7. What is r in -2/3*r + c*r**2 - 2/9*r**3 + 2/9 = 0?
1
Suppose -2*l + 5*f = -24, 0*f - 36 = -3*l + 2*f. Determine i so that 0*i**4 + 13*i**4 - i**2 + 5*i**5 + l*i**3 - 3*i**3 - 2*i = 0.
-1, 0, 2/5
Factor 4*q - 210*q**3 - 5*q**5 - 340*q**2 - 149*q - 28*q - 55*q**4 - 27*q.
-5*q*(q + 2)**3*(q + 5)
Factor -33*v**3 - 4*v**4 - v**2 + 10*v**4 - 12*v - 4*v**2 + 44*v**2.
3*v*(v - 4)*(v - 1)*(2*v - 1)
Let h(c) = 5*c**2 - 11*c + 8. Let d(p) = -66*p**2 + 144*p - 105. Let j = 1415 + -2138. Let i be 2/9 - j/27. Let g(x) = i*h(x) + 2*d(x). Solve g(t) = 0.
1, 2
Suppose -3*i + 4*x - 4 = 2, -7 = i - 3*x. Factor -u**2 - 3*u**i + 5*u**2 + 2*u.
u*(u + 2)
Let v = 29 - 27. Factor 36*o - 36*o - o**v + 3*o**2.
2*o**2
Let j(l) be the first derivative of 1/27*l**3 + 1/18*l**2 + 0*l - 22. Factor j(p).
p*(p + 1)/9
Solve 120*t + 3/2 + 2400*t**2 = 0.
-1/40
Let b = 207 + -123. Let f be b/12 + -1*5. Factor 1/4*w**f - 1/2*w + 1/4.
(w - 1)**2/4
Determine t so that 42/5 + 2/5*t**2 - 4*t = 0.
3, 7
Suppose 2/3*g**5 + 8/3*g**3 - 10/3*g - 8 + 12*g**2 - 4*g**4 = 0. What is g?
-1, 1, 3, 4
Factor -103*y**4 + 101*y**4 - 75*y**2 + 24*y**3 + 3*y**2.
-2*y**2*(y - 6)**2
Let n(a) = 243*a + 4860. Let i be n(-20). Suppose 4/13*u - 6/13*u**3 - 4/13*u**4 + 6/13*u**2 + i = 0. What is u?
-2, -1/2, 0, 1
Let c(k) be the second derivative of k**5/100 - k**4/15 + k**3/6 - k**2/5 - 72*k. Let c(x) = 0. What is x?
1, 2
Let c(a) be the first derivative of -4*a - 37 + 5/2*a**2 - 1/6*a**3 - 1/8*a**4. Factor c(q).
-(q - 2)*(q - 1)*(q + 4)/2
Let m be (-20)/(-3)*(-6)/(-75). Let w be -8*(-15)/40 - 1. Find r, given that -58/15*r**w + 8/3*r - m - 2/5*r**4 + 32/15*r**3 = 0.
1/3, 1, 2
Let j(y) = y**3 + 2*y**2 - 25*y + 38. Let z be j(2). Factor 10/11*p**3 + 2/11*p**z - 16/11 - 8/11*p + 12/11*p**2.
2*(p - 1)*(p + 2)**3/11
Let u(s) be the second derivative of s**5/30 + s**4/10 + s**3/15 - 29*s**2/2 - 33*s. Let h(m) be the first derivative of u(m). Let h(x) = 0. What is x?
-1, -1/5
Let h(u) = 4*u**2 + 10*u + 12. Let f(s) = 11*s**2 + 30*s + 34. Let q(y) = -6*f(y) + 17*h(y). Determine d so that q(d) = 0.
0, 5
Let x(u) = 3. Let a(k) = -k**2 - 2*k - 15. Let c = -3 - 12. Let t(q) = c*x(q) - 3*a(q). Factor t(n).
3*n*(n + 2)
Suppose -4*b + b = -3*m - 3, 2*m - b + 1 = 0. Let g be (3 - m) + 99/(-55). Factor 4/5 - g*a + 2/5*a**2.
2*(a - 2)*(a - 1)/5
Let o be (2060/13320)/((-1)/(-3)). Let d = o + 4/111. Determine y, given that -d*y**2 + 0 + 1/4*y + 1/4*y**3 = 0.
0, 1
Let r be 1/(6/8)*(-432)/(-396). Determine h so that -6/11*h**5 + 0 + 0*h - 8/11*h**3 + r*h**2 - 20/11*h**4 = 0.
-2, 0, 2/3
Let z(l) be the second derivative of -l**4/3 - 10*l**3/3 + 48*l**2 + 57*l. Find g such that z(g) = 0.
