*v**3 + 1/3*v**2 - 1/36*v**4. Determine t so that n(t) = 0.
-2, 1
Let f(h) = -2*h**3 + 70*h**2 + 250*h. Let i(a) = 5*a**3 - 141*a**2 - 499*a. Let m(z) = -13*f(z) - 6*i(z). Factor m(o).
-4*o*(o + 8)**2
Let o(j) be the third derivative of -j**5/120 + j**4/48 + j**3/6 - 6*j**2. Suppose o(p) = 0. Calculate p.
-1, 2
Let l = -320/9 + 36. Suppose -l + 2*m - 8/9*m**2 = 0. What is m?
1/4, 2
Factor -2/7*d**4 + 0*d + 0*d**2 + 0 + 4/7*d**3.
-2*d**3*(d - 2)/7
Let v be ((-12)/20)/(21/(-10)). Factor 4/7 - v*u**2 + 2/7*u.
-2*(u - 2)*(u + 1)/7
Let h(q) be the second derivative of -q**5/120 + q**4/12 + 2*q + 2. Find l such that h(l) = 0.
0, 6
Suppose -5*q = -4*x + 36, -2*x - q - 16 = -5*x. Suppose 4*z - x = 4. Factor 1/4*r**z + 1/2*r + 1/4.
(r + 1)**2/4
Let w = 24/23 - 26/69. Factor -w*l**2 + 4/3*l - 2/3.
-2*(l - 1)**2/3
Let x be 18/(-15)*-1 + -1. Let n(c) be the first derivative of 4/5*c**5 + 2 + 1/5*c**2 + 0*c + 6/5*c**4 + x*c**6 + 4/5*c**3. Factor n(q).
2*q*(q + 1)**3*(3*q + 1)/5
Let f(p) be the second derivative of -8*p**6/5 + 18*p**5/5 - 9*p**4/4 + p**3/2 + 4*p. Factor f(y).
-3*y*(y - 1)*(4*y - 1)**2
Factor -2/9*p + 0 + 1/9*p**4 - 1/3*p**2 + 0*p**3.
p*(p - 2)*(p + 1)**2/9
Let f(y) = 5*y**4 - y**3 + 3*y**2 + y - 4. Let c(a) = a**4 + a**2 - 1. Let b = 5 - 1. Let m(k) = b*c(k) - f(k). Factor m(q).
-q*(q - 1)**2*(q + 1)
Suppose t - 4 + 2 = 0. Suppose -2*m - x = -t, -4*x = -x + 6. Let 0*n - 2*n**3 + 2*n - n**2 + n**m = 0. Calculate n.
-1, 0, 1
Let j(z) = -z + 2. Let h be j(-4). Suppose l = 4*l - h. Factor -d**3 - d - 5*d**2 + d**2 + l*d**2.
-d*(d + 1)**2
Let s be (-8)/(-5) - (-12)/30. Suppose 0 = -6*p + s*p. Factor 0 - 2/9*a**5 + 0*a**2 + p*a + 0*a**4 + 2/9*a**3.
-2*a**3*(a - 1)*(a + 1)/9
Suppose 5*g = 2*g + 48. Suppose 3*r - g = -r. Factor -1/2*s**r + s + 0*s**2 + 1/2 - s**3.
-(s - 1)*(s + 1)**3/2
Let d(o) = -10*o**4 - 37*o**3 - 30*o**2 - 3*o. Let i(k) = 5*k**4 + 18*k**3 + 15*k**2 + 2*k. Let u(q) = -3*d(q) - 7*i(q). What is m in u(m) = 0?
-1, 0
Let z(v) = -v**3 - 12*v**2 + 13*v + 3. Let l be z(-13). Factor 3 - 36*d**2 - 28*d**l + 26*d - 41*d - 5.
-(2*d + 1)**2*(7*d + 2)
Suppose -70 = a + 4*a. Let g be (-12)/(-7) + (-4)/a. Find u, given that -6*u**g - u + 2*u**4 + 3*u + 2*u = 0.
-2, 0, 1
Let x(b) be the second derivative of -b**4/9 + 4*b**3/9 - 2*b**2/3 - 5*b. Solve x(c) = 0 for c.
1
Let c(p) be the third derivative of 0*p + 0 + 8/21*p**3 - 3*p**2 - 1/420*p**6 - 1/7*p**4 + 1/35*p**5. Factor c(d).
-2*(d - 2)**3/7
Let p be (5 + (-141)/27)*-3. Factor -p*h + 4/9*h**2 + 2/9 - 2/3*h**4 + 2/9*h**5 + 4/9*h**3.
2*(h - 1)**4*(h + 1)/9
Let z(x) = 6*x**2 + 18*x + 2. Let a be z(-3). Let m(d) be the first derivative of 0*d + 2/5*d**a + 2/3*d**3 + 3. Solve m(o) = 0.
