3. Let h(n) = 7*n**4 + n**3 - 6*n**2 - 2*n - 2. Let o(j) = 3*b(j) - 5*h(j). Solve o(k) = 0.
-1, 1/2
Let q = 8 - 4. Suppose 14 = q*u + 2*p - 2, 2*p - 13 = -3*u. Factor u*t + 9/2*t**2 + 21/2*t**4 - 18*t**3 + 0.
3*t*(t - 1)**2*(7*t + 2)/2
Let i(s) = s**3 + 6*s**2 - 7*s + 2. Let b be i(-7). Let q be (18/b)/3 + 0. Let -4/7*p + 0 + 18/7*p**2 - 2*p**q = 0. What is p?
0, 2/7, 1
Factor 6 - 14*y - 6*y - 12*y**2 + 3 - 1.
-4*(y + 2)*(3*y - 1)
Let z = -4/203 - -2878/1827. Factor -10/9*c**2 - 4/9 - z*c.
-2*(c + 1)*(5*c + 2)/9
Let j be (6/3)/(-2) + 4. Find u, given that 5*u**2 + 59*u**3 - j*u - 63*u**3 + u + u**4 = 0.
0, 1, 2
Let q(d) be the first derivative of 2*d**3/3 - d**2/2 - 13. Factor q(r).
r*(2*r - 1)
Let a(f) be the third derivative of -f**7/105 + f**6/6 - 17*f**5/30 + 2*f**4/3 - 27*f**2 - f. Factor a(w).
-2*w*(w - 8)*(w - 1)**2
Suppose -3*c - z + 5 = c, 4*z - 20 = -4*c. Suppose -w - 4*x - 14 = c, 0 = 4*w - 5*x - 28. Factor -5/3*u**3 - u**w + 0 + 2/3*u.
-u*(u + 1)*(5*u - 2)/3
Let t(w) be the second derivative of w**7/84 - w**6/12 + w**5/5 - w**4/6 - w. Let t(c) = 0. What is c?
0, 1, 2
Factor -15*b - 10*b**2 - 8*b - 55 + 47 - b.
-2*(b + 2)*(5*b + 2)
Let j(i) be the first derivative of -3*i**4/4 + 4*i**3 - 15*i**2/2 + 6*i + 15. Solve j(m) = 0 for m.
1, 2
Let z(h) be the first derivative of 0*h + 0*h**3 - 1/8*h**4 + 1/4*h**2 - 3. Solve z(y) = 0 for y.
-1, 0, 1
Let n = -1 + 20. Suppose -5*t = -6 - n. Factor 8 - 7*r**2 + t*r**2 - 4*r**2 + 2*r**3.
2*(r - 2)**2*(r + 1)
Let z(w) be the second derivative of -w**7/210 + 7*w**6/150 - 19*w**5/100 + 5*w**4/12 - 8*w**3/15 + 2*w**2/5 - 2*w. Find u such that z(u) = 0.
1, 2
Let w = 229/26 + -17/2. Determine m, given that -2/13*m**3 + 0 - 2/13*m - w*m**2 = 0.
-1, 0
Factor 18 - 5*q**2 + 6*q - q**2 - 20 + 2*q**3.
2*(q - 1)**3
Let f(d) be the second derivative of -d**6/40 + 3*d**4/16 + d**3/4 - 2*d. Determine q so that f(q) = 0.
-1, 0, 2
Let h = -242/3 - -81. Factor 0*v + 0*v**2 + h*v**3 + 0.
v**3/3
Let b = -4 - -4. Suppose -r - 2 + 6 = b. Factor -2*s**3 + r*s - 5*s - 2*s + s + 4*s**2.
-2*s*(s - 1)**2
What is s in 7 + 6*s - 3*s**3 - 3*s**2 - 4 - 3*s**3 = 0?
-1, -1/2, 1
Let w(c) be the third derivative of -1/200*c**6 + 1/40*c**4 + 2*c**2 + 0*c**3 + 0*c + 0*c**5 + 0. Factor w(i).
-3*i*(i - 1)*(i + 1)/5
Let t(g) be the first derivative of 621/20*g**5 - 3 - 15/4*g**3 + 81/8*g**6 - 9*g**2 + 417/16*g**4 + 3*g. Factor t(j).
3*(j + 1)**3*(9*j - 2)**2/4
Let l(b) = 3*b**2 - 8*b + 3. Let z(s) = s**2 - 4*s + 1. Suppose -5 - 4 = 3*g. Let h(m) = g*l(m) + 7*z(m). Factor h(q).
-2*(q + 1)**2
Let x(v) be the first derivative of v**3/24 + 9*v**2/16 - 5*v/4 + 2. Determine z so that x(z) = 0.