-8, 3
Let v(j) be the third derivative of j**6/50 - 43*j**5/150 + 7*j**4/60 - 55*j**2. Factor v(u).
2*u*(u - 7)*(6*u - 1)/5
Let w(b) = b**3 + 7*b**2 + 13*b + 5. Let v be w(-3). Factor 0*h + 0*h**3 - 3*h**v + 3/2 + 3/2*h**4.
3*(h - 1)**2*(h + 1)**2/2
Let n = -164285/6 + 27381. Let -1/3 - n*m**2 + 1/2*m = 0. What is m?
1, 2
Suppose 1 = 5*m - 6*m, -5*q = -5*m - 25. Let 0*c + 2/5*c**2 - 1/5*c**5 + 0 - 2/5*c**q + 1/5*c**3 = 0. What is c?
-2, -1, 0, 1
Let b = 7 + -33. Let n be (-13)/b*(11/3 + -1). Let 2/3*x**2 + 2/3 - n*x = 0. Calculate x.
1
Let l(g) be the first derivative of g**5/25 - 11*g**4/20 - g**3/15 + 11*g**2/10 + 68. Factor l(c).
c*(c - 11)*(c - 1)*(c + 1)/5
Let b(h) be the second derivative of -h**4/54 - 14*h**3/27 - 11*h - 7. Factor b(i).
-2*i*(i + 14)/9
Let n(x) = x**3 + 33 - 62 + x - 16*x**2 + 15. Let a be n(16). Factor k**3 - 1/2*k**a - 1/2*k**4 + 0*k + 0.
-k**2*(k - 1)**2/2
Suppose 5*d - 18 + 3 = 0. Find x, given that 5*x**3 - 13*x**3 + 8*x**2 - 8*x**4 + 2*x**3 + 10*x**d - 4*x = 0.
-1, 0, 1/2, 1
Let h(x) = 5*x - 10. Let m = 94 - 83. Let a be h(m). Determine o so that -a*o - 9 - 125/3*o**3 - 75*o**2 = 0.
-3/5
Let x(p) = p**3 + 6*p**2 + 6. Let z be x(-6). Suppose -z*m = -m - 10. Factor 0*j**2 - j**2 + 6 - 3 - m.
-(j - 1)*(j + 1)
Let t(o) = 11*o**3 + 3*o**2 - 8*o + 7. Let u(b) = -5*b**3 - b**2 + 4*b - 3. Let s(w) = -3*t(w) - 7*u(w). Factor s(k).
2*k*(k - 2)*(k + 1)
Let s(z) be the first derivative of 5*z**4/4 + 5*z**3/3 + 105. Find r such that s(r) = 0.
-1, 0
Let k be 1*7*4/14. Let v(y) be the second derivative of 2/15*y**3 + 0*y**k + 0 - 1/6*y**4 - y. Factor v(d).
-2*d*(5*d - 2)/5
Suppose p + 3*p = 8. Let s(h) be the first derivative of -1/2*h**3 + 3/2*h**p - 6 + 0*h - 3/8*h**4. Factor s(m).
-3*m*(m - 1)*(m + 2)/2
Let r(t) = 5*t - 40. Let q be r(13). Let n be (2*q/(-20))/(3/(-6)). Factor -1/6*m**n + 1/3*m**2 - 1/6*m - 1/6 - 1/6*m**4 + 1/3*m**3.
-(m - 1)**2*(m + 1)**3/6
Let s(l) be the second derivative of l**5/450 - l**4/90 - l**3/15 + l**2 + 6*l. Let q(y) be the first derivative of s(y). Find x, given that q(x) = 0.
-1, 3
Let f(b) be the third derivative of b**6/360 - 19*b**3/3 + 33*b**2. Let i(r) be the first derivative of f(r). Factor i(a).
a**2
Let i(x) be the second derivative of 0 + 1/14*x**5 - 16*x - 20/21*x**3 + 12/7*x**2 - 9/14*x**4. What is u in i(u) = 0?
-1, 2/5, 6
Let j(b) be the second derivative of b**7/210 - b**6/75 - b**5/25 + 2*b**4/15 - 173*b. Find p such that j(p) = 0.
-2, 0, 2
Let v be ((-2)/10)/((-21)/(225 + -15)). Factor 8/15*n - 2/5*n**3 - 8/15*n**v + 2/15*n**5 + 4/15*n**4 + 0.
2*n*(n - 1)**2*(n + 2)**2/15
Let r = -23602 - -23605. Determine j so that 0 + 7/2*j - 3/2*j**5 + j**4 + 6*j**r - 9*j**2 = 0.