-2/5, 0
Let s(d) be the third derivative of d**5/420 + d**4/42 - 5*d**3/42 - 17*d**2. Factor s(y).
(y - 1)*(y + 5)/7
Let k - 4*k**2 - k + 8 - 4*k = 0. Calculate k.
-2, 1
Let j be (-6)/(-2) - 9/5. Let -2/5*y**2 - 4/5 - j*y = 0. What is y?
-2, -1
Factor 0 - 1/7*s**4 + 1/7*s**2 - 5/7*s**3 + 5/7*s.
-s*(s - 1)*(s + 1)*(s + 5)/7
Let c be (1/(-3))/((-6)/108). Let v be 34/c + 1/3. Factor -12*t**2 - 14*t + 1 - 4 + v*t**2 + 5*t + 6*t**3 + 9*t**4 + 3*t**5.
3*(t - 1)*(t + 1)**4
Suppose 0 = -2*m + 5*h + 5, -h = 2*m - 0*m + 1. Determine n, given that -n**3 - 2*n**3 + 3*n**2 + m*n + 0*n = 0.
0, 1
Let q(f) = 2*f - 12. Let w be q(6). Suppose -m**2 + m**3 - m**4 + w*m**2 + 2*m**4 - m**5 = 0. Calculate m.
-1, 0, 1
Let m(n) be the first derivative of n**4/18 - 4*n**3/27 + n**2/9 + 3. Find w such that m(w) = 0.
0, 1
Let b(y) be the second derivative of y**4/78 + y**3/13 + 2*y**2/13 + 7*y. Factor b(l).
2*(l + 1)*(l + 2)/13
Let s(o) be the first derivative of -4/3*o - 43/6*o**4 + 16/3*o**3 + 8/3*o**5 + 3 + 1/3*o**2. What is w in s(w) = 0?
-1/4, 2/5, 1
Let l(p) be the third derivative of -p**6/2340 + p**5/260 - p**3/2 - p**2. Let z(s) be the first derivative of l(s). Let z(r) = 0. Calculate r.
0, 3
Let p(a) = -5*a**3 + 4*a**2 - 2*a. Let o be p(2). Let f be o/(-33) - 12/66. Factor -14/3*j**3 - j**2 - f + 3*j.
-(j + 1)*(2*j - 1)*(7*j - 2)/3
Suppose 2*v - 6 + 0 = 0. Factor 5*x + v*x**3 - 12*x**3 + 3*x**4 + 4*x + 3*x.
3*x*(x - 2)**2*(x + 1)
Let g(h) be the second derivative of 0 + 3/5*h**2 + 1/6*h**4 - 1/50*h**5 - 7/15*h**3 - 8*h. Factor g(n).
-2*(n - 3)*(n - 1)**2/5
Let r be (-44)/(-10) + (-8)/2. Solve 6/5*b**2 - 8/5*b + r = 0.
1/3, 1
Suppose -4*v - 9 = o - 0*v, o - v = 6. Let c be (-1 - -4)*(-16)/(-12). Factor -c*t**3 + t**2 + 7*t**3 - 4*t**o + t - t**4.
-t*(t - 1)*(t + 1)**2
Let h(u) = -9*u**2 + 6*u + 3. Suppose -3*k - 5*z - 10 = 0, 0 = -z - z - 10. Let d(i) = i**3 - 17*i**2 + 11*i + 5. Let n(y) = k*h(y) - 3*d(y). Factor n(m).
-3*m*(m - 1)**2
Let i(v) be the first derivative of -2*v**3/33 - v**2/11 + 4*v/11 - 14. Factor i(s).
-2*(s - 1)*(s + 2)/11
Let k(z) be the second derivative of -5*z**4/12 + 5*z**3/3 - 5*z**2/2 + z. Let k(w) = 0. What is w?
1
Let m(s) be the first derivative of -5 + 1/5*s - 1/5*s**3 - 1/5*s**2. Factor m(i).
-(i + 1)*(3*i - 1)/5
Suppose -2/7*l**3 + 3/7*l**4 + 0*l - 1/7*l**2 + 0 = 0. Calculate l.
-1/3, 0, 1
Let w(l) = -l**3 + 8*l**2 - 6*l - 5. Let h be w(7). Suppose 2*d + 6 = -4*u - d, 2*u = -h*d - 4. What is c in -2/3*c**4 + 0 + 0*c + u*c**2 + 0*c**3 = 0?
0
Let i(n) be the second derivative of n**8/5040 - n**7/2520 - n**6/1080 + n**5/360 - 5*n**3/6 - 5*n. Let b(g) be the second derivative of i(g). Factor b(y).
y*(y - 1)**2*(y + 1)/3
Suppose -3*g = h - 7, -3*h + 4*g = -h - 4. Let q(f) be the first derivative of -4/5*f**5 + 4/9*f**3 + 1/2*f**6 + 3 + 0*f - 1/6*f**h + 1/6*f**2. Factor q(r).
r*(r - 1)**2*(3*r + 1)**2/3
Let h(f) = f**2 + f + 1. Let m(n) = -n**3 - 5*n**2 - 7*n - 7. Let k(p) = 14*h(p) + 2*m(p). Factor k(j).
