 + 1)/3
Let x be 3*(2/8)/((-20)/(-80)). Factor -1/6*m**x - 1/6*m + 0 - 1/3*m**2.
-m*(m + 1)**2/6
Let a = -194389/660 + 2759/60. Let n = -248 - a. What is p in 2/11*p**3 - 6/11*p**2 + n*p - 2/11 = 0?
1
Let z(c) be the third derivative of c**5/60 - c**4/8 - c**3/6 - 4*c**2. Let r be z(4). What is j in -2*j - 3*j**2 + 3*j**4 - 9*j**3 + r*j**2 - j + 9*j**2 = 0?
0, 1
Factor 1386 - 1386 + 20*t + 2*t**2.
2*t*(t + 10)
Let l(s) = -s**3 + s. Let m(a) = -4*a**4 - 10*a**3 - 12*a**2 - 6*a. Let i(x) = -2*l(x) - m(x). Factor i(w).
4*w*(w + 1)**3
Let w(p) be the third derivative of p**7/630 + p**6/120 + p**5/90 - p**2. Factor w(c).
c**2*(c + 1)*(c + 2)/3
Let b(l) be the first derivative of 0*l - 2/7*l**2 - 2/21*l**3 + 8. Suppose b(p) = 0. What is p?
-2, 0
Let q(a) be the third derivative of a**10/226800 - a**8/10080 + a**7/3780 + a**5/60 - 3*a**2. Let n(y) be the third derivative of q(y). Factor n(h).
2*h*(h - 1)**2*(h + 2)/3
What is p in -5/11*p**4 + 2/11 + 3/11*p**2 - 7/11*p + 7/11*p**3 = 0?
-1, 2/5, 1
Let s(j) = -2*j**2 - 10*j - 8. Let x(i) be the third derivative of i**4/24 + i**3/6 - 3*i**2. Let y(z) = s(z) + 4*x(z). Let y(v) = 0. Calculate v.
-2, -1
Let i be ((-9)/(-6))/((-2)/(-20)). Let r be ((-12)/i)/((-4)/10). Let -b - 2 + 2 - 4*b**r = 0. What is b?
-1/4, 0
Let u be (-4 + 1)*1 + 3. Let g be u - 2*(-3)/30. Factor 0*x - 1/5 + g*x**2.
(x - 1)*(x + 1)/5
Determine g so that 2*g**5 - 5*g**4 - 41*g**2 - g**4 + 6*g**3 + 39*g**2 = 0.
0, 1
Suppose -9*s + 3*s + 7*s**2 - 4*s**2 - 3*s = 0. What is s?
0, 3
Let z = -17 + -123. Let i be ((-8)/z)/(3/21). Determine y so that 4/5*y + i*y**2 + 2/5 = 0.
-1
Let q(z) = -16 - 4*z + z**3 - 7*z + 5 - 6*z - 5*z**2. Let x(r) = r**3 + r**2 + r + 1. Let m(s) = q(s) + 2*x(s). Factor m(t).
3*(t - 3)*(t + 1)**2
Let h(u) = -2*u**3 - u. Let k(f) = f**3 + f**2. Let q(c) = -2*h(c) - 3*k(c). Factor q(b).
b*(b - 2)*(b - 1)
Suppose 5*f + 10 = -5*k, -4*f - 3*k = f + 2. Factor 0*l + 0 + 3/2*l**4 + 0*l**3 - 3/2*l**f.
3*l**2*(l - 1)*(l + 1)/2
Let v(g) be the second derivative of g**4/78 + 28*g**3/39 + 196*g**2/13 + 2*g + 5. Solve v(x) = 0.
-14
Factor -x**2 - x**2 - 3*x**3 + 2*x**2.
-3*x**3
Let 1/5*y**2 + 0 - 2/5*y = 0. Calculate y.
0, 2
Let i(o) be the first derivative of o**4/4 - 7*o**3/3 - o**2/2 + 7*o - 18. Find w such that i(w) = 0.
-1, 1, 7
Let t(u) = u**3 + 11*u**2 - 12*u + 7. Let r be t(-12). Let a(q) = q**2 + 2*q + 2. Let i be a(-2). Let r + 2*c**i - c - 3*c + 2*c - 11 = 0. What is c?
-1, 2
Let v(t) = t**2 + 7*t. Let j be v(-7). Suppose -5*i + 8*i - 6 = j, 2 = 4*b + i. Solve 2/7*x**4 - 4/7*x**3 + b*x**2 - 2/7 + 4/7*x = 0.
-1, 1
Let x be (-1)/(6/(-4)) + 0/4. Let 0 + 0*z - x*z**2 = 0. What is z?
0
Suppose 0 + 1/5*t + 1/5*t**2 = 0. What is t?
