1)
Suppose 0*m + 6 = -3*m, 2*k - 4 = -3*m. Factor h**3 + 2 - 9*h**2 - 5*h**3 + 0*h**k + 2*h**5 + 2*h**4 + 2*h + 5*h**2.
2*(h - 1)**2*(h + 1)**3
Let u(d) be the third derivative of d**5/30 - d**4/12 + 5*d**2. Factor u(x).
2*x*(x - 1)
Let f(h) be the first derivative of 0*h**2 + 0*h**4 + 0*h**3 + 6 + 0*h - 1/15*h**5. Find i such that f(i) = 0.
0
Let p(h) be the first derivative of -h**7/5040 + h**6/2160 + h**5/720 - h**4/144 + 2*h**3 - 6. Let m(b) be the third derivative of p(b). Factor m(s).
-(s - 1)**2*(s + 1)/6
Let i(h) be the first derivative of h**4/8 - h**3/3 - h**2/4 + h - 1. Solve i(x) = 0 for x.
-1, 1, 2
Let p(i) = -i**5 - i**4 + i**3 + i**2 + 1. Let z(j) = 6*j**3 + 12*j**2 + 6*j - 3. Let w(r) = 3*p(r) + z(r). Factor w(a).
-3*a*(a - 2)*(a + 1)**3
Suppose 2 + 10 = 2*y. Let k be (-9)/y*(0 + -2). Factor -3*q**3 + 2*q**k - 3*q + q + 3*q.
-q*(q - 1)*(q + 1)
Let d(l) = -5*l**3 + 9*l - 4. Let r(k) = 70*k**3 - 125*k + 55. Let z(i) = -55*d(i) - 4*r(i). Factor z(q).
-5*q*(q - 1)*(q + 1)
Factor -5/4*v**4 + 0 + 0*v - 1/2*v**2 - 7/4*v**3.
-v**2*(v + 1)*(5*v + 2)/4
Factor 0*r + 0 + 6/7*r**2 + 3/7*r**4 + 9/7*r**3.
3*r**2*(r + 1)*(r + 2)/7
Let m(y) be the second derivative of 0 + 1/2*y**3 + 3/4*y**4 + 4*y + 0*y**2 + 25/56*y**7 - 33/80*y**5 - 3/4*y**6. Factor m(k).
3*k*(k - 1)**2*(5*k + 2)**2/4
Let c(p) be the third derivative of p**7/280 - p**6/160 - p**5/80 + p**4/32 - 6*p**2. Factor c(f).
3*f*(f - 1)**2*(f + 1)/4
Suppose -3*g + 0*g - 2*u = 0, 2*u = -g. Let z be 4 + (3 - 1 - 6). What is d in g*d**2 + z - 1/4*d + 1/4*d**3 = 0?
-1, 0, 1
Let i = -11 + 16. Factor -8*w**2 - 36*w**4 + 14*w**i - 54*w**4 + 36*w**5 + 48*w**3.
2*w**2*(w - 1)*(5*w - 2)**2
Let w = -3/131 + 408/655. Factor 1/5 + 1/5*n**3 + w*n**2 + 3/5*n.
(n + 1)**3/5
Let l(z) be the first derivative of z**3/6 - z**2/2 + z/2 - 6. Factor l(i).
(i - 1)**2/2
Suppose 4*a - 3*g = -5*g + 2, -4*a - 1 = 3*g. Let d(k) be the second derivative of 2*k - 1/2*k**3 - k**a + 0*k**4 + 1/20*k**5 + 0. Suppose d(l) = 0. What is l?
-1, 2
Let d(r) = 5*r**2 + 8*r - 5. Let t be d(-4). Let p = t - 41. Let -1/3*c**3 + 1/3*c + 0 + 0*c**p = 0. What is c?
-1, 0, 1
Let m(l) = 3*l**4 - 4*l**3 - 3*l**2 + 4*l. Let g(c) = 3*c**4 - 3*c**3 - 3*c**2 + 3*c. Let s(j) = 4*g(j) - 3*m(j). What is y in s(y) = 0?
-1, 0, 1
Let s be 4/18 + 676/36. Suppose -2*w - 3*r = -19, -3*w + 7*r = 2*r + s. Factor -2/9*i + 2/3*i**w + 0 - 2/3*i**3 + 2/9*i**4.
2*i*(i - 1)**3/9
Suppose u - 2*u = -3. Suppose -5*d + u = -3*p, 27 = -3*d + 8*d + 3*p. Find c such that 4*c**5 - 3*c**2 - 5*c**3 - 3*c + d*c**4 + 2*c + 0*c**3 + 2*c = 0.
-1, 0, 1/4, 1
Let i(o) be the second derivative of o**4/15 + 2*o**3/15 - 7*o. Factor i(n).
