.
0, 1
Factor -11*j**4 + 5*j**5 + 19*j**3 + 41*j**2 - 51*j**2 - 9*j**4 + 6*j**3.
5*j**2*(j - 2)*(j - 1)**2
Let j(l) = -l**3 + 15*l**2 - l + 20. Let k be j(15). Let o(y) be the second derivative of 1/25*y**k + 1/20*y**4 + 0 - 3/10*y**3 - 3*y + 1/5*y**2. Factor o(h).
(h - 1)*(h + 2)*(4*h - 1)/5
Let m(u) = 3*u**2 - u - 1. Let z be m(-1). Determine r so that 6*r**5 - 12*r**4 + 18*r**4 - 3*r - z*r**5 - 6*r**2 = 0.
-1, 0, 1
Let g(l) = 4*l**2 - 2*l - 2. Let o(b) = b. Let f(r) = 2*g(r) + 18*o(r). Factor f(q).
2*(q + 2)*(4*q - 1)
Suppose -10 + 20*b - 8*b - b**2 - 26 = 0. What is b?
6
Factor 2*k**4 - 9 - 7 - 4*k**2 - 131*k + 107*k + 6*k**3.
2*(k - 2)*(k + 1)*(k + 2)**2
Factor 18/7*h**2 - 6/7*h**3 + 0 + 24/7*h.
-6*h*(h - 4)*(h + 1)/7
Let i be 140/(-21)*12/(-20). Factor 1/4*t**5 - t**i + t**2 + 3/4*t**3 + 0 - t.
t*(t - 2)**2*(t - 1)*(t + 1)/4
Let c(v) be the second derivative of -v**4/12 - 2*v**3/3 - 3*v**2/2 - v. Let h(d) = -3*d**2 - 11*d - 8. Let g(x) = -11*c(x) + 4*h(x). Let g(s) = 0. What is s?
-1, 1
Let p(a) = -a - 1. Let r be p(-3). Let k be r/(-3) + (-76)/(-6). Factor -12*t - 2*t**4 + 5*t**3 - k*t**2 - 13*t**3 + 4*t - 2.
-2*(t + 1)**4
Let g(n) = -2*n**2 - 33*n - 13. Let q(w) = -w**2 - 16*w - 7. Let d(k) = 4*g(k) - 9*q(k). What is m in d(m) = 0?
-11, -1
Let p(j) be the first derivative of 3*j**4/5 - 4*j**3/3 - 4*j**2/5 + 10. Suppose p(q) = 0. What is q?
-1/3, 0, 2
Factor -5*r**3 + 17*r + 10*r**2 + 18*r - 40*r.
-5*r*(r - 1)**2
Let x = 5 + 2. Find j such that x*j**4 - j**3 + 6*j**4 - 15*j**4 = 0.
-1/2, 0
Let m(c) be the third derivative of c**7/5040 - c**6/1440 + 7*c**4/24 - 4*c**2. Let i(z) be the second derivative of m(z). Factor i(s).
s*(s - 1)/2
Suppose -2*r - 15 = -7*r. Suppose 7*u - 12 = r*u. Let l(j) = 8*j**3 - 5*j + 3. Let a(o) = 23*o**3 - o**2 - 14*o + 8. Let c(k) = u*a(k) - 8*l(k). Factor c(x).
x*(x - 1)*(5*x + 2)
Let s(o) = o**3 - o - 2. Let w be s(0). Let i be (w - -2) + 36/14. Suppose -12/7*k**4 - 2/7*k + 0 + 12/7*k**2 - 16/7*k**3 + i*k**5 = 0. Calculate k.
-1, 0, 1/3, 1
Factor 10 + 4*j + 9*j + 2*j + 5*j**2 + 0.
5*(j + 1)*(j + 2)
Suppose 0 = -4*i + 3*i + 4*r + 47, i - 3*r - 44 = 0. Let p = i + -33. Suppose 2/3*l**5 + 2*l - 4/3*l**p + 0*l**4 - 8/3*l**3 + 4/3 = 0. What is l?
-1, 1, 2
Determine g so that -5/2*g**2 + 5/2*g + 5/2*g**4 - 5/2*g**3 + 0 = 0.
-1, 0, 1
Let p(k) be the second derivative of -2*k**6/105 - 6*k**5/35 - 4*k**4/7 - 16*k**3/21 - 2*k - 2. Suppose p(s) = 0. What is s?
-2, 0
Let z(k) = -k - 2. Let o be z(-6). Factor 9*a**o + 3*a**4 + 12*a**3 + 3*a**5 - 3 + 3.
3*a**3*(a + 2)**2
Suppose 5*j = 3*j + 6. Determine v so that 4*v**3 - j*v + 0*v - 3*v**5 + 2*v**3 = 0.
