.
1, 15
Let n(j) be the second derivative of -j - 1/10*j**5 + 0 - 1/6*j**4 + 1/3*j**3 + j**2. Factor n(d).
-2*(d - 1)*(d + 1)**2
Let k(f) be the first derivative of -2*f**3/27 - 7. Factor k(b).
-2*b**2/9
Let m(k) be the second derivative of -k**5/70 - k**4/42 + k**3/21 + k**2/7 + k. Factor m(y).
-2*(y - 1)*(y + 1)**2/7
Let l(i) be the first derivative of -i**3 - 3*i**2/2 - 3. Factor l(k).
-3*k*(k + 1)
Let i = 219 + -1529/7. Suppose -m + 2*n = -11, n = 3*m + 5 - 18. Determine p so that 6/7*p**m + i*p**4 + 0 - 2/7*p + 0*p**2 = 0.
-1, 0, 1/2
Suppose 2*x - 28 = -0*x. Find u, given that 4*u - 5*u - 1 - 8*u**3 + x*u**2 - 3*u - 1 = 0.
-1/4, 1
Let r be ((-6)/15)/((-18)/15). Let w(k) be the third derivative of -1/3*k**4 + 1/5*k**5 - 1/15*k**6 + 0*k + 1/105*k**7 + k**2 + 0 + r*k**3. Factor w(p).
2*(p - 1)**4
Let d(w) = -w**2 + 2*w + 3. Let g be d(2). Suppose -g*o = -4*o. Let 1/3*f + o*f**2 + 0 - 1/3*f**3 = 0. What is f?
-1, 0, 1
Suppose -3*m + 12 - 20 = -4*o, m + 2 = o. Determine n so that 6/5*n**2 + m*n + 2/5*n**3 - 8/5 = 0.
-2, 1
Let a(k) be the first derivative of 25*k**6/6 + 2*k**5 - 75*k**4/4 + 20*k**3/3 + 10*k**2 + 32. Solve a(d) = 0 for d.
-2, -2/5, 0, 1
Let v(s) be the second derivative of 1/18*s**3 + 1/9*s**4 - s + 0*s**2 + 0. Find l such that v(l) = 0.
-1/4, 0
Let k(n) be the third derivative of 2*n**7/105 - n**6/30 - n**5/15 + n**4/6 - 12*n**2. Factor k(h).
4*h*(h - 1)**2*(h + 1)
Suppose -16 = -4*c + 64. Let z be (-8)/c + 36/20. Solve -z*r**2 + 0 + 8/5*r**3 + 16/5*r**4 + 1/5*r = 0 for r.
-1, 0, 1/4
Factor -2/21*l - 2/21 + 2/21*l**3 + 2/21*l**2.
2*(l - 1)*(l + 1)**2/21
Let g be (-1582)/(-112) - (2 + -1). Let v = g + -493/40. Solve 2/5*i**2 - 2/5*i - v = 0.
-1, 2
Suppose 391 - 399 = -4*n. Let 1/2*r**3 + 3/2*r**n - 1/2*r - 3/2 = 0. What is r?
-3, -1, 1
Let m be (2/(-3))/((-2)/(-6)). Let u = -2 - m. Factor u*p**2 + 0*p - 1/3*p**5 + 0*p**4 + 1/3*p**3 + 0.
-p**3*(p - 1)*(p + 1)/3
Factor 12*r**2 + 18 - r**3 - 12 + 4*r**3 + 15*r.
3*(r + 1)**2*(r + 2)
Let i be (-9)/(9/(-5)) - 5. Solve -2/5*y + 12/5*y**2 - 18/5*y**3 + i = 0 for y.
0, 1/3
Let k be 2/(-12)*8*81/(-24). Let -b**2 - 6*b**3 + 1/2 + k*b**4 + 2*b = 0. Calculate b.
-1/3, 1
Let h(b) = -b**5 + b**3. Let g(m) = -5*m**4 - 3*m**5 - 7*m**2 + 4*m**5 - 11*m**3 - 3*m + m. Let r(u) = -g(u) - 2*h(u). Factor r(s).
s*(s + 1)**3*(s + 2)
Let i(a) be the first derivative of 0*a**3 + a**4 - 2*a + 2/5*a**5 + 3 - 2*a**2. Suppose i(p) = 0. Calculate p.
-1, 1
Let i(r) be the first derivative of -12*r**5/5 + 5*r**4 + 40*r**3/3 - 40*r**2 + 32*r - 4. Suppose i(h) = 0. Calculate h.
-2, 2/3, 1, 2
Let s(w) be the third derivative of w**6/60 - w**5/15 - w**4/12 + 2*w**3/3 + 7*w**2. Factor s(b).
