))/(4/6). Factor 2/9*q + 2/3*q**3 + 2/9*q**f + 2/3*q**2 + z.
2*q*(q + 1)**3/9
Let v(k) be the second derivative of k**4/3 - 10*k**3/3 - 12*k**2 - 11*k. Let v(o) = 0. What is o?
-1, 6
Let l(y) = 2*y**3 - 10*y**2 - 8*y + 8. Let a(f) = f**2 + f - 1. Let b = -7 - -2. Let s = 4 + b. Let z(o) = s*l(o) - 8*a(o). Solve z(i) = 0 for i.
0, 1
Let p = 194 - 589/3. Let b = p - -41/15. Factor 2/5*j**3 + 2/5 - 2/5*j - b*j**2.
2*(j - 1)**2*(j + 1)/5
Let l(j) be the first derivative of 2*j**2 + 4*j - 3 + 1/3*j**3. Find r such that l(r) = 0.
-2
Let p(y) be the first derivative of 3*y**5/5 - y**3 - 5. Factor p(q).
3*q**2*(q - 1)*(q + 1)
Let k(j) = -j**3 + j**2 + j. Let g(h) = h**5 - 2*h**4 - h**3 + 7*h**2 - 8*h + 2. Let v(y) = 3*g(y) + 3*k(y). Factor v(f).
3*(f - 1)**4*(f + 2)
Let l be (42/(-35))/(1/(-10)). Suppose -5*d + l = -k + 2, 3*d + 2*k = 6. Solve 0*h + 2/5*h**d - 2/5 = 0 for h.
-1, 1
Let y be (-1 - (-5)/(-1))*1/(-2). Let j(z) be the first derivative of -3/2*z**4 - 22/3*z**y + 8*z + 2 - 8*z**2. Factor j(l).
-2*(l + 2)**2*(3*l - 1)
Suppose -w + 0*w = 4*v + 15, -2*w + 35 = -5*v. Factor -1 - 5*z + 3 + 6*z**2 - 5*z + 10*z**4 - 20*z**3 + 14*z**2 - 2*z**w.
-2*(z - 1)**5
Let o = -1710 + 6943/4. Let u = -49/2 + o. Factor u*w**3 - 9/4*w**5 + 1 + 0*w + 15/4*w**4 - 15/4*w**2.
-(w - 1)**3*(3*w + 2)**2/4
Let n = -1/13317 + 69551/88780. Let k = n + -8/15. Factor -1/4*q**5 - 1/4*q**2 + 1/4*q**3 + 0*q + k*q**4 + 0.
-q**2*(q - 1)**2*(q + 1)/4
Let x(c) be the second derivative of 0 - 32*c**2 + 16/3*c**3 - 1/3*c**4 + c. What is s in x(s) = 0?
4
Let -9*p + 5*p**2 + p + 0*p + 3*p = 0. Calculate p.
0, 1
Let h be (-2)/(-2) + (-36)/(-4). Suppose z = 6*z - h. Factor -2*k**3 - 2*k + 2*k + z*k**4.
2*k**3*(k - 1)
Let z = 111 - 221/2. Factor 0 + z*h**2 + 0*h + 1/4*h**3.
h**2*(h + 2)/4
Let f(y) = -y**2 - 5*y + 4. Let j be f(-5). Suppose -j*g + h + 14 = 0, 5*g - 3*h - h = 12. Suppose -2*i**2 - 4*i**2 + 8*i**2 + 2*i - g = 0. Calculate i.
-2, 1
Let c = -12 + 18. Find t such that c*t**5 + 2 - 5*t**5 - 2 + t - 2*t**3 = 0.
-1, 0, 1
Factor 3*t**4 + 45*t**2 - 9*t**3 + 29*t - 2*t + 18*t**3 + 12*t**3.
3*t*(t + 1)*(t + 3)**2
What is o in -o**2 + 2 - 12*o**4 - 2*o**3 + 11*o**4 - 2 = 0?
-1, 0
Let t(g) be the first derivative of -4*g**5/15 - g**4/6 + 16*g**3/9 + 4*g**2/3 - 4. Let t(m) = 0. Calculate m.
-2, -1/2, 0, 2
Factor 0*n + 2/13*n**2 + 0.
2*n**2/13
Let i be 1/((-16)/(-5) + -3). Suppose 1 = -2*u + i. Factor 1/4*n**u + 0*n + 1/4*n**4 + 0 + 1/2*n**3.
n**2*(n + 1)**2/4
Let h(g) be the second derivative of g**8/8960 + g**7/3360 + g**4/4 + 6*g. Let a(q) be the third derivative of h(q). Suppose a(b) = 0. Calculate b.
-1, 0
Suppose -4*h + 12 = -z, z - 4*z = -3*h + 9. Factor -2*d + 2*d**2 - 2/3*d**h + 2/3.
