5
Factor 1/4*r + 0 - 1/4*r**2.
-r*(r - 1)/4
Suppose -c + 5 = 1. Factor -1/3*d + 1/3*d**3 + 2/3*d**c + 0 - 2/3*d**2.
d*(d - 1)*(d + 1)*(2*d + 1)/3
Let q be 0/((-4)/(-2) - 0). Let c(y) be the third derivative of -1/108*y**4 + 1/270*y**5 + q*y**3 + 2*y**2 + 0*y + 0. Factor c(j).
2*j*(j - 1)/9
Let 15*d**4 - 9*d**4 + 3*d + 2*d**5 - 3*d**5 - 2*d**5 - 6*d**2 = 0. Calculate d.
-1, 0, 1
Factor 2/11*y**2 + 4/11*y - 6/11.
2*(y - 1)*(y + 3)/11
Let r be 102*2/60 - 4/10. Factor 1/4*y**5 + 1/2*y**r + 3/4*y**4 - 3/4*y - 1/4 - 1/2*y**2.
(y - 1)*(y + 1)**4/4
Let g(q) be the third derivative of -q**9/6048 + q**8/1680 - q**6/360 + q**5/240 - 5*q**3/6 - q**2. Let l(o) be the first derivative of g(o). Factor l(d).
-d*(d - 1)**3*(d + 1)/2
Let c be 2 - (0 - -1)*4. Let h(g) = -3*g**3 + g**2 + 3*g + 1. Let r(d) = 7*d**3 - 3*d**2 - 7*d - 2. Let w(q) = c*r(q) - 5*h(q). Factor w(v).
(v - 1)*(v + 1)**2
Let r(h) be the third derivative of h**7/105 + h**6/30 - h**5/30 - h**4/6 - 6*h**2. Find f such that r(f) = 0.
-2, -1, 0, 1
Suppose 3*i + 0*i = 15. Let d(m) be the first derivative of 0*m - 1/10*m**4 + 2 + 1/5*m**2 - 1/5*m**i + 1/3*m**3. Determine o, given that d(o) = 0.
-1, -2/5, 0, 1
Let b(i) = 11*i**2 + 41*i + 54. Let a(x) be the first derivative of -5*x**3/3 - 10*x**2 - 27*x - 4. Let j(h) = 5*a(h) + 2*b(h). Factor j(w).
-3*(w + 3)**2
Let l(f) be the first derivative of f**4/10 + 4*f**3/15 + f**2/5 - 2. Let l(y) = 0. What is y?
-1, 0
Let k(i) be the second derivative of -i**5/200 + i**4/60 + i**3/60 - i**2/10 - 12*i. Factor k(m).
-(m - 2)*(m - 1)*(m + 1)/10
Let u(y) be the third derivative of -1/8*y**4 + 0 - 4*y**2 + 1/3*y**3 + 0*y + 7/120*y**6 - 1/70*y**7 - 1/20*y**5. Suppose u(h) = 0. Calculate h.
-2/3, 1
Let s = -28 - -34. Suppose 4/3 - 8/3*r**3 + 2*r**2 + s*r = 0. What is r?
-1, -1/4, 2
Let j(m) be the first derivative of -m**3/3 - 2*m - 5. Let p(k) = k**2 + k + 3. Let s(z) = 6*j(z) + 4*p(z). What is u in s(u) = 0?
0, 2
Let d be (-4)/26 - 50/(-156). Let b(n) be the second derivative of 2/3*n**3 + 0 + d*n**4 + 2*n + n**2. Factor b(t).
2*(t + 1)**2
Let f(k) be the second derivative of -3/160*k**5 + 0*k**2 + 1/48*k**4 + 1/240*k**6 + 0*k**3 + 0 + 7*k. Factor f(v).
v**2*(v - 2)*(v - 1)/8
Let 28*v**3 + 16*v**2 + 12*v**3 - 8*v**3 + 4*v**5 + 20*v**4 = 0. What is v?
-2, -1, 0
Let y(v) be the first derivative of v**6/51 - 6*v**5/85 + 3*v**4/34 - 2*v**3/51 + 6. Factor y(l).
2*l**2*(l - 1)**3/17
Let s be (-12)/(-16)*(-2 + 6). Determine f so that -f - 5/2*f**2 + 1/2 + 3*f**s = 0.
-1/2, 1/3, 1
Let n(x) be the second derivative of x**5/5 + 7*x**4/6 + 7*x**3/3 + 2*x**2 - 7*x. Suppose n(b) = 0. Calculate b.
-2, -1, -1/2
Let c be (-6)/(-51)*(-2)/6. Let l = 47/102 - c. Factor u + l*u**2 + 1/2.
