1
Let f be (-7)/(-2)*(-68)/(-119). Factor 1/2*k - 1/2*k**f + 0.
-k*(k - 1)/2
Let n(v) be the first derivative of v**6/36 + v**5/15 + v**4/24 + 4. Factor n(t).
t**3*(t + 1)**2/6
Let d = 6 - 6. Suppose 2*c - 4 = -d. Factor 0 + 1/3*w**c - 1/3*w**3 + 0*w.
-w**2*(w - 1)/3
Let s(k) = 14*k**2 - 2*k - 6. Let h(f) = f**2 - f - 1. Let r(a) = 10*h(a) - s(a). Factor r(q).
-4*(q + 1)**2
Let u(k) be the first derivative of 2*k**6 - 8*k**5/5 - 10*k**4 + 16*k**3 - 2*k**2 - 8*k + 11. Factor u(z).
4*(z - 1)**3*(z + 2)*(3*z + 1)
Suppose -2*y - y = -6. What is o in 4/3 + 4/3*o + 1/3*o**y = 0?
-2
Let b(s) = -3*s**2 - 9*s. Let c(f) = f**2 + 2*f. Let r(w) = -2*b(w) - 9*c(w). What is h in r(h) = 0?
0
Let m(u) be the first derivative of -1/10*u**4 - 2/15*u**3 + 0*u + 0*u**2 + 5. Determine b so that m(b) = 0.
-1, 0
Let d(s) be the second derivative of -s**4/36 + s**3/18 + s**2 - 8*s. Suppose d(j) = 0. Calculate j.
-2, 3
Let r(s) be the second derivative of s**5/80 + s**4/48 + s. Determine t, given that r(t) = 0.
-1, 0
Let k(w) be the second derivative of 12/5*w**5 + 4*w + 9/2*w**2 + 8*w**3 + 0 + 3/10*w**6 + 13/2*w**4. Factor k(g).
3*(g + 1)**2*(g + 3)*(3*g + 1)
Let p(x) be the third derivative of 0*x + 0*x**4 + 0 - 2*x**2 - 1/30*x**5 + 0*x**3 + 1/60*x**6. Let p(j) = 0. What is j?
0, 1
Let b = 10 + -4. Solve o + o**2 + 2*o + o**2 - b + o**2 = 0.
-2, 1
Let j(r) be the third derivative of -r**7/42 - 5*r**6/24 - 3*r**5/4 - 35*r**4/24 - 5*r**3/3 + 8*r**2. Find o, given that j(o) = 0.
-2, -1
Let x(g) be the first derivative of -g**6/60 - g**5/24 - g**4/24 - 7*g**3/3 + 2. Let q(j) be the third derivative of x(j). Factor q(a).
-(2*a + 1)*(3*a + 1)
Let l(i) be the third derivative of 0*i**3 + 0 - 1/20*i**5 + 0*i**4 + 0*i - 1/20*i**6 - 1/70*i**7 + 2*i**2. Factor l(m).
-3*m**2*(m + 1)**2
Let l(s) be the first derivative of s**9/3024 + s**8/840 + s**7/840 - 5*s**3/3 + 9. Let o(g) be the third derivative of l(g). Factor o(a).
a**3*(a + 1)**2
Let y be ((-14)/(-105))/((-4)/(-7)). Let u(i) be the second derivative of 16/15*i**3 + 0 + y*i**4 + 4/5*i**2 + 4*i. Factor u(s).
2*(s + 2)*(7*s + 2)/5
Suppose -5*s + 28 = 13. Find b such that -2/7*b**4 + 0 - 6/7*b**2 + 2/7*b + 6/7*b**s = 0.
0, 1
Let i(t) be the second derivative of -10*t + 0 + 3/2*t**2 - t**3 + 1/4*t**4. Let i(k) = 0. Calculate k.
1
Let z(g) = g + 9. Let s be z(-7). Solve -46*h**3 + 69*h**4 + 13*h**4 - 2*h**3 + 8*h**s - 42*h**5 = 0 for h.
0, 2/7, 2/3, 1
Factor -n**4 + n**2 - 62 + 62 - n**3 + n.
-n*(n - 1)*(n + 1)**2
Let a(r) = r**2 - 2*r - 2. Let u(w) = w + 1. Suppose 2*l + 5*n = 12, -5 = l - 3*n - 0*n. Suppose -1 = h + l. Let z(m) = h*a(m) - 4*u(m). Factor z(p).
-2*p**2
Suppose 0 = 3*c - 5 - 4. Let d(m) be the first derivative of 1 + 70/3*m**c - 8*m - 4*m**2. Factor d(j).
2*(5*j - 2)*(7*j + 2)
Let l be (-10)/15*(-1)/2. Let z(a) be the first derivative of -l*a**3 + a**2 - a - 1. Factor z(u).