-2*(d - 1)**3/3
Let j(q) = -5*q**4 - q**3 + 4*q**2 - 4. Let k(t) = -t**4 + t**2 - 1. Let a(p) = -j(p) + 4*k(p). Factor a(c).
c**3*(c + 1)
Let j(d) be the second derivative of 0 + 4/3*d**3 + d - 5/12*d**4 + 1/20*d**5 - 2*d**2. Solve j(r) = 0 for r.
1, 2
Let l(x) be the third derivative of -x**8/24192 + x**7/10080 + x**6/2160 + x**5/30 + x**2. Let j(v) be the third derivative of l(v). What is m in j(m) = 0?
-2/5, 1
Let p(h) be the second derivative of h**5/70 - 3*h**4/7 + 36*h**3/7 - 216*h**2/7 + 22*h. Determine l so that p(l) = 0.
6
Let j(a) = -2*a**2 + 11*a + 5. Let p(f) be the second derivative of f**4/12 - 5*f**3/6 - f**2 + 6*f. Let h(u) = -2*j(u) - 5*p(u). Factor h(m).
-m*(m - 3)
Let f = 12/13 - 58/91. Solve -2/7*p + f - 2/7*p**2 + 2/7*p**3 = 0.
-1, 1
Let o(v) be the third derivative of v**7/840 + v**6/60 + v**5/10 + v**4/6 + 2*v**2. Let i(k) be the second derivative of o(k). Factor i(t).
3*(t + 2)**2
Suppose 8*u**4 + 5*u**5 + 0 - 8/5*u**2 + 6/5*u**3 + 1/5*u = 0. What is u?
-1, 0, 1/5
Let r be (-12)/7*7/(-2). Suppose -22*s + 25*s = r. Factor -2/7*o**s + 0 + 4/7*o.
-2*o*(o - 2)/7
Let d be -3 - 4*(-4)/((-48)/(-9)). Factor -4/9*l**2 - 2/9*l**3 - 2/9*l + d.
-2*l*(l + 1)**2/9
Factor 1/7*j**3 - 1/7*j**2 + 0 + 1/7*j**4 - 1/7*j**5 + 0*j.
-j**2*(j - 1)**2*(j + 1)/7
Suppose 0 = -3*n + 4 - 1, 0 = -5*i + 2*n + 98. Suppose -5*o + 20 = -2*l, -3*o + i = 5*l + 2*o. Factor -2/3*y**2 + 0*y**3 + 1/3*y**4 + l*y + 1/3.
(y - 1)**2*(y + 1)**2/3
Let m = -23/7 - -81/14. Let -k - 2*k**3 + 0 - m*k**2 - 1/2*k**4 = 0. What is k?
-2, -1, 0
Suppose 5*a = 4*a + 4. Suppose 0 = -4*c + 3*c + a. Let 0*h**5 - 2*h + 4*h**2 + 4*h - 2*h**5 - c*h**4 = 0. Calculate h.
-1, 0, 1
Let p(a) = -a**2 + 12*a + 47. Let f be p(15). Let w(y) be the second derivative of 0*y**3 + 2*y + 1/30*y**4 + 0*y**f + 0 + 1/25*y**5 + 1/75*y**6. Factor w(v).
2*v**2*(v + 1)**2/5
Suppose 0*h + 13*h**2 - 6*h**3 - h**5 + 4*h**4 + 3*h**4 - 9*h**3 - 4*h = 0. Calculate h.
0, 1, 4
Suppose 0 + 2*u**5 + 378/5*u**2 + 306/5*u**3 + 108/5*u + 94/5*u**4 = 0. Calculate u.
-3, -2/5, 0
Suppose 0 = 7*s - 28 - 0. Factor -1/2 - 1/2*b**s + b**2 + 0*b**3 + 0*b.
-(b - 1)**2*(b + 1)**2/2
Let d be -2 - 2/4*-22. Factor -3*g**2 + d - 4*g - 5*g + 3*g.
-3*(g - 1)*(g + 3)
Let q = 40 + -196/5. Let -q + 2/5*x + 2/5*x**2 = 0. Calculate x.
-2, 1
Let t(a) be the second derivative of 1/6*a**3 + 0*a**6 + 0*a**4 + 0 - 4*a + 0*a**2 - 1/10*a**5 + 1/42*a**7. What is u in t(u) = 0?
-1, 0, 1
Solve 79*b**2 + 24*b**4 - 72*b**3 + 37*b**5 - 40*b**5 - 71*b + 17*b**2 + 23*b = 0 for b.
0, 2
Let o(a) be the second derivative of a**7/630 + a**6/60 + a**5/15 - 7*a**4/12 + 4*a. Let i(q) be the third derivative of o(q). Factor i(x).
