
Let u(l) = 23*l - 320. Let m be u(14). Let -v**3 - 1/2*v**4 + m*v - 2 + 3/2*v**2 = 0. Calculate v.
-2, 1
Let g = -5 - -7. Determine j, given that 4*j - g*j**4 + 2*j**5 + 2*j**3 - 12*j**3 + 4*j**3 + 2*j**2 = 0.
-1, 0, 1, 2
Let -63/4*x**2 - 3 - 27/4*x**3 - 12*x = 0. What is x?
-1, -2/3
Let t(r) be the first derivative of 1/8*r**4 - 1/2*r - 1 + 3/4*r**2 - 1/2*r**3. Let t(w) = 0. Calculate w.
1
Suppose -5*k + 49 = -2*m - 2*m, 5 = k + 4*m. Let s be ((-4)/(-16))/(3/k). Solve 0 + 1/4*n - s*n**2 = 0.
0, 1/3
Let a be 838/(-420) - (-11 + 9). Let i(d) be the third derivative of a*d**5 + 0*d**3 + d**2 + 0*d**4 + 0*d + 0. Factor i(g).
2*g**2/7
Let l = -3/38 + 85/114. Let v(w) be the first derivative of l*w**3 + 2*w**2 - 2 + 2*w. Factor v(k).
2*(k + 1)**2
Suppose 10 - 2 = 2*n. Let m = -26/7 + n. Factor 0 + 6/7*o**3 - 4/7*o**2 + 0*o**4 - m*o**5 + 0*o.
-2*o**2*(o - 1)**2*(o + 2)/7
Let c(z) be the third derivative of z**8/294 - 2*z**7/147 + z**5/21 - z**4/21 - 7*z**2. Suppose c(u) = 0. What is u?
-1, 0, 1/2, 1, 2
Let s(b) = b**2 - 2*b. Let p be s(4). Suppose 4*a + p = 2*v, -2*a - 1 - 11 = -5*v. Determine g, given that 4/5*g**v + 2/5*g**3 + 2/5*g + 0 = 0.
-1, 0
Let w(s) be the third derivative of 1/840*s**7 + 0*s**4 + 1/240*s**6 + 0*s - 4*s**2 + 0 + 0*s**3 + 1/240*s**5. Factor w(u).
u**2*(u + 1)**2/4
Factor 0 - 12/7*r - 6/7*r**2 + 6/7*r**3.
6*r*(r - 2)*(r + 1)/7
Suppose i - 5*i + 14 = -3*g, -5*i + 4 = 3*g. Let q(n) be the second derivative of 0 - 4/5*n**i - 1/30*n**4 + 4/15*n**3 - n. What is v in q(v) = 0?
2
Let r(f) = f + 5. Let q be r(-3). Suppose q*d - 4 = d. Factor -3 - d + 5 - 2*n**2 - 4*n.
-2*(n + 1)**2
Suppose 2*q + 2*w + 10 = 0, -5*q - 9*w = -5*w + 20. Factor q + 2/7*h**4 + 0*h - 2/7*h**3 - 4/7*h**2.
2*h**2*(h - 2)*(h + 1)/7
Let x(i) be the second derivative of -7*i**6/15 - 6*i**5/5 - i**4/2 + 2*i**3/3 - 6*i. Factor x(c).
-2*c*(c + 1)**2*(7*c - 2)
Let z(s) be the third derivative of s**6/40 + 23*s**5/100 + 4*s**4/5 + 6*s**3/5 - 6*s**2. Suppose z(h) = 0. Calculate h.
-2, -3/5
Let k = 19 - 27. Let g = k + 8. Factor p**5 + 0*p + g*p**2 + 0 + 1/3*p**3 + 4/3*p**4.
p**3*(p + 1)*(3*p + 1)/3
Let v(d) = -2*d**2 - 4*d + 10. Let s(u) = 6*u**2 + 11*u - 31. Let q(p) = -2*s(p) - 7*v(p). Factor q(o).
2*(o - 1)*(o + 4)
Let 22*d**3 - 18 - 195*d**2 + 49*d**3 + 145*d + 24*d**3 - 12 - 15*d**4 = 0. What is d?
1/3, 1, 2, 3
Let c = 9/14 - -211/42. Let f = -10/21 - -15/7. Find q, given that f*q - c*q**3 + 1/3 - 1/3*q**2 + 4*q**4 = 0.
-1/3, -1/4, 1
Let r(b) = 3*b**4 - 5*b**3 + 2*b**2 - 4*b - 4. Let p(v) = 3*v**4 - 4*v**3 + v**2 - 5*v - 5. Let q(m) = 4*p(m) - 5*r(m). Solve q(k) = 0 for k.
0, 1, 2
Suppose -2*g + 5 - 3 = 0. Find j, given that -g - 2*j**2 - 17 + 0 + 0*j + 12*j = 0.
