Let w(n) be the second derivative of 1/2*n**3 - n**2 + 0 + 2*n - d*n**4. Factor w(l).
-(l - 2)*(l - 1)
Let y(d) be the first derivative of -d**4/2 + 4*d**3/3 - d**2 - 12. Find j such that y(j) = 0.
0, 1
Let h be 4 - (0 + (-680)/(-175)). Let z(y) be the first derivative of 0*y**4 + 1/21*y**6 + h*y**5 + 0*y - 1/7*y**2 - 3 - 4/21*y**3. Factor z(x).
2*x*(x - 1)*(x + 1)**3/7
Factor k**2 + 0*k**2 + 2*k**3 - 4*k + k**2.
2*k*(k - 1)*(k + 2)
Suppose -302 + 338 = 9*o. Let -1/8*m**o + 0 - 1/8*m**3 + 0*m + 0*m**2 = 0. What is m?
-1, 0
Suppose -5*f + z - 3*z + 32 = 0, -3*z + 33 = 5*f. Let m be (1/f)/(2/6). Solve 1/4 + 0*d**3 - m*d**2 + 1/4*d**4 + 0*d = 0.
-1, 1
Let q = -981 + 73576/75. Let g(n) be the third derivative of 1/60*n**4 + 0*n - q*n**5 + 0*n**6 + 0*n**3 + 0 - 1/840*n**8 + n**2 + 2/525*n**7. Factor g(m).
-2*m*(m - 1)**3*(m + 1)/5
Suppose 0 = -7*r + r + 2*r. Factor 0 + 8/3*b**4 + 0*b**2 + 2*b**5 + 2/3*b**3 + r*b.
2*b**3*(b + 1)*(3*b + 1)/3
Let u = 10 + -6. Suppose -5*o + 28 + 16 = -f, o + 3*f = -u. Suppose 5*r**2 - 13*r**2 - 3 + 1 + o*r = 0. Calculate r.
1/2
Let f(y) be the second derivative of -y + 0*y**3 + 1/63*y**7 + 0*y**6 + 0*y**4 + 0*y**2 + 0 - 1/30*y**5. Solve f(o) = 0.
-1, 0, 1
Let s(t) = t**2 + 5*t + 3. Let a be s(-5). Factor -w**4 + 4*w**5 + 0*w**4 + 3*w**4 - a*w**5.
w**4*(w + 2)
Let v(q) be the first derivative of -2*q**3/15 + 6*q**2 - 90*q - 42. Factor v(s).
-2*(s - 15)**2/5
Facto