(u + 1)**2/2
Let s(h) be the second derivative of h**5/5 + 5*h**4/3 + 14*h**3/3 + 6*h**2 - 5*h. Factor s(p).
4*(p + 1)**2*(p + 3)
Suppose -2*y + 4*q - 38 = -6, 3 = q. Let h be 3/(-3) + (-14)/y. Solve h*n**2 - 2/5*n + 0 = 0.
0, 1
Let b(o) = -o**3 - 6*o**2 - 4*o - 10. Let w be b(-4). Let m = w + 28. What is g in 2/9*g**3 + 0 + 2/9*g**4 - 2/9*g**m - 2/9*g = 0?
-1, 0, 1
Let w(v) = -v + 5. Let y be w(5). Let j(r) be the second derivative of 1/100*r**5 + 0*r**4 - 2*r + y + 0*r**2 - 1/150*r**6 + 0*r**3. Solve j(z) = 0.
0, 1
Find d, given that -2/7*d**2 + 17/7*d**4 + 0 + 20/7*d**5 + 0*d - 5/7*d**3 = 0.
-1, -1/4, 0, 2/5
Let o(j) = j**2 - j - 2. Let f be o(3). Let x(m) be the third derivative of -1/180*m**5 - 2*m**2 + 0*m + 0*m**f + 0 + 0*m**3. Let x(v) = 0. What is v?
0
Suppose -12 = 3*t - 0. Let s = t - -6. Factor 0 + 0*z - 4 + 0*z - 2*z + 2*z**s.
2*(z - 2)*(z + 1)
Let p(a) = 18*a - 196. Let j be p(11). Let 1/6*y**3 + 5/6*y**j + 7/6*y + 1/2 = 0. Calculate y.
-3, -1
Let f(a) = a**3 + 12*a**2 + 12*a + 13. Let t be f(-11). Factor -4*p**3 + t*p**2 + 4*p - 3*p**4 - 4 + 1 + 4.
-(p - 1)*(p + 1)**2*(3*p + 1)
Find h such that -h - 11*h - 36*h - 4*h**3 - 32 - 24*h**2 = 0.
-2
Let m = 2 - -1. Let j be (-28)/(-8) + (-6)/4. What is q in -q**2 + m*q**j - q**2 + 2*q = 0?
-2, 0
Suppose u = -2*u. Find c such that 0*c + u*c**2 - 1/2*c**4 + 0 + c**3 = 0.
0, 2
Let k(h) = -14*h**3 - h**2 + 1. Let o be k(-1). Factor -14*u + u**4 - u**3 + o*u.
u**3*(u - 1)
Factor 6 + 3*v**2 - v - 3*v + 5*v + 8*v.
3*(v + 1)*(v + 2)
Let x(y) be the second derivative of y**5/300 - y**4/60 + y**3/30 + y**2 + 3*y. Let o(q) be the first derivative of x(q). What is r in o(r) = 0?
1
Suppose 2*w - g - 41 = 0, 4*w + 17 = -2*g + 111. Suppose 4*f - w = d, 5 = -3*d - 1. Let 3*j**5 + 0*j**f - 2*j**3 - j**5 = 0. What is j?
-1, 0, 1
Let r(u) be the first derivative of -u**7/490 + u**6/315 + u**5/70 - u**4/21 + 4*u**3/3 + 5. Let h(t) be the third derivative of r(t). Factor h(v).
-4*(v - 1)*(v + 1)*(3*v - 2)/7
Let c(i) be the second derivative of -2/13*i**2 - 3*i + 0 - 2/39*i**4 - 5/39*i**3 - 1/130*i**5. Factor c(o).
-2*(o + 1)**2*(o + 2)/13
Let m(w) = 10*w**2 - 5. Let q(y) = 9*y**2 - 4. Let n(g) = 4*m(g) - 5*q(g). Factor n(o).
-5*o**2
Let c(m) be the second derivative of -m**7/42 - m**6/15 - m**5/20 - 29*m. What is n in c(n) = 0?
-1, 0
Let w(x) be the third derivative of -2/3*x**3 - 1/12*x**4 + 1/10*x**5 + 2*x**2 + 0 + 0*x. Factor w(p).
2*(p - 1)*(3*p + 2)
Let k(d) be the first derivative of -2/3*d**2 - 2/3*d - 1 - 2/9*d**3. Factor k(w).
-2*(w + 1)**2/3
Let y(w) be the third derivative of -w**5/420 + w**4/168 + 5*w**2. Factor y(c).
-c*(c - 1)/7
Let w(h) = -4*h + 1. Let b be w(-1). Determine y so that -3*y**4 + 23*y**3 - 5 - b*y**3 + 8*y**4 + 17*y**2 + 1 = 0.
