82 - i. Factor -u*j + 0 - 2/7*j**5 + 4/7*j**3 + 0*j**2 + 0*j**4.
-2*j*(j - 1)**2*(j + 1)**2/7
Suppose -2*n - 2*h + 5 = -5, -2*h + 16 = 5*n. Factor 1/3*y**n + 0*y + 0.
y**2/3
Let h(i) be the first derivative of -2*i**3/3 + 10*i**2 - 57. Factor h(v).
-2*v*(v - 10)
Factor -1/5*c**3 - 2/5*c + 0 - 3/5*c**2.
-c*(c + 1)*(c + 2)/5
Let a(b) be the second derivative of 0 + b + 20/3*b**3 - 9/10*b**5 - b**4 - 8*b**2. Solve a(n) = 0.
-2, 2/3
Suppose 0 = -p + 6*p - 25. Let m = p - 3. Factor f**2 + f**4 - 3*f**3 - 2*f**m - f**5 + 4*f**3.
-f**2*(f - 1)**2*(f + 1)
Factor 0*b**2 + 0*b + 0*b**4 - 2/7*b**3 + 0 + 2/7*b**5.
2*b**3*(b - 1)*(b + 1)/7
Let g(p) = -2*p + 1. Let t be g(6). Let c = 14 + t. Suppose 0 + 1/5*q**c + 0*q + 0*q**2 - 1/5*q**4 = 0. Calculate q.
0, 1
Let u(h) be the second derivative of -h**5/40 - 5*h**4/24 - h**3/3 + 27*h. Let u(m) = 0. What is m?
-4, -1, 0
Let a = -8 + 12. Let t(k) be the second derivative of -5/12*k**3 - 5/12*k**a - 1/4*k**2 - 1/12*k**6 - 1/84*k**7 - 1/4*k**5 + 0 - 3*k. Factor t(y).
-(y + 1)**5/2
Let g(f) be the second derivative of 0 - 4/33*f**3 + 0*f**2 + 4*f + 14/33*f**4 - 49/110*f**5. Factor g(n).
-2*n*(7*n - 2)**2/11
Let k(z) = z**2 + 13*z + 26. Let w = 30 + -41. Let r be k(w). Factor 0 + 3/2*v**r + 6*v**3 + 0*v + 6*v**2.
3*v**2*(v + 2)**2/2
Let y(b) be the second derivative of b**5/28 - b**4/84 + 2*b. Factor y(d).
d**2*(5*d - 1)/7
Suppose 10 = 4*w + w. Factor -w*u**2 - 4*u - u + 2*u**3 + 4*u - 2 - u**5 + 3 + u**4.
-(u - 1)**3*(u + 1)**2
Suppose 8 = z - 5*k, -5*z - 5 = -6*z + 2*k. Let m(q) be the first derivative of -3/4*q**4 + 5 + 0*q**2 - 3/5*q**5 + 0*q + 0*q**z. Solve m(p) = 0 for p.
-1, 0
Factor y**4 - y**2 + 1/2*y + 0*y**3 + 0 - 1/2*y**5.
-y*(y - 1)**3*(y + 1)/2
Let d = 5/204 - 2/255. Let o(c) be the second derivative of 0 + d*c**5 + 2*c - 4/3*c**2 + 2/3*c**3 - 1/6*c**4. Let o(k) = 0. Calculate k.
2
Let w(x) = -4*x + 1. Let d(u) = -u**2. Let g be 18/24 - (-2)/8. Let b = g - -2. Let m(i) = b*d(i) - w(i). Suppose m(c) = 0. Calculate c.
1/3, 1
Factor 22*u - 242 - 1/2*u**2.
-(u - 22)**2/2
Let z(o) be the first derivative of -o**5/15 - o**4/3 + o**3/9 + 2*o**2/3 + 36. Find p such that z(p) = 0.
-4, -1, 0, 1
Let j = 8 - 6. Suppose 0 = -2*c - 0*i + 4*i + 8, -8 = 5*c + 4*i. Determine h, given that 1/2*h**j + 1/2*h + c = 0.
-1, 0
Let k(r) = -2*r - 8 + 0 + 22. Let w be k(7). Find u such that 1/4*u**2 + 0*u - u**3 + w = 0.
0, 1/4
Let m(r) be the second derivative of -r**7/105 + 2*r**6/75 + r**5/50 - r**4/15 + 27*r. Find n, given that m(n) = 0.
-1, 0, 1, 2
Let i = -5 + 9. Suppose 3*x = -2*v + 7*v + i, -5*v = -5*x + 10. Let 6/7*s**2 + 2/7*s**4 + 2/7*s + 0 + 6/7*s**x = 0. What is s?
-1, 0
What is g in 1/4*g**2 + 1/2*g + 0 = 0?
-2, 0
Factor -16*c**2 + 2/3*c**4 + 0*c**3 - 32 - 128/3*c.