-(u - 1)**2
Let o(n) be the second derivative of n**7/3780 - n**6/540 - n**4/4 - 3*n. Let q(p) be the third derivative of o(p). Factor q(b).
2*b*(b - 2)/3
Let a = -10 - -9. Let i be a*((-2)/1 + -1). Suppose -1/3*c**2 - 2/3*c + 2/3*c**i + 1/3 = 0. Calculate c.
-1, 1/2, 1
Factor -1/3*u**2 + 0 + 2/3*u.
-u*(u - 2)/3
Let v be -1 + 5*2*10/75. Let o(b) be the second derivative of -1/6*b**4 + 2*b + 0*b**2 + 1/10*b**5 - v*b**3 + 1/15*b**6 + 0. Solve o(g) = 0 for g.
-1, 0, 1
Let t(z) = 0 + 2*z + 1 - 2 - z. Let k be t(5). Factor 2*y**4 - k*y**3 + 2*y**5 - 3*y**5 + y**3 + 2*y**3.
-y**3*(y - 1)**2
Suppose -23*c + 18 = -17*c. Find r, given that 1 + 5/4*r**2 - c*r = 0.
2/5, 2
Let z be 2/7 - 85/420. Let q(t) be the second derivative of t - z*t**3 + 0 - 1/8*t**2 - 1/48*t**4. Factor q(s).
-(s + 1)**2/4
Suppose 2*c - 4*b = 16, -5*c + b + 0*b + 13 = 0. Let z be (c/(-6))/(2/(-12)). Factor 0*q**4 + z*q**3 + q**3 - 3*q**4.
-3*q**3*(q - 1)
Suppose 26 = 4*j - 6. Let q be j/(-6)*(-34)/4. Suppose -26/3*i**4 + 7/3*i**5 + 2/3 - 1/3*i - 16/3*i**2 + q*i**3 = 0. What is i?
-2/7, 1
Let q(i) be the second derivative of 5*i**7/42 + 3*i**6/5 + 7*i**5/20 - 13*i**4/6 - 2*i**3 + 4*i**2 + 38*i. Let q(p) = 0. What is p?
-2, -1, 2/5, 1
Determine k, given that 2/9*k - 4/9*k**3 + 2/9*k**5 - 4/9*k**2 + 2/9 + 2/9*k**4 = 0.
-1, 1
Let c(w) = -w. Let t(k) = k**3 - 7*k**2 - 9*k + 2. Let a be t(8). Let g(x) = -x**2 - 10*x - 4. Let y(s) = a*c(s) + g(s). What is f in y(f) = 0?
-2
Suppose 0*o = 2*o + 5*q - 25, -5*o - 4*q + 20 = 0. Let j(s) be the first derivative of -5/2*s**4 + 1 + 2*s**2 + 2*s**3 + o*s. Suppose j(x) = 0. What is x?
-2/5, 0, 1
Let z(s) = -4*s**4 - 20*s**3 - 52*s**2 - 44*s - 12. Let l(j) = -j**3 + j**2 + j. Let a(i) = 4*l(i) + z(i). Factor a(n).
-4*(n + 1)**3*(n + 3)
Let u = -1 - -3. Let a = 27/35 - -1/35. Find d such that 0*d**u + 0 + 0*d - a*d**4 + 2/5*d**3 + 2/5*d**5 = 0.
0, 1
Let y be (0/1)/((-6)/3). Suppose y = -0*a - 5*a + 3*v + 22, -12 = 3*v. Factor a*o**2 + 5*o**3 + 6*o**2 - 5*o**3 - 2*o - 6*o**3.
-2*o*(o - 1)*(3*o - 1)
Let b(c) be the third derivative of -5*c**2 + 0*c - 1/9*c**3 + 0*c**4 + 1/90*c**5 + 0. Factor b(v).
2*(v - 1)*(v + 1)/3
Suppose -5*t + 4*u = 5, -t - 4*u = -0 + 1. Let i = -1/2 - t. Factor -3/2*m**2 - i + 1/2*m**3 + 3/2*m.
(m - 1)**3/2
Factor -18*m + 17*m**2 - 17*m**2 + 57*m**3 + 12*m**4 + 57*m**2.
3*m*(m + 2)*(m + 3)*(4*m - 1)
Let l be (-4)/12 - 1338/(-45). Find a such that 24/5 - 36*a + 378/5*a**2 - l*a**3 = 0.
2/7, 2
Let c(u) = u - 4. Let g be c(9). Let 4/5 + 19/5*p**3 + g*p**5 - 23/5*p**2 - 8/5*p + 11*p**4 = 0. What is p?
-1, 2/5
Factor -7*c**5 - 6*c**3 + 9*c**5 - 2*c**3.