2*(b - 2)*(b - 1)*(b + 1)
Factor 8 - 10 + 2*y**2 - 3*y + 1 - 5*y**2 - y**3.
-(y + 1)**3
Let x(q) be the first derivative of -1/2*q**4 - 4 - 3*q**2 - 2*q - 2*q**3. Determine f so that x(f) = 0.
-1
Suppose -p = -5*l - 2*p + 121, -p + 1 = 0. Suppose -y + l = 3*y. Factor -2*d + 6*d**3 + 0*d + 4*d**3 + 2*d**2 + y*d**4.
2*d*(d + 1)**2*(3*d - 1)
Let a(i) be the third derivative of i**6/900 - i**5/225 + 2*i**2. Determine b, given that a(b) = 0.
0, 2
Let q = 1030 - 5149/5. Suppose -1/5*s**5 + 0 + q*s**3 + 1/5*s**2 + 0*s - 1/5*s**4 = 0. Calculate s.
-1, 0, 1
Let n(i) be the third derivative of -i**5/540 + i**3/54 + 26*i**2. Determine h so that n(h) = 0.
-1, 1
Let u(x) be the first derivative of x**8/168 - 2*x**7/105 + x**6/180 + x**5/30 - x**3 - 1. Let v(p) be the third derivative of u(p). Let v(m) = 0. Calculate m.
-2/5, 0, 1
Suppose a - 5*a = 0. Suppose -v + 4 = -a*v. Factor 2*o + o**4 + o**3 + 3*o**2 - v*o**3 + o**3 - 4*o**4.
-o*(o - 1)*(o + 1)*(3*o + 2)
Let t(i) be the second derivative of -i**6/45 + i**5/5 - 2*i**4/3 + 8*i**3/9 + 26*i. Suppose t(a) = 0. Calculate a.
0, 2
Suppose -7*w = -8*w - 1. Let g(s) = s**2 + 2*s - 2. Let k(j) = -j. Let c(m) = w*g(m) - k(m). What is l in c(l) = 0?
-2, 1
Let c(g) = -14*g**3 - 2*g - 6. Let r(o) = 5*o**3 + o + 2. Let l(d) = -4*c(d) - 11*r(d). Determine s, given that l(s) = 0.
-2, 1
Let d = 209 + -206. Determine v so that -2/3*v**d + 4/3*v + 0 + 2/3*v**2 = 0.
-1, 0, 2
Let m(r) be the second derivative of -5*r**7/14 - 7*r**6/10 + 9*r**5/20 + 7*r**4/4 + r**3 + 13*r. Suppose m(n) = 0. What is n?
-1, -2/5, 0, 1
Let n be 18/(-4)*(-8)/18. Suppose n*y + 18 = 8*y. Factor -1/5*m**2 - 4/5*m**5 + 0 - 11/5*m**4 - 9/5*m**y + 1/5*m.
-m*(m + 1)**3*(4*m - 1)/5
Let c be 5*(5 - (-426)/(-90)). Solve c*k**2 - 7/3*k - 2/3 = 0.
-1/4, 2
Let t(f) be the third derivative of 0*f**3 - 1/24*f**4 + 0*f + 0 + 1/60*f**5 - 3*f**2. Determine d, given that t(d) = 0.
0, 1
Let v(m) be the third derivative of 0 + 3*m**2 - 1/360*m**6 - 1/6*m**3 + 0*m + 0*m**5 + 1/24*m**4. Let c(w) be the first derivative of v(w). Factor c(y).
-(y - 1)*(y + 1)
Let y be (-3)/5 + (-3)/(-5). What is t in 0*t**2 + 10/7*t**5 - 4/7*t**3 - 6/7*t**4 + y + 0*t = 0?
-2/5, 0, 1
Let l(u) be the second derivative of -u**5/10 + u**4/6 + 2*u**3/3 + 2*u. Factor l(f).
-2*f*(f - 2)*(f + 1)
Suppose -s - 1 = -7*g + 5*g, -3*s + 9 = 0. Factor -1/2*x + 1/4*x**g + 1/4.
(x - 1)**2/4
Let r = 323/1413 + -1/157. Determine c so that -2/3*c**5 + 4/3*c**2 + 8/9*c**3 - r*c - 4/9 - 8/9*c**4 = 0.
-1, 2/3, 1
Let c(h) be the third derivative of -h**9/5040 + h**8/560 - h**7/210 + h**4/24 + h**2. Let p(n) be the second derivative of c(n). Factor p(j).
-3*j**2*(j - 2)**2
Let r = -1257 - -2571/2. Let z = -28 + r. Factor -3/4*y**3 + 0 + 1/4*y**2 + z*y.
