tive of u(y). Factor g(p).
(p - 1)**2*(p + 1)/5
Let q(l) = l**2 + 1. Let p be q(-1). Suppose -8*r + 3*r - p = -4*i, 0 = -3*i + 5*r - 1. Factor -4*v**2 + 8*v**2 - 2*v**3 + 4*v**i.
2*v**2*(v + 2)
Let j(i) = -i - 2. Let w be j(-2). Let m be (39 + -14)*8/100. Factor w + 7/3*n**4 + n**m + 2/3*n - 4*n**3.
n*(n - 1)**2*(7*n + 2)/3
Let t(m) = -2*m**2 - 8*m + 3. Let d be t(-4). Factor -13*j**d + 7*j**3 - 28*j**2 + 4 - 40*j - 20.
-2*(j + 2)**2*(3*j + 2)
Determine d so that -2/11*d**2 + 16/11 - 4/11*d = 0.
-4, 2
Let j(l) = 3*l**2 - 1. Let g(r) = -8*r**4 + 28*r**3 - 30*r**2 - 4*r + 10. Let i(m) = -g(m) - 2*j(m). Determine k, given that i(k) = 0.
-1/2, 1, 2
Determine q, given that -9/10 + 1/10*q**2 - 4/5*q = 0.
-1, 9
Let y(x) = -1. Let j(g) = 81*g**3 + g - 9 - 36*g**2 - 4*g + 7*g. Let s(b) = -10*b + 76. Let p be s(4). Let c(a) = p*y(a) - 4*j(a). Solve c(k) = 0.
0, 2/9
Let j(a) be the second derivative of -5/7*a**2 + 20*a + 0 - 12/7*a**4 + 8/35*a**5 - 13/7*a**3. Solve j(y) = 0 for y.
-1/4, 5
Let p(x) be the second derivative of 8*x + 3/40*x**5 + 0*x**2 + 0 + 1/4*x**4 + 1/4*x**3. What is s in p(s) = 0?
-1, 0
Let s(v) be the second derivative of -1/9*v**3 - 22 + 0*v**5 - 1/90*v**6 + 0*v**2 + 1/12*v**4 - 2*v. Solve s(c) = 0 for c.
-2, 0, 1
Let f(l) be the second derivative of -2*l**6/45 - 2*l**5/15 + l**4/9 + 4*l**3/9 + 36*l. Let f(a) = 0. What is a?
-2, -1, 0, 1
Let 0 - 2/5*j**4 + 72/5*j**3 + 132/5*j - 202/5*j**2 = 0. What is j?
0, 1, 2, 33
Let x(y) be the first derivative of y**6/4 + 9*y**5/10 + 3*y**4/4 - 210. Factor x(w).
3*w**3*(w + 1)*(w + 2)/2
Determine g, given that 2/3*g**3 - 3174 + 3266*g - 278/3*g**2 = 0.
1, 69
Factor -11/2*v - 13/2*v**3 + 1 + 19/2*v**2 + 3/2*v**4.
(v - 2)*(v - 1)**2*(3*v - 1)/2
Let p = 108/869 + 62/79. Solve 4/11*v**2 - 10/11*v**5 + 0 - 4/11*v**4 + 0*v + p*v**3 = 0 for v.
-1, -2/5, 0, 1
Suppose 73*q = 70*q + 9. Let w be 4/(-2) - (-7 - -2). Let 0*g**3 - w*g**3 + g**2 + g**q - g**4 + 0*g**3 + 2*g = 0. Calculate g.
-2, -1, 0, 1
Let v(p) be the third derivative of p**6/24 + p**5/6 - 65*p**4/24 + 25*p**3/3 + 288*p**2. What is j in v(j) = 0?
-5, 1, 2
Suppose -2*u = 3*c, -8*c + 13*c - 4*u - 44 = 0. Solve -12/5 - 9/5*n**5 + 29/5*n**2 + 29/5*n**3 - 16/5*n - 21/5*n**c = 0 for n.
-3, -2/3, 1
Let p(d) be the second derivative of -d**5/150 - 7*d**4/90 - 11*d. Factor p(r).
-2*r**2*(r + 7)/15
Let a(f) = -2*f**2 + 4*f - 7. Let r(w) = 5*w**2 - 2*w - 4*w + 11 - 2*w**2. Let x(h) = -8*a(h) - 5*r(h). Solve x(p) = 0.
1
Factor 16/5*t**2 + 0 + 4/5*t**3 - 4/5*t**4 - 16/5*t.