-10, 1
Let o(z) be the third derivative of z**10/151200 - z**9/60480 - z**8/20160 + z**7/5040 + z**5/30 + z**2. Let a(d) be the third derivative of o(d). Factor a(u).
u*(u - 1)**2*(u + 1)
Let n(q) be the second derivative of -q**10/30240 - q**9/5040 - q**8/2240 - q**7/2520 + q**4/12 + 2*q. Let r(m) be the third derivative of n(m). Factor r(i).
-i**2*(i + 1)**3
Factor 0 + 1/5*y**4 - 2/5*y**3 - 3/5*y**2 + 0*y.
y**2*(y - 3)*(y + 1)/5
Factor 16/3 + 1/3*y**2 - 8/3*y.
(y - 4)**2/3
Suppose -3*c = -0*c + 12, -4*d + 4*c = 8. Let k be 2 - (2 + 1 + d). Factor 8*x**3 - 4*x**2 - 5*x**4 + x**k - 5*x**3 + 5*x**3.
x**2*(x - 2)**2*(x - 1)
Let q(t) = -5*t**2 + 6*t. Let y(x) = -x**2 + x. Let j(u) = q(u) - 6*y(u). Suppose j(h) = 0. What is h?
0
Let b = 14 + -11. Let f = b - 8/3. Factor -2/3*h + f + 1/3*h**2.
(h - 1)**2/3
Suppose -5*q + 6 = -2*q. Find y such that 3*y**4 - y**2 - 7*y**3 + 4*y**3 + y**q = 0.
0, 1
Let j be 6 - 1 - (-4 - -1). Suppose -6 = -4*z + 2*v - v, 0 = z + 3*v - j. Factor 8*p - 10/3*p**z - 8/3.
-2*(p - 2)*(5*p - 2)/3
Solve -8*j**3 + 23*j + 11*j - 28*j**2 - 46*j = 0 for j.
-3, -1/2, 0
Let y(k) = 2*k + 21. Let t be y(-9). Factor -2/3*p**t + 0*p + 2/3*p**5 + 0*p**4 + 0*p**2 + 0.
2*p**3*(p - 1)*(p + 1)/3
Suppose -12*s = -3*s. Suppose 0 - 1/3*v**2 + s*v = 0. Calculate v.
0
Factor i**2 + 0*i**2 - 4*i + 0*i**2 + 3*i**2 + 1.
(2*i - 1)**2
Let n(k) be the first derivative of -4*k**6/15 + k**5/5 + k**4/3 + 7*k + 5. Let h(p) be the first derivative of n(p). Factor h(y).
-4*y**2*(y - 1)*(2*y + 1)
Find j such that -3 - 2 + 3 - j**3 + 6 - 3*j**2 = 0.
-2, 1
Suppose -5*u = 2*m + 17, 5*m + 11 = -3*u + u. Let k = 1 - u. What is z in -5*z**k - 3*z**2 + 4*z**4 + 4*z**2 = 0?
-1, 0, 1
Factor 3*x + 3/2*x**2 + 3/2.
3*(x + 1)**2/2
Let z(h) = h - 6. Let r be z(10). Let m be 10/r - (2 - 0). Factor 3/2*q - m - 3/2*q**2 + 1/2*q**3.
(q - 1)**3/2
Let o(u) = -u**4 + u - 1. Let a(y) = -6*y**4 - 4*y**3 + 4*y - 4. Let c(s) = a(s) - 4*o(s). Factor c(i).
-2*i**3*(i + 2)
Let f = -803 - -10457/13. Let j = f + 3/26. Factor -j*n - 1 - 1/2*n**2.
-(n + 1)*(n + 2)/2
Let w = 68 + -121/2. Find d, given that 6*d + 0 - 6*d**2 - 39/2*d**3 - w*d**4 = 0.
-2, -1, 0, 2/5
Let z(r) = 4*r**2 + 6*r + 6. Let s(k) = 4*k + 2. Let u(t) = -9*t - 5. Let y(d) = -7*s(d) - 3*u(d). Let l(h) = 2*y(h) - z(h). Factor l(o).
-4*(o + 1)**2
Let o(k) be the first derivative of k**3/3 + 5*k**2 + 25*k - 2. Solve o(u) = 0.
-5
What is p in 11*p**3 + p - 1 - 12*p**3 - 2*p**2 + 3 = 0?
-2, -1, 1
Let d(m) be the second derivative of -m**8/1680 + m**6/360 - m**3/2 - 2*m. Let l(t) be the second derivative of d(t). Let l(f) = 0. What is f?
-1, 0, 1
Let m(t) be the first derivative of -t**3 - 3*t**2 - 48. Factor m(l).
-3*l*(l + 2)
Let i(p) = -p + 1. Let a = -6 - 4. Let d(s) = -2*s**3 + 8*s**2 + 2*s - 10. Let v(x) = a*i(x) - d(x). Factor v(t).