-y*(y - 1)*(3*y + 2)/4
Let t(x) = 6*x**3 + 6*x**2 - 5*x - 7. Let l(d) = -7*d**3 - 5*d**2 + 6*d + 6. Let o = -11 + 7. Let m(a) = o*t(a) - 6*l(a). Factor m(c).
2*(c - 1)*(3*c + 2)**2
Let u(p) = p**3 - 6*p**2 + 7*p - 6. Let o be u(5). Factor 4*n**3 - o*n**3 + 12*n**4 + 2*n**3 - 4*n**3.
2*n**3*(6*n - 1)
Factor -221 + 229 + 90*f**2 + 8*f**2 - 56*f.
2*(7*f - 2)**2
Let h = -29/8 + 161/40. Determine a, given that h + 1/5*a - 1/5*a**3 - 2/5*a**2 = 0.
-2, -1, 1
Suppose 5*o - 5*d = 45, -3*o - d = 2 - 33. Let u be (-108)/7*(-14)/o. Factor 16/5 + 8/5*v**4 + 10*v**3 + 88/5*v + u*v**2.
2*(v + 2)**3*(4*v + 1)/5
Let r be 2 - (-3)/(162/(-96)). Find b, given that -2/9*b**2 + 0*b + 2/9*b**4 + 2/9*b**3 + 0 - r*b**5 = 0.
-1, 0, 1
Let f(r) be the first derivative of -r**5/210 + r**4/84 + 2*r**3/21 - r**2/2 - 1. Let x(v) be the second derivative of f(v). Factor x(y).
-2*(y - 2)*(y + 1)/7
Let y(h) be the third derivative of 0 - 1/96*h**4 + 1/480*h**6 + 0*h + 2*h**2 + 0*h**3 - 1/80*h**5 + 1/280*h**7. Suppose y(z) = 0. Calculate z.
-1, -1/3, 0, 1
Let g(m) be the second derivative of -m**4/4 + 3*m**2/2 + 4*m. Suppose g(k) = 0. Calculate k.
-1, 1
Let u(c) = -4*c**2 + 4*c + 8. Let y(b) = -4*b**2 + 4*b + 8. Let v(q) = 3*u(q) - 2*y(q). Factor v(p).
-4*(p - 2)*(p + 1)
Let t(y) be the third derivative of -y**5/150 + y**4/10 - y**3/3 - 8*y**2. Suppose t(g) = 0. What is g?
1, 5
Let h(z) = 5*z + 42. Let x be h(-8). Let 0*g - 2/3 + 2/3*g**x = 0. Calculate g.
-1, 1
Let w(c) = -15*c - 1. Let o be w(-1). Let b = 20 - o. Determine s so that -2*s**3 - s**2 + b*s**3 - s**2 - 2*s**4 = 0.
0, 1
Suppose 5 + 3 = 2*q. Find h, given that -4*h**4 + 7*h**q - 9*h**2 - h - 5*h = 0.
-1, 0, 2
Let d = 548/3 - 182. Let -2/3*h + d*h**3 - 2*h**4 - 4/3 + 10/3*h**2 = 0. What is h?
-1, -2/3, 1
Let z(y) be the third derivative of 0 - 3/245*y**7 + 0*y**3 - 2*y**2 + 1/42*y**5 + 0*y - 1/84*y**4 - 1/140*y**6. Suppose z(m) = 0. Calculate m.
-1, 0, 1/3
Let x(p) be the second derivative of 5*p**8/1008 - p**7/126 + p**6/270 - p**3/3 + 2*p. Let a(c) be the second derivative of x(c). Solve a(n) = 0 for n.
0, 2/5
Let d(t) be the second derivative of t**4/24 - t**3/8 + t**2/8 - 4*t. Suppose d(a) = 0. Calculate a.
1/2, 1
Let n(y) be the second derivative of 2*y**6/45 - y**5/60 + 6*y. Factor n(m).
m**3*(4*m - 1)/3
Let j(g) = g**3 + g**2 + g - 1. Let c(f) = -3*f**3 + 5*f**2 - 13*f + 7. Let n(o) = -3*c(o) - 6*j(o). Factor n(m).
3*(m - 5)*(m - 1)**2
Let x = 23/8 - 19/8. Solve -1/2 - 7/4*b + 7/4*b**3 + x*b**2 = 0 for b.
-1, -2/7, 1
Let t(k) = -k - 2. Let x be t(-5). Factor -n + 3*n**2 - n**x + 4*n**2 - n**2 - 4*n**2.
-n*(n - 1)**2
Let g(w) be the third derivative of 1/216*w**8 + 0*w - 4/315*w**7 + 1/180*w**6 - w**2 + 0*w**3 + 1/135*w**5 + 0 + 0*w**4. Find t such that g(t) = 0.
-2/7, 0, 1
Let i(s) be the first derivative of -1/