-4*t*(t - 2)*(t - 1)*(t + 2)/5
Let f(g) = 13*g**2 - 48*g - 13. Let k be f(4). Factor 0*q + 4/11*q**k + 1/11*q**2 + 0.
q**2*(4*q + 1)/11
Suppose -5*a + a + 5*w - 24 = 0, -5*a - 5*w + 15 = 0. Let q(k) = -k**2 + k + 2. Let n be q(a). Find c, given that n + 6*c**3 + 3/2*c**4 + 0*c + 6*c**2 = 0.
-2, 0
Let g(m) be the second derivative of -32*m + 0*m**2 - 4/7*m**3 + 3/140*m**5 + 1/14*m**4 + 0. Factor g(x).
3*x*(x - 2)*(x + 4)/7
Let s(u) = 13*u**3 + 42*u**2 + 11*u. Let q(p) = -p**3 - p. Let i(h) = -3*q(h) - s(h). Find v such that i(v) = 0.
-4, -1/5, 0
Let t(l) = 3*l**2 - 522*l + 22707. Let g(o) = 2*o**2 - 348*o + 15138. Let v(u) = 8*g(u) - 5*t(u). What is h in v(h) = 0?
87
Let b = -14226 + 14228. Factor 0*d**b + 0*d + 0*d**3 + 21/5*d**5 + 12/5*d**4 + 0.
3*d**4*(7*d + 4)/5
Let y(q) be the first derivative of q**7/2520 + q**6/1080 - q**5/360 - q**4/72 - 10*q**3/3 + 8. Let p(m) be the third derivative of y(m). Solve p(n) = 0 for n.
-1, 1
Suppose 3*q - 2*q - 31 = 0. Let p = 48 - q. Determine w, given that 91 + p - 68*w**3 + 36*w**2 + 72*w**3 + 108*w = 0.
-3
Let q(o) be the first derivative of -o**8/10080 + o**7/2520 + o**6/540 - o**5/90 + o**3/3 - 3. Let b(a) be the third derivative of q(a). Factor b(z).
-z*(z - 2)**2*(z + 2)/6
Let g(l) be the first derivative of 7*l**6/8 - 3*l**5/10 - 21*l**4/8 + l**3 + 21*l**2/8 - 3*l/2 + 63. Determine w, given that g(w) = 0.
-1, 2/7, 1
Let f be (-357)/(-18)*2/(-28). Let z = f - -5/3. Let s + z + 3/4*s**2 = 0. Calculate s.
-1, -1/3
Let c(r) be the second derivative of -r**6/9 - 3*r**5/5 - 17*r**4/18 + 4*r**2/3 - 267*r. Determine h, given that c(h) = 0.
-2, -1, 2/5
Let v(i) be the second derivative of i**7/560 - i**6/240 + 10*i**3/3 + 7*i. Let b(x) be the second derivative of v(x). Factor b(t).
3*t**2*(t - 1)/2
Let o(g) = -g**4 + 32*g**3 - 2*g**2 - 8*g + 4. Let a(r) = -r**4 + 38*r**3 - 3*r**2 - 8*r + 4. Let i(v) = 5*a(v) - 6*o(v). Determine q so that i(q) = 0.
-2, 1, 2
Let h(w) = -2*w**2 - 14*w + 90. Let m be h(-11). Suppose 4 - 6 = -t. Let -5*i**m - 1/5 + t*i = 0. What is i?
1/5
Let n(d) be the second derivative of -d**7/210 - d**6/15 - 2*d**5/5 - 4*d**4/3 + 5*d**3/2 - 13*d. Let a(q) be the second derivative of n(q). Factor a(k).
-4*(k + 2)**3
Let c(p) be the third derivative of p**6/60 - 2*p**5/3 + 4*p**2 - 8*p. Factor c(n).
2*n**2*(n - 20)
Factor -76*w + 841/3*w**3 + 8/3 + 522*w**2.
(w + 2)*(29*w - 2)**2/3
Let i(j) be the second derivative of 9*j**4/2 + 13*j**3/2 + 3*j**2 + 2*j - 17. Find x, given that i(x) = 0.
-1/2, -2/9
Suppose 30/7 - 2*w**2 + 22/7*w - 6/7*w**3 = 0. Calculate w.
-3, -1, 5/3
Let o(k) be the first derivative of -3*k**4/4 + 487*k**3/3 - 19845*k**2/2 + 6561*k - 248. Factor o(l).
-(l - 81)**2*(3*l - 1)
Let z(t) = 8*t - 14. Let q be z(2). Factor 3/4*p - 1/2 - 1/4*p**q.
-(p - 2)*(p - 1)/4
Let l = -2117/5 - -2118/5. Factor 1/5*c**3 - l*c**5 + 0 + 0*c**2 + 0*c**4 + 0*c.