2*c**3*(c - 2)*(c + 2)
Let n(w) be the third derivative of w**9/1944 - w**8/630 + w**7/1260 + w**6/810 + w**3/6 + 7*w**2. Let q(r) be the first derivative of n(r). Factor q(t).
2*t**2*(t - 1)**2*(7*t + 2)/9
Let h(k) be the second derivative of -k**4/102 - 2*k**3/51 - 2*k. Suppose h(s) = 0. What is s?
-2, 0
Let i = 146 - 142. Determine v so that 4/7 + i*v**3 - 2*v**5 - 8/7*v**2 + 4/7*v**4 - 2*v = 0.
-1, 2/7, 1
Suppose -4*k + 1 = 9. Let h = -2 - k. Solve h + 2/3*y**2 + 0*y = 0.
0
Determine r so that 2*r**4 + 24*r**2 + 92*r**3 + r**4 - 65*r**3 = 0.
-8, -1, 0
Let l = -13 - -15. Factor 3*h + h**2 + 2 - 7*h**2 + 4*h**l.
-(h - 2)*(2*h + 1)
Let w(f) be the first derivative of -1/12*f**3 - 2 - 1/4*f - 1/4*f**2. Factor w(g).
-(g + 1)**2/4
Let t(h) = h**2 - h. Let u(i) = -i**3 + 2*i**2 - 5*i. Let v(f) = 12*t(f) - 3*u(f). Factor v(p).
3*p*(p + 1)**2
Let s be -1 + (-1)/((-2)/6). Suppose -o - o**s + 5*o**2 + 2*o + o = 0. Calculate o.
-1/2, 0
Factor -4/7*s - 18/7*s**3 + 0 - 22/7*s**2.
-2*s*(s + 1)*(9*s + 2)/7
Let k = -2 - -6. Suppose -2*f = -k*f + 10. Determine x, given that 3*x**2 + 3*x**5 - 4*x**4 + 2*x + x**2 - 5*x**f = 0.
-1, 0, 1
Let i(m) be the first derivative of -m**6/30 - 4*m**5/25 - m**4/4 - 2*m**3/15 + 18. Factor i(g).
-g**2*(g + 1)**2*(g + 2)/5
Let 0 + 2/11*l**3 - 4/11*l**2 + 0*l = 0. What is l?
0, 2
Let r be (-10)/(-21)*(-3132)/(-90). Let q = 18 - r. Factor 4/7*v - 6/7*v**2 - q*v**3 + 0.
-2*v*(v + 1)*(5*v - 2)/7
Let p = -11 - -13. Factor -2*o**4 + 125*o + 2*o**p - 125*o.
-2*o**2*(o - 1)*(o + 1)
Let c(m) be the second derivative of -m**5/80 + m**4/16 - 2*m**2 - 5*m. Let n(g) be the first derivative of c(g). Find z such that n(z) = 0.
0, 2
Suppose a = -a - l + 4, 0 = -4*a + 3*l + 18. Suppose -4*x + 2 + a*x + 2*x**2 - 3*x + 0*x = 0. What is x?
1
Let h be (-126)/(-30) - (-1)/(-5). Factor -a**4 + 0*a**4 + h*a**4 - 6*a**4 + 9*a**2 - 6*a.
-3*a*(a - 1)**2*(a + 2)
Let a = 9 - 5. Suppose -7 = a*q + 5*j, 2*q - 10 = 3*q + 4*j. Find b such that -b + b**5 + 4*b - 4*b + 0*b**5 - 2*b**2 + q*b**4 = 0.
-1, 0, 1
Let h = 571/124810 - -1/5349. Let u(q) be the third derivative of 0*q**4 + h*q**5 + 0*q**6 + 0*q - 1/735*q**7 + 0 - q**2 + 0*q**3. Let u(c) = 0. What is c?
-1, 0, 1
Suppose 0 = -2*a + q + 3, -10 = 4*a + 2*q - 36. Factor -1/2*i**2 + i - 5/2*i**a + 0 - 4*i**3.
-i*(i + 1)**2*(5*i - 2)/2
Determine f so that -41*f + 13 - 4 + f**2 + 47*f = 0.
-3
Let m(h) be the first derivative of 9*h**4/2 - 40*h**3/3 - 23*h**2 + 12*h - 9. Factor m(v).
2*(v - 3)*(v + 1)*(9*v - 2)
Let p(z) = z**3 - 7*z**2 + z - 3. Let m(r) = 2*r**3 - 13*r**2 + 6*r + 7. Let n be m(6). Let x be p(n). Factor 0*c**3 + 1/4*c**x - 1/4*c**5 + 0*c**2 + 0*c + 0.
-c**4*(c - 1)/4
Find z, given that 7*z**4 - 3*z**2 + 6*z**3 - 9*z**4 - z**4 = 0