-2*j**2*(j - 2)
Suppose 4*d - 4*q - 18 = -5*q, 5*q + 30 = 4*d. Find f, given that 2*f**5 - 14*f**d - 225*f**4 + 72*f**2 - 16*f + 52*f**3 - 32 + 209*f**4 = 0.
-2, -1, 2/3, 2
Let r(s) be the first derivative of -2*s**6/15 - 12*s**5/25 + 16*s**3/15 - 3. Let r(g) = 0. Calculate g.
-2, 0, 1
Let q = 92 + -826/9. Factor 2/9*z - q*z**2 + 0.
-2*z*(z - 1)/9
Let s(u) be the third derivative of u**7/105 - 2*u**6/15 + 11*u**5/15 - 2*u**4 + 3*u**3 + 25*u**2. Factor s(i).
2*(i - 3)**2*(i - 1)**2
Let q(j) be the second derivative of 1/10*j**6 + j**3 + 5/4*j**4 + 3*j + 0 + 3/5*j**5 + 0*j**2. Find a such that q(a) = 0.
-2, -1, 0
Let y(d) = d**5 + d**4 - d**3 + d**2 - 1. Let m(s) = -s**5 - 5*s**4 - 2*s**3 + 10*s**2 + 2. Let o(q) = -m(q) - 2*y(q). Factor o(f).
-f**2*(f - 3)*(f - 2)*(f + 2)
Let h(y) be the second derivative of y**2 - 1/8*y**4 + 0 + 1/40*y**6 + y + 0*y**5 + 0*y**3. Let f(s) be the first derivative of h(s). Find p such that f(p) = 0.
-1, 0, 1
Factor -33*k - 40*k**2 - 7*k**3 - 1 - 9*k**3 - 8.
-(k + 1)*(4*k + 3)**2
Suppose -3*l = -8*l. Let w(x) be the first derivative of 2/3*x**3 + l*x - x**2 - 1. Find v such that w(v) = 0.
0, 1
Suppose 5*q - 3*h + 30 = 0, q - 4*h - 29 = 2*q. Let w be 3/q - 2/(-3). Suppose w*o**3 + 2/3*o**2 + 0 + 1/3*o = 0. Calculate o.
-1, 0
Let y(u) = -u**3 + 5*u**2 + u - 3. Let c be y(5). Let -21*h + 6 + 15*h**2 - 4*h**2 + 4*h**c = 0. What is h?
2/5, 1
Let w be (64/(-24))/((-60)/18). Factor 0 - 2/5*y**5 - w*y**4 + 0*y**3 + 2/5*y + 4/5*y**2.
-2*y*(y - 1)*(y + 1)**3/5
Let i(j) be the third derivative of -2*j**6/15 - 8*j**5/15 - 5*j**4/6 - 2*j**3/3 - 2*j**2. Determine c, given that i(c) = 0.
-1, -1/2
Let -x**2 + 4*x**2 + 58*x - 36 - 16*x + 2*x**4 - x**2 - 10*x**3 = 0. What is x?
-2, 1, 3
Let r = 6 + 2. Suppose -3*a = -20 + r. Suppose -2*v**a + 3*v**4 - 2*v**2 + v**2 = 0. Calculate v.
-1, 0, 1
Solve -136/19*l - 406/19*l**3 + 396/19*l**2 + 16/19 - 20/19*l**4 + 150/19*l**5 = 0 for l.
-2, 1/3, 2/5, 1
Let g(i) be the third derivative of i**7/840 + i**6/240 + i**5/240 - 8*i**2. Factor g(y).
y**2*(y + 1)**2/4
Factor -x - 1/4*x**2 - 1.
-(x + 2)**2/4
Let r(y) be the third derivative of y**5/20 + y**4 + 8*y**3 + 2*y**2. Factor r(q).
3*(q + 4)**2
Let h(a) be the first derivative of a**6/12 + a**5/2 + 3*a**4/8 - 3*a**3/2 + 5. Factor h(f).
f**2*(f - 1)*(f + 3)**2/2
Find o such that 2*o + 4*o**3 - o**2 - 7*o - 3*o**2 - 3*o = 0.
-1, 0, 2
Let s(z) be the first derivative of -5*z**3/3 + 2. Factor s(t).
-5*t**2
Suppose 0 = 2*g - 6*g + 20. Suppose -g*o - 21 + 51 = 0. Factor 10*f**4 - o + 14*f - 6*f**2 + 2 - 10*