-c**3*(c - 1)*(c + 1)/5
Let b(c) be the first derivative of -3*c**5/80 - c**4/16 + c**3/8 + 3*c**2/8 - 19*c + 3. Let w(r) be the first derivative of b(r). Factor w(j).
-3*(j - 1)*(j + 1)**2/4
Let w be 3/((-816)/(-544) + -3*2/20). Suppose 11/2*b**3 + 19/2*b**2 - 3/2*b**4 + w*b + 0 = 0. Calculate b.
-1, -1/3, 0, 5
Suppose 5*z - 846 = -4*z. Factor 27*t**3 - 3 - 25*t**2 - 55*t - 3 + z*t - 47*t**2.
3*(t - 2)*(3*t - 1)**2
Let b(s) be the second derivative of -s**4/84 + 3*s**3/7 - 17*s**2/14 - 41*s - 2. Factor b(a).
-(a - 17)*(a - 1)/7
Let i(v) be the third derivative of -4/21*v**7 + 0*v - 5/336*v**8 + 25/6*v**4 - 38*v**2 - 19/24*v**6 - 2/3*v**5 + 0 + 40/3*v**3. Suppose i(d) = 0. What is d?
-4, -2, -1, 1
Suppose -3218 = 15*f + 1162. Let p = 295 + f. What is d in -1/7*d**p - 15/7*d**2 - 75/7*d - 125/7 = 0?
-5
Let b(t) be the second derivative of -169*t**5/20 - 143*t**4/6 + 50*t**3/3 - 4*t**2 + 22*t + 1. Factor b(w).
-(w + 2)*(13*w - 2)**2
Let l(r) = -4*r**2 - 8*r + 24. Let u(g) be the second derivative of -g**4/3 - 3*g**3/2 + 12*g**2 - 25*g. Let t(f) = -5*l(f) + 4*u(f). Factor t(y).
4*(y - 2)*(y + 3)
Let f(t) = 12*t**3 + 24*t**2 + 60*t + 28. Let n(z) = 22*z**3 + 49*z**2 + 119*z + 57. Let j(s) = -7*f(s) + 4*n(s). Factor j(h).
4*(h + 1)*(h + 2)*(h + 4)
Let p(n) be the second derivative of n**5/30 - n**4/9 + n**3/9 - 364*n. Factor p(l).
2*l*(l - 1)**2/3
Let x(h) be the second derivative of h**6/60 - h**5/8 + 3*h**4/8 - 7*h**3/12 + h**2/2 + 52*h. Factor x(f).
(f - 2)*(f - 1)**3/2
Let w(o) = -2*o**3 - 6*o**2 + 2*o + 1. Let m(x) = x**2 - x - 1. Let b(q) = -5*m(q) + w(q). Let b(z) = 0. What is z?
-6, -1/2, 1
Let n(i) = 6*i**2 - 1. Let d be n(1). Let o(z) be the second derivative of 0*z**4 + 1/9*z**3 + 1/90*z**6 + 0 - 1/30*z**d - 1/6*z**2 - 3*z. Factor o(l).
(l - 1)**3*(l + 1)/3
Let k(r) be the third derivative of -r**7/280 - 13*r**6/480 - 11*r**5/240 + 5*r**4/96 + r**3/4 + 2*r**2 + 46. Determine l so that k(l) = 0.
-3, -1, 2/3
Let s(y) be the third derivative of y**5/120 + 31*y**4/48 - 8*y**3/3 + 693*y**2. Determine r, given that s(r) = 0.
-32, 1
Let i(n) be the second derivative of -6241*n**4/132 - 316*n**3/33 - 8*n**2/11 + n + 176. Factor i(k).
-(79*k + 4)**2/11
Factor 17/8*x**3 - 1/8*x**4 + 59/8*x + 5/2 + 57/8*x**2.
-(x - 20)*(x + 1)**3/8
Let y(h) = -35*h**2 + 34*h. Let z(s) = -4*s**2 - s. Let g(r) = 5*y(r) - 45*z(r). Factor g(m).
5*m*(m + 43)
Let m(u) be the first derivative of -u**4/14 + 2*u**3/7 + u**2/7 - 6*u/7 - 41. Determine h so that m(h) = 0.
-1, 1, 3
Let 3/7*g**2 + 2700/7 - 180/7*g = 0. Calculate g.
30
Let q(d) be the third derivative of 0*d - 25/27*d**3 - 6*d**2 - 1/270*d**5 - 5/54*d**4 + 0. Factor q(w).
-2*(w + 5)**2/9
Let g(o) = -17*o**2 + 17*o - 8. Let r(x) = 69*x**2 - 68*x + 33. Let i(y) = 13*g(y) + 3*r(y). Suppose i(b) = 0. What is b?
1/2, 5/7
Suppose 2 = -18*v + 17*v. Let o 