-1, 0
Factor -2/9 - 1/9*q**3 - 4/9*q**2 - 5/9*q.
-(q + 1)**2*(q + 2)/9
Find q, given that -7/4*q**2 - 1/4*q**5 + 0*q + 1/4*q**3 + 1 + 3/4*q**4 = 0.
-1, 1, 2
Find z such that 0 + 2*z**3 - 4/7*z + 10/7*z**2 = 0.
-1, 0, 2/7
Let b be -1 - 2 - 69/6. Let q = b + 15. Factor 0 + 0*c - 1/2*c**3 + q*c**2.
-c**2*(c - 1)/2
Let 0*f + 1/5*f**2 + 0 + 3/5*f**3 = 0. Calculate f.
-1/3, 0
Let a(s) = -s**2 - 11*s + 12. Let z be a(-12). Let q(l) be the second derivative of -1/21*l**4 + 0*l**2 - 1/70*l**5 + 3*l + z*l**3 + 0. Factor q(n).
-2*n**2*(n + 2)/7
Let x(y) be the third derivative of -3*y**2 + 0*y**3 + 0 + 1/480*y**6 - 1/96*y**4 + 1/240*y**5 + 0*y - 1/840*y**7. Factor x(p).
-p*(p - 1)**2*(p + 1)/4
Let m(h) be the second derivative of -h + 0*h**2 + 0 - 2/27*h**3 - 1/18*h**4 - 1/90*h**5. Solve m(b) = 0.
-2, -1, 0
Let w(t) be the second derivative of -3*t**7/14 - 2*t**6 - 99*t**5/20 + t**4 + 18*t**3 + 24*t**2 - t. Find c such that w(c) = 0.
-4, -2, -1, -2/3, 1
Let o = 749/9 - 83. Let k(p) be the first derivative of -3 + 4/27*p**6 - o*p**5 + 10/27*p**3 - 1/9*p**2 - 1/6*p**4 + 0*p. Suppose k(g) = 0. Calculate g.
-1, 0, 1/4, 1
Let q(g) be the first derivative of -g**5/60 - g**4/36 + 3*g - 3. Let s(c) be the first derivative of q(c). Factor s(j).
-j**2*(j + 1)/3
Let m(k) be the first derivative of -k**6/140 + k**5/70 - k**4/84 - k**3 - 3. Let x(p) be the third derivative of m(p). Factor x(s).
-2*(3*s - 1)**2/7
Let o(q) be the first derivative of 7*q**4/2 + 19*q**3/2 - 2*q + 9. Factor o(s).
(s + 2)*(4*s - 1)*(7*s + 2)/2
Let j(y) be the third derivative of -7/60*y**6 - 7/30*y**4 - 2/15*y**3 + 0 + 2*y**2 - 1/42*y**7 + 0*y - 23/100*y**5. Factor j(p).
-(p + 1)**2*(5*p + 2)**2/5
Let j(n) be the second derivative of -n**5/5 - 2*n**4 - 6*n**3 - 4*n. Determine a, given that j(a) = 0.
-3, 0
Let x(u) = 6*u**4 - 3*u**3 + 3*u**2 - 3. Let o(t) = t**4 - t**3 + t**2 - 1. Let f(c) = 3*o(c) - x(c). Determine l, given that f(l) = 0.
0
Factor 16*a + 0*a**2 + 2*a**2 - 10*a**2 + 4*a**2 - 16.
-4*(a - 2)**2
Let n(i) be the second derivative of -i**7/357 + i**5/85 - i**3/51 + 40*i. Factor n(b).
-2*b*(b - 1)**2*(b + 1)**2/17
Let v(y) be the third derivative of -y**5/45 - 8*y**4/27 + 8*y**3/9 - 23*y**2. Factor v(t).
-4*(t + 6)*(3*t - 2)/9
Suppose -5*u - 17 - 28 = 0. Let z be u/(-405) + 2/10. Let 0 + z*s**2 + 0*s = 0. Calculate s.
0
Let t = 27 - 27. Let o(j) be the third derivative of 0*j + 1/80*j**6 - 1/40*j**5 - 1/420*j**7 + 2*j**2 + 0*j**3 + 1/48*j**4 + t. Solve o(c) = 0.
0, 1
Let a(y) be the third derivative of y**6/900 + y**3/6 - 2*y**2. Let m(s) be the first derivative of a(s). Factor m(p).
2*p**2/5
Let b(z) be the third derivative of 3*z**5/20 - 5*z**4/8 + z**3 - 4*z**2. Factor b(f).
3*(f - 1)*(3*f - 2)
Let x(g) = g**2 - 8*g - 20. Let q be x(10). Suppose 0 + 2/15*f**2 + q*f = 0. What is f?