-1, 0, 1
Let r(i) = 2*i**2 + 2*i - 3. Let p(k) = k**2 + k - 2. Let m(a) = -5*p(a) + 3*r(a). Let c(j) = -8*j**2 - 5*j - 8. Let z(f) = 3*c(f) + 21*m(f). Factor z(s).
-3*(s - 1)**2
Let 12*h - 5*h + 11*h - 36*h**4 - 93*h**3 + 0*h + 51*h**2 = 0. What is h?
-3, -1/4, 0, 2/3
Suppose 5*j + 5 - 30 = 0. Suppose -9 = 2*s - j*s. Solve -171*k**4 + 64*k**3 - 8*k**2 + 8*k**s + 9*k**4 = 0.
0, 2/9
Factor -8*z + 10 + z + 12*z - 5*z**2.
-5*(z - 2)*(z + 1)
Let n(i) = -4*i**2 + 19*i + 7. Let u(j) = 2*j**2 - 10*j - 4. Let p be 19/(-3) - (-2)/6. Let t(c) = p*n(c) - 11*u(c). Factor t(q).
2*(q - 1)**2
Let i = -26 + 29. Let g(n) be the third derivative of -1/3*n**4 - 1/3*n**3 + 0*n - 1/105*n**7 - 1/5*n**5 + 0 - 1/15*n**6 - i*n**2. Factor g(z).
-2*(z + 1)**4
Let d(c) be the first derivative of -c**5/20 + 7*c**4/12 - 5*c**3/2 + 9*c**2/2 - 3*c + 2. Let f(a) be the first derivative of d(a). Factor f(w).
-(w - 3)**2*(w - 1)
Suppose -11*t - 42 = -75. Solve 1/3*c + 2/3*c**4 - 2/3*c**2 + 0 - 1/3*c**5 + 0*c**t = 0 for c.
-1, 0, 1
Let b = 7 + -3. Solve -3*r**4 - b*r**3 + 0*r - 4*r**2 - r**3 - r + r**4 = 0 for r.
-1, -1/2, 0
Let k(p) be the second derivative of -1/24*p**4 - 1/40*p**5 + 0*p**2 + 4*p + 0 + 1/6*p**3. Find x, given that k(x) = 0.
-2, 0, 1
Suppose t = -6 - 3. Let j = -7 - t. Factor 2/9*w + 2/9*w**j + 0.
2*w*(w + 1)/9
Suppose g + 3*g = -12. Let x = g + 3. Factor -1/3*u + x - 1/3*u**2.
-u*(u + 1)/3
Let n(k) be the second derivative of 0 - 4/25*k**5 - 1/15*k**3 - 7*k + 3/35*k**7 + 0*k**2 + 2/25*k**6 - 1/5*k**4. Determine c, given that n(c) = 0.
-1, -1/3, 0, 1
Let n(k) be the second derivative of k**4/4 - 3*k**2/2 + 7*k. Factor n(y).
3*(y - 1)*(y + 1)
Suppose z - 2*y = -2*z + 42, 5*y - 15 = 0. Let i = z - 9. What is x in 3*x**5 - i*x - x**5 - 25*x**3 - 4*x**5 - 1 - 16*x**4 - 19*x**2 - 2*x**5 = 0?
-1, -1/2
Let m(s) = -s**3 - 6*s**2 - 6*s - 1. Let f be m(-5). Solve -12*j**2 + 0*j**2 - 2*j - 33*j**2 + j**2 + f + 42*j**3 = 0 for j.
-2/7, 1/3, 1
Let w(d) be the first derivative of d**2 + 1/120*d**5 + 1/12*d**3 + 0*d + 1/24*d**4 - 1. Let g(k) be the second derivative of w(k). Find y, given that g(y) = 0.
-1
Let m(y) be the first derivative of 2 - y**3 + 1/2*y**2 - 1/5*y**5 + 0*y + 3/4*y**4. Factor m(p).
-p*(p - 1)**3
Let d be ((-5)/3)/((-3)/36). Suppose -4*a + 4*q = -d, -1 = -4*a + 5*q + 23. Determine g so that -g - a - 1/4*g**2 = 0.
-2
Factor 0 + 0*x - 1/3*x**2.
-x**2/3
Let m(y) = -3*y**3 - 17*y**2 + 2*y. Let p(z) = 0*z - 5*z + 4*z + z**3 + 6*z**2. Let l(u) = 3*m(u) + 8*p(u). Factor l(r).
-r*(r + 1)*(r + 2)
Let p(x) = -x**3 - 4*x**2 + 3*x. Let j(v) be the third derivative of v**6/120 + v**5/60 - v**4/24 + 2*v**2. Let n(f) = 6*j(f) + 3*p(f). What is z in n(z) = 0?
0, 1
Let h be 1147/744 + (-6)/4. Let b(o) be the second derivative of 0 + 3*o + 0*o**2 - 1/84*o**7 + 1/60*o**6 + 1/40*o**5 + 0*o**3 - h*o**4. Solve b(y) = 0 for y.