-2, -1, 2/5
Let l(i) be the second derivative of i**5/20 + i**4/2 - i**3 + 7*i**2/2 + 4*i. Let t be l(-7). Factor -2/3*f**3 - 8/3*f**4 + 2*f**5 + t*f + 4/3*f**2 + 0.
2*f**2*(f - 1)**2*(3*f + 2)/3
Factor -5/2*s - 5*s**2 + 5*s**4 + 5/2*s**5 + 0 + 0*s**3.
5*s*(s - 1)*(s + 1)**3/2
Suppose 109 = -4*a + 337. Let 98*m**4 + a*m**2 + 162*m**3 + 79*m**4 + 66*m**5 + 3*m + 3*m = 0. What is m?
-1, -1/2, -2/11, 0
Let i be 440/(-120) - (2*-1 - 2). Let 1/3*g - 1/3*g**3 + i*g**2 - 1/3 = 0. What is g?
-1, 1
Solve x**5 + 5*x**2 - 5*x + 2 + 6*x**2 - 2*x**4 - 2*x**4 - 9*x**2 + 4*x**3 = 0.
-1, 1, 2
Let x = 0 + 1/3. Suppose -a - 4*b + 8 = -2*a, -a = b - 2. Suppose x*t + a - 1/6*t**3 - 1/6*t**2 = 0. What is t?
-2, 0, 1
Let x(i) be the third derivative of -i**6/900 + i**5/300 - 2*i**3/3 - i**2. Let q(v) be the first derivative of x(v). Factor q(s).
-2*s*(s - 1)/5
Let s(g) = -3*g**2 - 3*g + 6. Let a(k) = -16*k**2 - 16*k + 30. Let f(v) = -2*a(v) + 11*s(v). Factor f(l).
-(l - 2)*(l + 3)
Let t(g) be the second derivative of g**6/360 + g**5/120 + g**3/6 + 2*g. Let j(u) be the second derivative of t(u). What is q in j(q) = 0?
-1, 0
Let a(v) be the third derivative of -v**7/84 + v**6/16 - 5*v**4/12 + 10*v**2. Factor a(r).
-5*r*(r - 2)**2*(r + 1)/2
Let k(a) be the second derivative of -a**5/5 + 4*a**4/3 - 2*a**3 + 15*a. Find g, given that k(g) = 0.
0, 1, 3
Factor 18/7 + 2/7*z**2 + 12/7*z.
2*(z + 3)**2/7
Let u(i) be the third derivative of 4*i**7/1365 + 7*i**6/260 + 11*i**5/130 + 19*i**4/156 + i**3/13 + 22*i**2. Determine n so that u(n) = 0.
-3, -1, -1/4
Let l(j) = -j**3 - 5*j**2 - 27*j - 23. Let q(c) = -c**2 - 1. Let p(f) = -3*l(f) - 12*q(f). Solve p(x) = 0.
-3
Let w(s) be the first derivative of -9*s**4 + 64*s**3/3 + 8*s**2 + 38. Factor w(p).
-4*p*(p - 2)*(9*p + 2)
Suppose -3*w + 2 + 58 = 5*u, 2*u - 33 = -3*w. Let x = u + -7. Factor -3*y**x + 6*y**3 + 26 - 26 - 3*y**4.
-3*y**2*(y - 1)**2
Suppose -4*f = -3*s + 3, -3 = -3*s - 0*s. Suppose 9 - 5 = 2*p. Find j, given that f*j - 1/4*j**p + 1/4 = 0.
-1, 1
Let j(h) be the third derivative of h**8/1512 - h**6/135 - h**5/135 + h**4/36 + 2*h**3/27 - 20*h**2. Suppose j(x) = 0. What is x?
-1, 1, 2
Let k(j) = 3*j**2 - 2*j + 1. Let g be k(1). Let i be 0/((-8)/(8/g)). Suppose 1/2*q**3 - 1/4*q**2 + 0*q - 1/4*q**4 + i = 0. Calculate q.
0, 1
Let d(t) be the third derivative of 0 - 2/3*t**3 - 9*t**2 - 1/3*t**4 - 1/15*t**5 + 0*t. Factor d(s).
-4*(s + 1)**2
Let o be 4/(-10) + (-51)/(-15). Let r be 7/28 - 45/(-12). Let -1/3*d**2 + 0 - d**o - d**r + 0*d - 1/3*d**5 = 0. Calculate d.
-1, 0
Let j(o) = -o**2 + o. Let t(w) = 2*w**2 - w - 1. Let v be ((-4)/6)/((-2)/(-3)). Let f(d) = v*t(d) - 3*j(d). Determine k, given that f(k) = 0.
1
Let q(k) be the first derivative of k**4/16 - k**3/12 - 7. Solve q(f) = 0.
0, 1