4*(x + 1)*(x + 2)
Let o(q) be the first derivative of -q**6/12 + 3*q**4/8 + q**3/3 + 3. Suppose o(c) = 0. What is c?
-1, 0, 2
Factor 2/5*f**4 - 2/5 + 4/5*f + 0*f**2 - 4/5*f**3.
2*(f - 1)**3*(f + 1)/5
Let t(o) be the third derivative of -o**5/15 + o**4/6 + 7*o**2. Factor t(l).
-4*l*(l - 1)
Let g(x) be the third derivative of -8/39*x**3 - 1/39*x**4 + 1/156*x**6 + 1/65*x**5 + 0*x + 0 + 2*x**2 + 1/1365*x**7. Let g(p) = 0. Calculate p.
-2, 1
Let t(l) = -5*l**3 - 2*l**2 + 7*l**2 + l**3. Suppose y + y = -8. Let q(p) = -2*p**3 + 2*p**2. Let z(c) = y*t(c) + 9*q(c). Determine m so that z(m) = 0.
-1, 0
Suppose 0 = -w - 4 + 5. Suppose 3 - w = o. Solve 1/3*b**4 - 2/3*b - 1/3*b**o + b**3 + 0 - 1/3*b**5 = 0 for b.
-1, 0, 1, 2
Let m(l) be the first derivative of -4 + 1/8*l**4 - 1/6*l**3 + 1/2*l - 1/4*l**2. What is u in m(u) = 0?
-1, 1
Let g(m) be the third derivative of 1/48*m**5 - 1/480*m**6 - m**2 + 0*m + 1/6*m**3 - 1/12*m**4 + 0. Factor g(w).
-(w - 2)**2*(w - 1)/4
Suppose 3*b - 6*b = 0. Let c(u) be the third derivative of -1/12*u**4 + 2/3*u**3 + u**2 - 1/15*u**5 + 0*u + b + 1/60*u**6. Suppose c(q) = 0. Calculate q.
-1, 1, 2
Factor 4 + 21/2*b + 5/4*b**2.
(b + 8)*(5*b + 2)/4
Suppose 0*w = 3*d - 5*w + 7, w = -d - 5. Let p(j) = -j**2 - 5*j. Let l be p(d). Factor -1/3*k - 1/3*k**5 - 4/3*k**2 + 0 - 4/3*k**l - 2*k**3.
-k*(k + 1)**4/3
Let h(n) be the first derivative of -n**8/2800 + n**7/1400 + n**6/600 - n**5/200 - n**3 - 5. Let k(f) be the third derivative of h(f). Factor k(x).
-3*x*(x - 1)**2*(x + 1)/5
Let r(y) be the second derivative of -2*y + 0 - 1/2*y**2 + 1/270*y**5 - 1/54*y**4 + 1/27*y**3. Let p(k) be the first derivative of r(k). Factor p(q).
2*(q - 1)**2/9
Let w(z) be the third derivative of 1/120*z**6 + 0*z + 9/8*z**4 - 3/20*z**5 - 9/2*z**3 + 0 + 6*z**2. Factor w(b).
(b - 3)**3
Factor -2*n**3 - n**2 + 13*n**2 - 108*n + 90*n.
-2*n*(n - 3)**2
Let v be 6/33 - 76/660. Let s(o) be the second derivative of 1/10*o**5 - v*o**6 + 0*o**2 - o + 0*o**3 + 0*o**4 + 0. Factor s(y).
-2*y**3*(y - 1)
Let i(z) be the third derivative of 4*z**2 - 1/180*z**5 + 1/18*z**3 + 0 + 0*z + 1/360*z**6 - 1/72*z**4. Factor i(m).
(m - 1)**2*(m + 1)/3
Let h(i) be the second derivative of i**5/20 + i**4/12 - i**3/6 + i**2/2 - 2*i. Let w(d) = d**4 - 8*d**3 + 2*d**2 - 3. Let x(z) = -4*h(z) - w(z). Factor x(l).
-(l - 1)**4
Let n(p) = -p**3 - 4*p**2 + 4*p. Let z be n(-5). Let g(k) be the second derivative of -k - 1/6*k**3 - 2/15*k**6 + 0 + 0*k**z + 0*k**2 + 1/4*k**4. Factor g(l).
-l*(l + 1)*(2*l - 1)**2
Let v(d) be the third derivative of d**8/84 - 8*d**7/105 + d**6/10 + 4*d**5/15 - 2*d**4/3 + d**2 - 3. Suppose v(m) = 0. Calculate m.
-1, 0, 1, 2
Let t(o) be the first derivative of o**3 - o**2 - 2*o + 7. Let n be t(2). Factor 2/3*b + 0 + n*b**4 + 2*b**3 - 10/3*b**2.
2*b*(b + 1)*(3*b - 1)**2/3
Let a = -88615/84 + 1055. Let q(i) be th