3
Factor 2*k**4 + k**4 + 7 - 15*k**3 + 17*k**2 + 10*k**2 - 21*k - 1.
3*(k - 2)*(k - 1)**3
Let c(r) be the first derivative of -3*r**4/4 - 6*r**3 - 33*r**2/2 - 18*r - 55. Let c(j) = 0. What is j?
-3, -2, -1
Let a(n) = -3*n**3 - 5*n**2 + 10*n + 6. Suppose d - 132 = 5*d. Let c(s) = 14*s**3 + 24*s**2 - 51*s - 31. Let p(b) = d*a(b) - 6*c(b). Factor p(v).
3*(v - 1)*(v + 2)*(5*v + 2)
Let p = 12 - 9. Let a = p + -1. Find f, given that -13*f**3 - 2*f + 11*f**3 - a*f**2 + 6*f**2 = 0.
0, 1
Factor -3/2*x**2 + x + 0.
-x*(3*x - 2)/2
Let i(c) be the third derivative of 1/108*c**4 + 5*c**2 + 0*c + 0 - 1/540*c**6 + 1/27*c**3 - 1/270*c**5. Factor i(g).
-2*(g - 1)*(g + 1)**2/9
Find f, given that -3*f - 10*f**2 + 299 - 2*f + 5*f**3 - 289 = 0.
-1, 1, 2
Let q(m) be the first derivative of -7*m**5/50 + m**4/8 + 3*m**3/10 - m**2/4 - m/5 - 14. Find v, given that q(v) = 0.
-1, -2/7, 1
Suppose s - 5 = -j, 7 + 9 = 5*s + 2*j. Solve 0*r**2 - 3*r - s*r**2 + 26*r**4 + 18*r**3 - r + 10*r**5 = 0 for r.
-1, 0, 2/5
Suppose -3*v = -2*u + 2 - 1, -2*u + 25 = 5*v. Factor -2/3*s - 38/3*s**v + 14/3*s**4 - 4/3 + 10*s**2.
2*(s - 1)**3*(7*s + 2)/3
Let b be ((-46)/(-276))/(2/9). Let 0 - 3/2*o**2 - 3/4*o - b*o**3 = 0. What is o?
-1, 0
Solve 41*g**2 - 24*g**2 - 20*g**2 - 12*g = 0 for g.
-4, 0
Suppose -4*k - 5*i = -9*k + 15, -i = -3*k + 11. Factor 1/4*c**k - 1/4*c**2 + 0 - 3/4*c**3 + 1/2*c + 1/4*c**5.
c*(c - 1)**2*(c + 1)*(c + 2)/4
Let w(a) be the third derivative of -a**7/2520 - a**6/720 + a**5/60 + a**4/24 + 3*a**2. Let l(x) be the second derivative of w(x). Solve l(h) = 0 for h.
-2, 1
Find r such that 113 - 66*r + 149 - 18 + 119 + 3*r**2 = 0.
11
Let y be ((-12)/18*-1)/(2/9). Suppose 1 - 1/2*w**y + 2*w**2 - 5/2*w = 0. Calculate w.
1, 2
Factor -47*m**4 - 2*m**3 + 2*m**2 + 2*m**2 + 45*m**4.
-2*m**2*(m - 1)*(m + 2)
Let d(o) be the third derivative of 3*o**8/1120 - o**7/420 - o**6/45 + o**5/15 + o**4/8 - o**2. Let k(s) be the second derivative of d(s). Factor k(y).
2*(y + 1)*(3*y - 2)**2
Let l be (0 - (-2)/6)/((-2)/(-18)). Let t be ((-4)/10)/(1/(-5)). Let 3*v**5 + v + 5*v**3 - 11*v**l + t*v = 0. Calculate v.
-1, 0, 1
Let m = -20 - -20. Let u(n) be the first derivative of -1/6*n**4 + m*n + 0*n**3 + 1 + 0*n**2. Let u(d) = 0. What is d?
0
Determine k, given that -1/5*k**5 + 0 + 0*k**3 + 1/5*k - 2/5*k**2 + 2/5*k**4 = 0.
-1, 0, 1
Let o(g) be the second derivative of 0*g**2 - 2/15*g**6 + 3*g - 1/5*g**5 + 0 + 0*g**3 + 0*g**4 - 1/42*g**7. Solve o(f) = 0 for f.
-2, 0
Factor 722/3*a**2 - 326/3*a**3 - 640/3*a + 46/3*a**4 - 2/3*a**5 + 200/3.
-2*(a - 10)**2*(a - 1)**3/3
Let p(o) be the first derivative of 1 + 0*o**2 - 2*o + 2/3*o**3. Factor p(v).