2*(c - 6)*(c + 2)**3/3
Let z(s) be the first derivative of 2*s**3/3 + 3*s**2 + 4*s + 8. Suppose z(f) = 0. Calculate f.
-2, -1
Suppose 4*y - 24 - 24 = 0. Suppose 0*x - 4*x = -y. Factor 4*w**3 - w**x - 2*w**3 - w**4.
-w**3*(w - 1)
Let v = -12 + 17. Let g(z) = 7*z**5 - 3*z**4 - 9*z**3 + z**2 + 2*z - 3. Let t(x) = -6*x**5 + 2*x**4 + 8*x**3 - 2*x + 2. Let b(i) = v*t(i) + 4*g(i). Factor b(w).
-2*(w - 1)**2*(w + 1)**3
Let w = -62 - -62. Solve w + 0*b - 2/5*b**2 + 2/5*b**3 = 0.
0, 1
Let l = -48 + 51. Let -26/3*z**l + 4/3 - 4*z**2 - 4*z**4 + 2*z = 0. What is z?
-1, -2/3, 1/2
Suppose -4*y + 27 = -5*x - 9, -8 = 2*x. Let f be 6/(-10) + (0 - -1). Solve 2/5*v - 4/5*v**y + 4/5*v**2 + 0*v**3 - f*v**5 + 0 = 0 for v.
-1, 0, 1
Let w(r) be the first derivative of -3/4*r**3 - 2 - 5/12*r**4 - 1/2*r**2 - 3/40*r**5 - r. Let n(p) be the first derivative of w(p). Solve n(j) = 0 for j.
-2, -1, -1/3
Let x(w) be the second derivative of 1/105*w**7 + 0 + 2/75*w**6 + 3*w - 1/15*w**3 - 1/15*w**4 + 0*w**5 + 0*w**2. Factor x(s).
2*s*(s - 1)*(s + 1)**3/5
Let j = 523/4 + -130. Let f be 33/20 - 4/10. Let 0 - j*x**4 + 3/4*x**2 - x**5 + f*x**3 - 1/4*x = 0. Calculate x.
-1, 0, 1/4, 1
Let h(g) be the first derivative of g**4/16 + g**3/4 - 5*g**2/4 - 40. Factor h(v).
v*(v - 2)*(v + 5)/4
Let j(o) = 21*o**4 + 41*o**3 + 9*o**2 + 11*o - 11. Let i(a) = -4*a**4 - 8*a**3 - 2*a**2 - 2*a + 2. Let b(t) = -11*i(t) - 2*j(t). Factor b(m).
2*m**2*(m + 1)*(m + 2)
Let m(c) = -c**2 + 5*c - 3. Let p be m(2). Factor -j + 0*j - 5*j**2 + p*j**2 + j**2.
-j*(j + 1)
Let r(a) be the first derivative of 0*a - a**3 - 1 - 3/4*a**4 + 3/2*a**2 + 3/5*a**5. Factor r(d).
3*d*(d - 1)**2*(d + 1)
Let l(w) be the third derivative of w**6/2340 - w**4/156 - 5*w**3/6 + 3*w**2. Let m(k) be the first derivative of l(k). Factor m(x).
2*(x - 1)*(x + 1)/13
Let c(p) be the third derivative of -p**8/336 + p**7/210 + p**6/40 - p**5/60 - p**4/12 + p**2. Determine w so that c(w) = 0.
-1, 0, 1, 2
Suppose 5*v - 20 = -h + 3*h, -2*v + 5*h = -29. Factor -2*y - 9*y**4 + 22*y**2 + 2*y**3 + 2*y**4 - 15*y**v.
-y*(y - 1)*(y + 1)*(7*y - 2)
What is c in -2*c**2 - 4*c**3 + 26*c**2 + 22*c**3 - 2*c**3 - 2*c**4 - 2*c**5 = 0?
-2, 0, 3
Let d(q) = -3*q**4 + 3*q**3 + 3*q**2 + 3*q + 3. Let t(j) = 9*j**4 - 9*j**3 - 8*j**2 - 8*j - 8. Let h(u) = -8*d(u) - 3*t(u). Factor h(c).
-3*c**3*(c - 1)
Let k(v) = -v**3 + 13*v**2 + 13*v + 17. Let t be k(14). Suppose 2*o = -3*l + 4, -t*l - 2 = -2*l + 4*o. Factor -1/3 + 2/3*w - 1/3*w**l.
-(w - 1)**2/3
Let c(k) be the second derivative of 0 + 0*k**2 - 8*k - 3/20*k**5 - 7/90*k**6 - 5/36*k**4 - 1/63*k**7 - 1/18*k**3. Suppose c(d) = 0. What is d?
-1, -1/2, 0
Let a be 1/(3*(-2)/(-2)). Let m be 32/(-112) - 4/(-42)*10. Solve -1/3*l**2 + m - a*l = 0.