0
Let y(z) be the second derivative of -z**7/840 - z**6/360 + z**5/24 - z**4/8 - 2*z**3/3 + 5*z. Let b(n) be the second derivative of y(n). What is h in b(h) = 0?
-3, 1
Let t(g) be the first derivative of g**3/2 - g**2 + g/2 + 23. Determine p so that t(p) = 0.
1/3, 1
Let i(z) be the first derivative of 0*z - 2 - 1/6*z**4 + 2/9*z**3 + 0*z**2. Factor i(g).
-2*g**2*(g - 1)/3
Let q(g) be the first derivative of 4 - 1/8*g**4 - 1/12*g**2 - 2/9*g**3 + 2/15*g**5 + 1/9*g**6 + 0*g. Suppose q(d) = 0. Calculate d.
-1, -1/2, 0, 1
Let s be 681/(-55) + 4/22. Let q = 559/45 + s. Determine a, given that 0 + 4/9*a**2 + q*a**3 + 2/9*a = 0.
-1, 0
Factor -3*q**2 + 0*q**4 - 3*q**4 + 2*q**4 + 3*q**3 + 0*q**4 + q.
-q*(q - 1)**3
Let y(h) be the third derivative of -1/525*h**7 - 1/75*h**6 - 1/15*h**4 - 1/15*h**3 - 1/25*h**5 + 0 + 0*h + 2*h**2. Factor y(o).
-2*(o + 1)**4/5
Let m = 55/6 - 26/3. Solve 0 + m*d**3 + 1/2*d**2 + 0*d = 0 for d.
-1, 0
Suppose 2*g + 22 = 4*g. Let r(o) = -o**2 + 10*o + 13. Let k be r(g). Factor -1/2*c**k - 1/2*c + 1.
-(c - 1)*(c + 2)/2
Let g = -116 - -119. Find p such that 1/5*p**4 + 1/5*p**g + 0*p + 0 - 2/5*p**2 = 0.
-2, 0, 1
Let q(j) be the second derivative of j**5/130 - j**4/78 - j**3/39 + j**2/13 + j. Factor q(c).
2*(c - 1)**2*(c + 1)/13
Suppose -y - 5 = -6*y. Suppose -y = -2*n + 5. Factor -5*i**4 + i**3 - i**2 - 2*i**4 + 3*i**5 + 4*i**n.
i**2*(i - 1)**2*(3*i - 1)
Let t = 4 - 2. Factor 5 - 4 - 2*h - 2*h**2 + 0*h**t + 3*h**2.
(h - 1)**2
Let r(x) = x**2 + 8*x + 3. Let f be r(-8). Suppose 0 = -f*u - 0 + 6. Suppose 2*o**3 + o**3 - 3*o**3 + o**3 + 2*o + 3*o**u = 0. What is o?
-2, -1, 0
Let l(k) = 4*k. Let p be l(1). Suppose 45 = 3*b + 3*h, p*b + 5*h - 18 = 45. Solve u**4 + 10*u**3 - 4 - 3*u**4 - 18*u**2 + 2*u + b*u = 0.
1, 2
What is n in -8/7*n + 0 + 10/7*n**2 = 0?
0, 4/5
Let x be (-6)/15 - 5/(50/(-4)). Let -4/7*b**2 - 2*b**4 + x*b + 0 - 18/7*b**3 = 0. Calculate b.
-1, -2/7, 0
Factor -k**3 + 7/5*k**2 + 0 + 1/5*k**4 - 3/5*k.
k*(k - 3)*(k - 1)**2/5
Let h be 5*((-12)/15)/(-2). Let y be (-2)/(-7) + (11 - 11). Factor y*n**h - 8/7*n + 8/7.
2*(n - 2)**2/7
Let f = 16 + -15. Suppose b - 4 = 5*z, -b + 4*z + 3 = -f. Determine a so that 33*a**b + 63/2*a**5 - 4*a**2 + 0*a + 2*a**3 + 0 = 0.
-2/3, 0, 2/7
Let z(x) be the first derivative of 4*x**3/3 + 14*x**2 + 7. Factor z(n).
4*n*(n + 7)
Let p = 7/3 + -71/33. Factor 2/11*v + p*v**2 + 0.
2*v*(v + 1)/11
Let s(d) = d**2 - 30*d + 191. Let v be s(21). Let -1/6*j**v + 1/3 - 1/6*j = 0. What is j?
-2, 1
Factor 2/7*i**3 - 2/7*i**5 + 0*i**2 + 0 + 0*i**4 + 0*i.
-2*i**3*(i - 1)*(i + 1)/7
Let t = -97 + 99. Suppose 1/6*w - 1/6*w**t + 0 = 0. Calculate w.
0, 1
Factor -1/3*y**2 + 1/3*y**4 + y**3 + 0 - y.
y*(y - 1)*(y + 1)*(y + 3)/3
Let 