4*n*(n + 1)/5
Let q = 389/168 + -46/21. Factor 0*t + 0 + 0*t**2 + 1/4*t**4 - 1/8*t**3 - q*t**5.
-t**3*(t - 1)**2/8
Factor 2/7*m**3 - 2/7*m - 6/7*m**2 + 6/7.
2*(m - 3)*(m - 1)*(m + 1)/7
Let x = -49 - -21. Let q = x - -31. What is u in -4/9*u**q + 2/9 + 0*u**2 - 2/9*u**4 + 4/9*u = 0?
-1, 1
Let p be (-20)/(-16) + 2 + -1 + -2. Let 0*u**2 + 0 + 0*u - 1/4*u**4 - p*u**3 = 0. Calculate u.
-1, 0
Let c(x) be the second derivative of x**5/60 - 5*x**4/36 + 7*x**3/18 - x**2/2 - 4*x. Let c(u) = 0. What is u?
1, 3
Suppose -2 = 22*c - 23*c. Let d(i) be the second derivative of 3*i - 1/15*i**5 + 0*i**c + 0 + 2/9*i**3 + 7/45*i**6 - 7/18*i**4. What is h in d(h) = 0?
-1, 0, 2/7, 1
Suppose 4*o - 3*c = 177, 0 = 2*o - 7*o - 2*c + 227. Let t be o/(-18)*4/(-25). Factor -1/5*l**3 + t*l**2 + 0*l + 0.
-l**2*(l - 2)/5
Let j be (-4)/14 + (-2)/(-7). Let z = j - -2. Factor -t**3 - z*t**3 + 2 - 4*t**3 - 4*t + t - 12*t**2.
-(t + 1)**2*(7*t - 2)
Let j(b) = -2*b**2 - 24*b - 34. Let i(r) = -r**3 - r**2 - 1. Let q(x) = 2*i(x) - j(x). Factor q(n).
-2*(n - 4)*(n + 2)**2
Let t(f) be the first derivative of -9/2*f**2 + 0*f**3 + 3/4*f**4 + 6*f + 4. Let t(l) = 0. What is l?
-2, 1
Let t(p) be the third derivative of -p**7/840 - p**6/480 + p**5/80 + p**4/96 - p**3/12 - 5*p**2. Factor t(j).
-(j - 1)**2*(j + 1)*(j + 2)/4
Let i(c) be the first derivative of 3*c**6/4 + 3*c**5/2 - 3*c**4/4 + 15. Factor i(g).
3*g**3*(g + 2)*(3*g - 1)/2
Let x(u) be the third derivative of -u**8/1512 - u**7/945 - 11*u**2. Solve x(f) = 0.
-1, 0
Let y(t) be the first derivative of 14*t**3/15 + 9*t**2/5 + 4*t/5 - 11. Solve y(h) = 0.
-1, -2/7
Factor 3*r**2 - 8*r - 5*r**2 + 2*r**2 + 10*r**2.
2*r*(5*r - 4)
Suppose -2*d - 4*y = 2*d - 4, -3*y - 45 = -5*d. Let u = d - 6. Factor -3*h**3 + 3*h + u + 2*h**3 + 0*h**3 + 2.
-(h - 2)*(h + 1)**2
Let 0*s + 0*s**2 + 0 - 2/5*s**4 + 0*s**3 = 0. What is s?
0
Let h(g) be the second derivative of g**8/20160 + g**7/7560 - g**6/2160 - g**5/360 + g**4/4 - 3*g. Let f(t) be the third derivative of h(t). Factor f(s).
(s - 1)*(s + 1)**2/3
Let h(y) = -2*y**4 - 5*y**3 + 4*y**2 - 5*y - 7. Let d(t) = t**4 + 2*t**3 - 2*t**2 + 2*t + 3. Let w(b) = -5*d(b) - 2*h(b). Factor w(s).
-(s - 1)**2*(s + 1)**2
What is g in 0 + 2/13*g - 2/13*g**3 + 0*g**2 = 0?
-1, 0, 1
Let q(b) = 21*b**2 + 24*b + 3. Let g(c) be the third derivative of c**5/60 + c**4/24 + 2*c**2. Let i(a) = 18*g(a) - q(a). Factor i(o).
-3*(o + 1)**2
Let v = -6 - -4. Let f = v - -5. Determine n, given that 5*n**5 - 4*n**5 - 4*n**f + 2*n + n**5 = 0.
-1, 0, 1
Determine r, given that 1/10*r**2 + 3/10*r - 2/5 = 0.
-4, 1
Suppose -3*d + 16 = -d. Let x = d - 6. Let -4*l - 2*l**2 + 0*l**2 + x*l = 0. Calculate l.
-1, 0
Let u(n) = 6*n**2 + 3*n + 6. Let s(v) = 5*v**2 + 4*v + 4. Let l(c) = 3*s(c) - 2*u(c). Factor l(w).