-7/3, 0, 1
Let b(k) be the first derivative of k**5/20 - k**4/9 + k**3/18 + 8*k - 13. Let n(s) be the first derivative of b(s). Factor n(h).
h*(h - 1)*(3*h - 1)/3
Let m(t) = 2*t**4 - 144*t**3 - 198*t**2 + 792*t - 473. Let f(g) = g**4 - 48*g**3 - 66*g**2 + 264*g - 157. Let w(a) = 7*f(a) - 2*m(a). Factor w(s).
3*(s - 17)*(s - 1)**2*(s + 3)
Suppose 0 = -2*b + 4*b. Suppose -3*x + 7 - 1 = b. Factor -3*y - 3*y**4 - x*y - 4*y**3 + 10*y**3 + 3 - y.
-3*(y - 1)**3*(y + 1)
Let l(u) be the third derivative of -u**5/150 + 2*u**4/5 + 5*u**3/3 - 203*u**2. Determine m, given that l(m) = 0.
-1, 25
Let s(l) be the first derivative of -l**4/2 + 12*l**2 + 32*l - 13. Factor s(n).
-2*(n - 4)*(n + 2)**2
Let d(b) be the third derivative of -b**5/20 + 6*b**4 - 288*b**3 - 77*b**2. Solve d(o) = 0.
24
Suppose -9 = -4*j + 3*t, -6*t = -3*j + j + 18. Factor 4/7*m**3 - 8/7*m + j + 4/7*m**2.
4*m*(m - 1)*(m + 2)/7
Let o = -464 - -466. Let p(b) be the second derivative of 0*b**o - 2*b + 1/36*b**4 - 1/90*b**6 + 0 + 1/18*b**3 - 1/60*b**5. Suppose p(g) = 0. What is g?
-1, 0, 1
Let n = 44 - 32. Suppose n*z**3 + 25*z**2 + 62*z**5 + 5*z - 168*z**5 - 25*z**4 + 86*z**5 + 3*z**3 = 0. Calculate z.
-1, -1/4, 0, 1
Let v(k) be the second derivative of 1/36*k**4 + 0 - 5/18*k**3 + 1/2*k**2 + 1/60*k**5 - 11*k. Find u, given that v(u) = 0.
-3, 1
Let x(w) be the second derivative of -w**4/60 - 11*w**3/5 - 1089*w**2/10 + 8*w - 1. Factor x(p).
-(p + 33)**2/5
Let b(n) be the third derivative of n**10/151200 - n**9/12096 + 11*n**5/60 + n**2. Let g(f) be the third derivative of b(f). Factor g(k).
k**3*(k - 5)
Let s(u) be the second derivative of 0*u**3 + 3/80*u**5 - 1/24*u**4 + 0*u**6 + 0*u**2 - 1/168*u**7 - 18*u + 2. Factor s(d).
-d**2*(d - 1)**2*(d + 2)/4
Let y = 22 + -17. Factor -1 - 4*c**4 - c - 3 + 2*c**3 + 10*c**2 + c**5 - 2*c**2 - 2*c**y.
-(c - 1)**2*(c + 1)**2*(c + 4)
Let i(l) be the first derivative of 7 + 2/19*l**2 + 2/57*l**3 + 2/19*l. Let i(g) = 0. What is g?
-1
Let y(h) be the second derivative of 0*h**3 - h - 1/48*h**6 + 0 + 1/20*h**5 + 0*h**2 + 1/336*h**7 - 1/24*h**4. Solve y(j) = 0 for j.
0, 1, 2
Let i(v) be the third derivative of 14*v**2 + 0 - 1/40*v**5 - 1/12*v**3 + 0*v + 1/16*v**4 + 1/240*v**6. Factor i(n).
(n - 1)**3/2
What is g in 10*g**4 - 12*g**2 + 0 - 10*g**3 + 5*g**5 + 5*g + 5 - 8*g**2 + 5 = 0?
-2, -1, 1
Let 6/5*n + 1/10*n**2 - 13/10 = 0. What is n?
-13, 1
Let j(o) be the first derivative of -125*o**4/4 + 425*o**3 + 540*o**2 + 220*o + 21. Let j(g) = 0. What is g?
-2/5, 11
Let m(l) be the third derivative of -l**5/60 + 5*l**4/12 - 8*l**3/3 + 4*l**2. Find b, given that m(b) = 0.
2, 8
Suppose 6 = 5*o - 4. Factor n**2 - 4*n**2 - 18*n**3 + 4*n**2 + 8*n**4 + 3*n**o.
2*n**2*(n - 2)*(4*n - 1)
Let q(j) be the first derivative of 0*j + 1/10*j**5 + 3/8*j**4 + 1/2*j**3 + 1/4*j**2 - 7. Factor q(i).
i*(i + 1)**3/2
Let a be (1*-5)/(5 + -6). Suppose -21 = -a*z +