2*(v - 1)*(v + 1)
Let v(o) be the third derivative of -1/60*o**5 - 1/24*o**4 + 0 + 0*o - 1/18*o**3 - 1/360*o**6 - o**2. Find a such that v(a) = 0.
-1
Let i(c) be the second derivative of 0*c**2 + 1/54*c**4 - 2*c + 0 + 1/1620*c**6 + 2/3*c**3 + 1/180*c**5. Let m(h) be the second derivative of i(h). Factor m(r).
2*(r + 1)*(r + 2)/9
Suppose -3*i - 19 = -5*j, -15 = -5*i - 0*i - j. Find y such that -10*y**2 + i*y**2 - 8*y**2 - 20*y + 0*y - 8 - 4*y**3 = 0.
-2, -1
Let n(p) be the third derivative of 1/48*p**4 + 0*p**3 + 1/120*p**5 + 0 + 0*p - p**2. Factor n(r).
r*(r + 1)/2
Let s(d) be the first derivative of -d**6/15 - 6*d**5/25 - d**4/5 + 4*d**3/15 + 3*d**2/5 + 2*d/5 + 22. Determine o, given that s(o) = 0.
-1, 1
Let b be 34/(-51) - (2 + -3). Let i(k) be the second derivative of -1/9*k**4 - 5/18*k**3 - b*k**2 + 0 + 3*k - 1/60*k**5. Determine z, given that i(z) = 0.
-2, -1
Suppose 4*a - 3*a = -p + 3, 4*a - 2*p - 24 = 0. Suppose -a*y + 11 = -4. Find j, given that 4*j**3 - y*j**3 - 3*j**3 - 2*j**4 = 0.
-1, 0
Let r(b) be the second derivative of -1/21*b**3 + 1/70*b**5 - 1/7*b**2 - 3*b + 0 + 1/42*b**4. Factor r(p).
2*(p - 1)*(p + 1)**2/7
Factor -23/5*u + 7/5*u**2 + 6/5.
(u - 3)*(7*u - 2)/5
Let c(h) = -8*h**5 + 18*h**4 - 44*h**3 - 18*h**2. Let k(f) = -f**5 + 2*f**4 - 5*f**3 - 2*f**2. Let m(b) = 6*c(b) - 52*k(b). Find d such that m(d) = 0.
-1, 0, 1
Factor -40 + 40*d + d**2 + 9*d**2 + 56*d.
2*(d + 10)*(5*d - 2)
Suppose -3*g = -3*y - 12, -5*y - 2*g + 10 = 2. Let h(v) be the first derivative of 2/5*v - 3/10*v**2 + 1 + y*v**3 + 1/20*v**4. Solve h(k) = 0 for k.
-2, 1
Let t(i) = i**2 + 5*i. Let w(u) = -2*u**2 - 11*u - 1. Let h(z) = 13*t(z) + 6*w(z). Let h(x) = 0. What is x?
-2, 3
Let p be ((-6)/(-5))/((-28)/(-70)). Solve 2 - 2 + 3*f**5 - 3*f**p = 0 for f.
-1, 0, 1
Suppose -2 = -2*i + 2. Let q = 4 - i. Factor 4*f**2 - 2 - q*f**3 + 2.
-2*f**2*(f - 2)
Let f(h) be the first derivative of -h**3/7 - 3*h**2 - 21*h - 7. Determine z so that f(z) = 0.
-7
Let b(o) be the first derivative of o**6/720 - 2*o**3/3 - 7. Let l(i) be the third derivative of b(i). Suppose l(v) = 0. What is v?
0
Factor 0*x - 1/4*x**4 - 1/4*x**2 - 1/2*x**3 + 0.
-x**2*(x + 1)**2/4
Let y(b) be the second derivative of 0 + 39/20*b**5 + 1/2*b**6 - 2*b**3 + 0*b**2 - b + b**4. Let y(m) = 0. Calculate m.
-2, -1, 0, 2/5
Let s(w) be the third derivative of -w**8/168 - 4*w**7/105 - w**6/10 - 2*w**5/15 - w**4/12 + 7*w**2. Determine c, given that s(c) = 0.
-1, 0
Factor 6*c - 2*c**3 - 8*c**3 - 3*c**4 - 3*c**4 + 2*c + 8*c**2.
-2*c*(c - 1)*(c + 2)*(3*c + 2)
Let z(c) be the first derivative of c**6/3 + 2*c**5/5 - c**4 - 9. Factor z(f).
2*f**3*(f - 1)*(f + 2)
Let c be (-2)/(-4)*4 - -1. Determine j, given that -3 - 4*j - 14*j**2 + j**3 - 11*j**3 + c = 0.
-1, -2/5, 0
Let n(b) = -b**2 + 19*b - 32. Let g be n(17). Let v(f) be the third derivative of 1/180*f**5 - 1/360*f**6 + 0*f**4 - f**g + 0 + 0*