2*t*(t - 2)**2
Let j = 4 - 0. Factor -3*y**3 + 6 - 4 + 3*y**2 + 3*y - j - 1.
-3*(y - 1)**2*(y + 1)
Let l be 2*1*(-17 + 18). Let x(m) be the second derivative of m**2 + l*m + 1/4*m**4 + 0 - 7/6*m**3. Factor x(s).
(s - 2)*(3*s - 1)
Let i(k) = k**3 + k**2 - k. Let o(v) = 21*v**5 - 27*v**4 - 21*v**3 + 21*v**2. Let d(x) = 6*i(x) + o(x). Let d(r) = 0. What is r?
-1, 0, 2/7, 1
Factor 6033*k**3 - 2*k**4 + 1536 - k**4 - 5964*k**3 + 960*k - 320*k**2 - 184*k**2.
-3*(k - 8)**3*(k + 1)
Let z = 732/7 + -104. Factor -4/7*k**3 + 0 - z*k - 8/7*k**2.
-4*k*(k + 1)**2/7
Factor -1/3*w - 1 + 1/3*w**3 + w**2.
(w - 1)*(w + 1)*(w + 3)/3
Suppose 16*x - 9/2*x**3 - 6 - 15/2*x**2 = 0. What is x?
-3, 2/3
Suppose 5*q - 25 - 5 = -5*x, 3*x - 18 = q. Let z = x + -4. Factor 20*u**3 + 20*u**2 + z*u**5 + 2 + 9*u**4 + 10*u + 0*u**5 + u**4.
2*(u + 1)**5
Suppose 0*o - 3*o = -6. Let a(u) be the third derivative of 0*u + 1/24*u**4 + 1/30*u**5 + 0*u**3 + 1/120*u**6 + 2*u**o + 0. Find n such that a(n) = 0.
-1, 0
Let z(g) be the second derivative of -g**5/4 - 35*g**4/12 - 55*g**3/6 - 25*g**2/2 - 32*g. What is r in z(r) = 0?
-5, -1
Let s be (39/52)/((-2)/(-8)). Let a(k) be the second derivative of k + 0 + 0*k**4 + 0*k**5 + 0*k**6 + 1/14*k**7 + 0*k**2 + 0*k**s. Factor a(i).
3*i**5
Let k = 4 - 2. Suppose h + 3 = k*h. Determine n so that -2*n**4 + 0*n**4 + n**h - 1 + 1 + n**5 = 0.
0, 1
Let x(s) be the first derivative of -3*s**4/4 + s**3 + 3*s**2/2 - 3*s - 5. Factor x(m).
-3*(m - 1)**2*(m + 1)
Let j(b) be the first derivative of -b - 2*b**3 - 1 - 2*b**2 - b**4 - 1/5*b**5. Factor j(n).
-(n + 1)**4
Suppose 3*p - 1 = -n, 3*p = 3*n - 8 + 29. Let -2/9*w**p - 2/9 + 4/9*w = 0. Calculate w.
1
Let y(c) be the third derivative of -c**7/840 + c**6/480 + c**2. Factor y(k).
-k**3*(k - 1)/4
Let u(c) be the third derivative of c**8/840 - 3*c**7/175 + 23*c**6/300 - 7*c**5/150 - 2*c**4/5 + 16*c**3/15 - 15*c**2. Determine d so that u(d) = 0.
-1, 1, 4
Let d = 113/3 + -449/12. Let y(i) be the third derivative of 3*i**2 + 0 + 1/30*i**5 + 2/3*i**3 + d*i**4 + 0*i. Factor y(j).
2*(j + 1)*(j + 2)
Let j(m) be the third derivative of -m**5/12 + 5*m**4/12 - 5*m**3/6 + 54*m**2. Suppose j(k) = 0. Calculate k.
1
Let m(y) = y + 17. Let l be m(-11). Let o(z) be the first derivative of -1/4*z**4 + 1/10*z**5 - 3 + 0*z**3 + 0*z**2 + 1/12*z**l + 0*z. What is i in o(i) = 0?
-2, 0, 1
Let v(x) be the second derivative of -1/2*x**3 + x**4 + 0*x**2 + 1/5*x**6 - 3/4*x**5 + 5*x + 0. What is d in v(d) = 0?
0, 1/2, 1
Suppose -4/5*u + 1/10*u**2 + 8/5 = 0. Calculate u.
4
Suppose -h = -5*h + 8. Let g = -1055/7 - -151. Factor 0*i + g*i**h - 2/7*i**3 + 0.
-2*i**2*(i - 1)/7
Factor -1/6*c - 1/2*c**2 + 1/6*c**4 + 1/3 + 1/6*c**3.
(c - 1)**2*(c + 1)*(c + 2)/6
Factor 3/4*k**4 - 3*k + 9/4*k**2 - 3 + 3*