-1, 0, 1
Let q = 1012 - 7072/7. Factor 18/7 - q*y + 2/7*y**2.
2*(y - 3)**2/7
Let y(u) = -13*u**5 - u**4 - 13*u**3 - 9*u - 9. Let l(r) = -3*r**5 - 3*r**3 - 2*r - 2. Let b(m) = 9*l(m) - 2*y(m). Find k such that b(k) = 0.
0, 1
Let f(g) be the third derivative of 0*g - 1/1512*g**8 - 4*g**2 + 7/270*g**5 - 1/60*g**6 - 1/54*g**4 + 1/189*g**7 + 0 + 0*g**3. Let f(v) = 0. What is v?
0, 1, 2
Let x(v) be the second derivative of 0 - 1/3*v**3 - 1/6*v**4 - 3*v + 0*v**2. Let x(p) = 0. Calculate p.
-1, 0
Let o(a) be the third derivative of a**8/112 - a**6/20 + a**4/8 + 12*a**2. Solve o(g) = 0.
-1, 0, 1
Let c(m) be the third derivative of m**6/24 - 5*m**4/8 + 5*m**3/3 + 8*m**2. Factor c(w).
5*(w - 1)**2*(w + 2)
Suppose 4*v - v = 12. Let f(o) = -3*o**2 + o. Suppose -7*r - 9 = -4*r. Let x(t) = -2*t**2 + t. Let b(g) = r*f(g) + v*x(g). Factor b(i).
i*(i + 1)
Let u be (-2)/(-14)*3462/30. Let p = u - 81/5. Factor -2/7*m + 0*m**2 + p*m**3 + 0.
2*m*(m - 1)*(m + 1)/7
Let p(l) be the third derivative of 0 + 1/90*l**5 + 0*l**4 + 3*l**2 + 0*l**3 + 0*l + 1/540*l**6. Solve p(b) = 0.
-3, 0
Let q(f) be the second derivative of f**6/20 - 3*f**5/20 + f**4/8 + 14*f. Let q(a) = 0. What is a?
0, 1
Let v(u) be the third derivative of -u**6/72 - u**5/40 + u**4/144 - 19*u**2. Factor v(q).
-q*(q + 1)*(10*q - 1)/6
Let g(c) = c**5 - c**3 + c**2 - c + 1. Let z(o) = 20*o**5 - 4*o**4 - 20*o**3 + 28*o**2 - 24*o + 24. Let x(p) = 24*g(p) - z(p). Solve x(s) = 0 for s.
-1, 0, 1
Let w = 697/5 + -139. Let f(b) be the first derivative of 0*b**2 - 2/3*b**3 + b**4 + 3 - w*b**5 + 0*b. Factor f(g).
-2*g**2*(g - 1)**2
Let b = 106 - 421/4. What is y in -3/4*y + 1/4 + b*y**2 - 1/4*y**3 = 0?
1
Let s(y) = -y**5 - y**4 - y**3 - y**2 + y. Let r(b) = -5*b**5 - 4*b**4 + 4*b**3 - 4*b**2 - 2*b + 2. Let g(v) = r(v) - 3*s(v). Solve g(p) = 0.
-2, -1, 1/2, 1
Let g = -45 - -48. Let i(y) be the third derivative of 1/240*y**6 + 1/210*y**7 + 0*y**5 + 0 + 0*y + 0*y**4 - 2*y**2 + 0*y**g. Find r, given that i(r) = 0.
-1/2, 0
Let d = 22 - 20. Let f(l) be the third derivative of 0 + 1/540*l**6 + 1/36*l**4 + 1/90*l**5 + 1/27*l**3 + l**d + 0*l. Determine o so that f(o) = 0.
-1
Let q be (6/8)/((-1995)/152)*-30. Factor 2/7*g**2 + 18/7 - q*g.
2*(g - 3)**2/7
Suppose 0 = -3*b + s - 2, b - 2*s = -3 - 1. Suppose b = d + 2 - 8. Solve 2 - 3 + 2 + 3*t**2 - d*t + 2 = 0.
1
Suppose 9/4 + 1/4*d**2 - 3/2*d = 0. What is d?
3
What is w in -1/5*w**4 + 2/5*w + 4/5*w**3 + 0 - w**2 = 0?
0, 1, 2
Let q be 14*(2/4 - 0). Let r(b) be the second derivative of 1/147*b**q - 1/35*b**5 + 1/21*b**3 - 1/7*b**2 - 1/105*b**6 + 1/21*b**4 + 0 - 2*b. Factor r(n).
2*(n - 1)**3*(n + 1)**2/7
Let m = 119923/3308 + -2/827. Let z = m + -36. Solve d**2 - 3/4*d**3 + z*d - 1/2 = 0.
-2/3, 1
Let n(a) be the thi