3*w*(w + 2)
Let q(j) = j + 6. Let l be q(-6). Let o = 114 - 796/7. Find g, given that -2/7*g**3 - 2/7*g**4 + 2/7*g + l + o*g**2 = 0.
-1, 0, 1
Factor -u**2 - 3*u - 2*u**2 + 7*u**2 - u**2.
3*u*(u - 1)
Let l(p) = -8*p**2 - 8*p. Let t(a) = 4*a**2 + 4*a. Let u(s) = -6*l(s) - 11*t(s). Find x, given that u(x) = 0.
-1, 0
Let b be 6*(0 + (-2)/(-4))/1. Let d(n) be the third derivative of 0*n - 1/144*n**4 + 1/360*n**5 + 0*n**3 + b*n**2 + 0. Factor d(x).
x*(x - 1)/6
Factor -3*y**5 + 3*y**3 - 3470*y**2 + 3470*y**2.
-3*y**3*(y - 1)*(y + 1)
Let g be 30/(-36) - (-1)/2. Let a = -1/12 - g. Factor 1/4 - a*n**2 + 0*n.
-(n - 1)*(n + 1)/4
Let c(q) be the third derivative of 0*q**3 + 1/72*q**4 - 5*q**2 + 0 + 0*q + 1/180*q**5. Find x, given that c(x) = 0.
-1, 0
Let l = -1/325 + 361/11700. Let x(r) be the second derivative of r - l*r**4 + 0*r**2 + 0*r**3 - 1/60*r**5 + 0. Find z such that x(z) = 0.
-1, 0
Factor -48*p**3 - 682 - 3*p**4 + 826 + 48*p - 140*p**2 - p**4.
-4*(p - 1)*(p + 1)*(p + 6)**2
Let n = -919 - -2789/3. Solve 16*i**2 + 2/3 - 6*i - n*i**3 = 0 for i.
1/4, 1
Let a(k) be the second derivative of k**6/6 - 5*k**4/12 + 9*k. Let a(n) = 0. What is n?
-1, 0, 1
Let z(o) = -o**4 - o**2 - 1. Let t(m) = -4*m**4 + m**3 - m - 5. Let a(n) = t(n) - 3*z(n). Factor a(x).
-(x - 2)*(x - 1)*(x + 1)**2
Let o be -3 + (1 + -4 - -8). Suppose -3*q + 3*q**o + 0*q**2 - 3*q = 0. What is q?
0, 2
Factor -4/5*v - 18/5*v**4 + 0 - 26/5*v**2 - 8*v**3.
-2*v*(v + 1)**2*(9*v + 2)/5
Find a such that -a**2 + 0*a - 1/3*a**3 + 0 = 0.
-3, 0
Let l be (-1)/2 + (3 - 2). What is p in -5/4*p**2 - 7/4*p - l = 0?
-1, -2/5
Suppose 0 = 5*d - 0. Let j(g) be the third derivative of 2*g**2 + d*g**5 + 0 + 0*g - 1/40*g**6 + 3/8*g**4 - g**3. Let j(y) = 0. What is y?
-2, 1
Factor -3/7*i**4 - 12/7*i + 0*i**2 + 9/7*i**3 + 0.
-3*i*(i - 2)**2*(i + 1)/7
Let f(r) be the third derivative of r**5/40 + 3*r**4/16 + 3*r**2. Factor f(v).
3*v*(v + 3)/2
Let g(i) = -3*i**3 - 2*i**2 + 5. Let m(p) = -p**3 - p**2 + 2. Let h(j) = 2*g(j) - 5*m(j). Factor h(c).
-c**2*(c - 1)
Let p(c) be the first derivative of -c**3/4 - 21*c**2/2 - 147*c - 20. Solve p(g) = 0.
-14
Let z = -18 + 25. Suppose -2*m + z*m = 10. Factor 0*c**3 - 2*c - c**3 + 2*c**m + 3*c**3 + 0*c - 2*c**4.
-2*c*(c - 1)**2*(c + 1)
Let q = -1 + 3. Let a(w) be the first derivative of 5/4*w**4 - 3/8*w**q - 1 + 1/2*w - w**3. Factor a(f).
(2*f - 1)**2*(5*f + 2)/4
Suppose 0 = 26*g - 21*g - 10. Determine m so that 0*m**g + 0*m + 3/2*m**4 + 0 - 3*m**3 = 0.
0, 2
Let y(v) be the third derivative of -v**9/22680 - v**8/10080 - v**4/12 - 3*v**2. Let a(n) be the second derivative of y(n). Factor a(k).
-2*k**3*(k + 1)/3
Let r(d) = d**2 + d - 4. Let b be r(-3). What is x in 11*x**2 + 2 - 2 - 12*x**b + x**3 = 0?
0, 1
Let w be 24/228 + (-4)/(912/(-14)). Suppose 0 = 4*n - 4 - 4. Factor -1/6