-2, 1
Solve 20/3*q**3 - 25/3*q + 5/3*q**5 + 10/3*q**2 + 10/3 - 20/3*q**4 = 0.
-1, 1, 2
Let m(x) be the second derivative of x**6/120 + x**5/80 + 14*x. Factor m(d).
d**3*(d + 1)/4
Let m(l) be the second derivative of -l**2 - 2*l + 0 - 5/12*l**4 - 5/6*l**3. Let g(b) = 11*b**2 + 11*b + 5. Let x(j) = 4*g(j) + 9*m(j). Factor x(p).
-(p - 1)*(p + 2)
Let v = 14/51 + 1/17. Let j = 42 + -42. Factor -1/3 + j*s + 0*s**3 - v*s**4 + 2/3*s**2.
-(s - 1)**2*(s + 1)**2/3
Let c(i) = i**3 - i**2 + i + 1. Suppose 39 = 4*o - 4*f - 9, -60 = -5*o + 2*f. Let m(a) = -10*a**3 + 12*a**2 - 12*a - 12. Let h(g) = o*c(g) + m(g). Factor h(x).
2*x**3
Suppose 4*s - 4*t = 12 + 12, 0 = -2*s - t. Let y be -1 - -1*(-2 - -5). Let 3 - 3 + 0*p**y + 4*p - 2 - s*p**2 = 0. Calculate p.
1
Factor 0 - 1/3*c**4 + 5/3*c**3 + c - 7/3*c**2.
-c*(c - 3)*(c - 1)**2/3
Let x(p) = p**2 - p + 1. Let o(f) = 5*f**2 - 7*f + 8. Let q(v) = o(v) - 6*x(v). Factor q(n).
-(n - 1)*(n + 2)
Factor -4*y**2 + 16*y - 168*y**3 + 92*y**3 - 12*y**2 - 176*y**3.
-4*y*(7*y + 2)*(9*y - 2)
Let k(x) be the first derivative of -x**3/3 - 13*x**2/2 + 3*x - 2. Let y(u) = -7*u + 2. Let a be -1 - (-2*3)/1. Let d(t) = a*y(t) - 3*k(t). Factor d(z).
(z + 1)*(3*z + 1)
Let m(l) = l**2 - 11*l - 10. Let d be m(12). Let a be ((-6)/4)/(3/(-4)). Find z, given that -5*z**4 + z**5 - a*z**5 + 6*z**4 - z + 1 - 2*z**d + 2*z**3 = 0.
-1, 1
Let f(x) be the first derivative of -x**4/42 + 2*x**3/21 - x**2/7 - x + 2. Let z(q) be the first derivative of f(q). Factor z(j).
-2*(j - 1)**2/7
Let s(f) = -2*f**2 + 2*f - 4. Let d = 4 + -8. Let v(y) = -3*y**2 + 4*y - 7. Let n(k) = d*v(k) + 7*s(k). Factor n(c).
-2*c*(c + 1)
Let g(o) = o**3 - 4*o**2 + 2. Let v be g(4). Factor -2 + 2*q + 1 - 6*q**v + 2 + 5*q**2 - 2*q**3.
-(q - 1)*(q + 1)*(2*q + 1)
Let f(i) be the first derivative of i**4/28 - 2*i**3/7 + 6*i**2/7 - 8*i/7 - 22. Solve f(b) = 0 for b.
2
Let s(y) be the second derivative of y**5/60 - y**4/6 - y**3/18 + y**2 - 6*y. Suppose s(p) = 0. What is p?
-1, 1, 6
Let b(x) be the second derivative of 6*x**7/7 - 22*x**6/15 - 7*x**5/5 + 11*x**4/3 - 4*x**3/3 - 2*x. Let b(a) = 0. Calculate a.
-1, 0, 2/9, 1
Let i(v) = -6*v**3 + 6*v**2 - 3. Let g(y) = 13*y**3 - 13*y**2 + 7. Let n be (-2 - -1) + 6/(-3). Let p(r) = n*g(r) - 7*i(r). Factor p(j).
3*j**2*(j - 1)
Let l = -10 + 10. Suppose l = d + 2 - 5. Factor -7*w + w - 3*w**2 + d*w.
-3*w*(w + 1)
Let i(t) be the second derivative of 0 + 0*t**3 + 1/42*t**4 + 3*t + 0*t**2. Factor i(p).
2*p**2/7
Let h = -138 + 138. Find m such that 1/3*m**4 + 0*m - 1/3*m**2 + h + 0*m**3 = 0.
-1, 0, 1
Factor 16/7*k - 38/7*k**2 + 2*k**3 + 8/7.
2*(k - 2)*(k - 1)*(7*k + 2)/7
Determine w so that -14/5*w - 4/5 - 2*w**2 = 0.
-1, -2/5
Let k be 2/(4 + (-1 - -3)). Find z such that -1/3*z - 2/3*z**