 = 0.
-1, 0, 1
Factor 3/2 - 23/4*n + 7/4*n**2.
(n - 3)*(7*n - 2)/4
Let a(t) = t + 4. Let s be a(3). Suppose 1 - s = -3*i. Factor -3*q**i - 2*q**2 - 2*q + 2*q**2.
-q*(3*q + 2)
Let y(n) be the first derivative of 13*n**4/16 + 2*n**3 + 9*n**2/8 - n/2 + 7. Factor y(c).
(c + 1)**2*(13*c - 2)/4
What is x in -2/17*x**2 - 4/17*x + 0 = 0?
-2, 0
Solve -10 - 35*z**5 + 4*z**4 - 6*z**4 - 35*z + 20*z**2 - 2*z**4 - 6*z**4 + 70*z**3 = 0.
-1, -2/7, 1
Let n be (-1 - -1)/((-46)/23). Let x(i) be the second derivative of -1/6*i**4 + 0*i**2 - i + 0 + 1/10*i**5 + n*i**3. Factor x(p).
2*p**2*(p - 1)
Let m(j) = j**2 + 6*j + 7. Let a = -13 - -8. Let k be m(a). Factor -b - 4*b**4 + 0*b**4 + 6*b**2 + 4*b**3 - k + 0*b**4 - 3*b**5.
-(b - 1)*(b + 1)**3*(3*b - 2)
Let g = 86 + -56. What is d in 24*d**3 - 4*d**2 - g*d**5 - 8*d + 32*d**2 + 14*d**5 - 28*d**4 = 0?
-2, -1, 0, 1/4, 1
Let w(q) be the first derivative of -q**6/120 + 3*q**5/80 - q**3/6 + 2*q - 5. Let b(z) be the first derivative of w(z). Factor b(y).
-y*(y - 2)**2*(y + 1)/4
Let o(p) = p**4 + 2*p**3 + 3*p**2 + 2*p - 4. Let d(x) = -x**4 - 3*x**3 - 4*x**2 - 2*x + 5. Let z(s) = -4*d(s) - 5*o(s). Factor z(w).
-w*(w - 2)*(w - 1)*(w + 1)
Suppose -12 + 78*o - 117*o**2 - 123/2*o**3 + 114*o**4 - 63/2*o**5 = 0. What is o?
-1, 2/7, 1/3, 2
Let i(l) be the second derivative of -3*l + 2/27*l**4 + 0 + 1/90*l**5 + 5/27*l**3 + 2/9*l**2. Factor i(k).
2*(k + 1)**2*(k + 2)/9
Let b = -2/403 + 2023/1612. Let h = 3/2 - b. Find t, given that 1/4*t**5 + 1/4*t**4 - 1/2*t**3 + 1/4*t + h - 1/2*t**2 = 0.
-1, 1
Let s(o) be the third derivative of o**6/8 - 3*o**5/5 + 9*o**4/8 - o**3 - 5*o**2. Factor s(n).
3*(n - 1)**2*(5*n - 2)
Let p(s) = -4*s**3 + 20*s**2 + 12*s - 28. Let n(i) = -i**4 - 4*i**3 + 21*i**2 + 13*i - 29. Let j(x) = 4*n(x) - 3*p(x). Find c such that j(c) = 0.
-2, 1, 2
Let f(i) be the first derivative of 2*i**3/21 + 8*i**2/7 + 32*i/7 + 26. Solve f(h) = 0.
-4
Solve 1/7*n**2 + 3/7*n + 2/7 = 0 for n.
-2, -1
Let a be ((-8)/84)/(1/6*-2). Find f, given that 0 - a*f**3 + 4/7*f**2 - 2/7*f = 0.
0, 1
Solve -3*l**2 + l**2 - l**2 + 3*l + 0*l = 0 for l.
0, 1
What is n in 8/3*n**4 - 2/3*n**5 - 8/3*n**3 - 4/3*n**2 - 4/3 + 10/3*n = 0?
-1, 1, 2
Let r(f) be the first derivative of f**5/40 + f**4/12 + f**3/12 - 4*f + 4. Let v(q) be the first derivative of r(q). Factor v(x).
x*(x + 1)**2/2
Solve -x**4 - 900*x + 90*x**3 - 4*x**4 - 629 - 305*x**2 + 129 = 0.
-1, 10
Suppose -4 = -x - x. Let h be -2 + (x - 16/(-12)). Factor 2/3*u**2 + h + 2*u.
2*(u + 1)*(u + 2)/3
Let o(u) be the first derivative of -1/10*u**6 - 2 + 0*u**2 + 2*u - 1/3*u**3 + 1/4*u**4 + 1/10*u**5. Let m(j) be the first derivative of o(j). Factor m(l).
-l*(l - 1)*(l + 1)*(3*l - 2)
Let r(l) be the second derivative of -2*l**4/3 + 2*l**3/3 - l**2/4 + l. Determine t, given that r(t) = 0.
1/4
Let r(j) = -j**2 + j - 5. Let z(b) be the third derivative of b**3/6 - 3*b**2. Let m(x) = -r(x) - 5*z(x). Factor m(u).
u*(u - 1)
Let b be (-46)/39 + (-1 - 7/(-3)). Suppose 2/13*y**2 + b*y - 4/13 = 0. What is y?
-2, 1
Let i(r) be the second derivative of -1/168*r**7 + 1/80*r**5 + 1/60*r**6 + 0*r**2 + 0 - 7*r - 1/24*r**4 + 0*r**3. Let i(n) = 0. Calculate n.
-1, 0, 1, 2
Let a(f) be the third derivative of f**5/12 + 5*f**4/6 + 10*f**3/3 - 8*f**2. Factor a(b).
5*(b + 2)**2
Let l(h) = h**2 + h + 2. Let o be l(0). Factor 4*z + 2*z**2 + 7 - o - 3.
2*(z + 1)**2
Find b such that 0*b + b - 6*b**4 + 5*b**2 - 3*b**4 + 3*b**3 = 0.
-1/3, 0, 1
Let k(y) be the first derivative of -2*y**5/5 + y**4/2 + 2*y**3/3 - y**2 - 7. Suppose k(j) = 0. Calculate j.
-1, 0, 1
Let x = -25/112 - -2/7. Let c(j) be the first derivative of 0*j**2 - x*j**4 - 2 + 1/12*j**3 + 0*j. Factor c(p).
-p**2*(p - 1)/4
Let y(i) = -i**2 - 7*i - 4. Let z be y(-5). Solve z*p**3 + 4*p**2 + p**5 + 8 + 4*p**4 + p - 8 = 0 for p.
-1, 0
Let k(v) be the first derivative of -6/5*v**2 + 4/25*v**5 + 3/5*v**4 + 4/15*v**3 - 8/5*v - 6. What is u in k(u) = 0?
-2, -1, 1
Let y(c) = -2*c**4 - 5*c**3 + 9*c**2 - 7. Let o(w) = w**3 - w**2 + 1. Let a(s) = -5*o(s) - y(s). Let a(k) = 0. Calculate k.
-1, 1
Let w = 15 - 15. Factor -2*d + w*d**2 - 2*d**3 - d**2 - 3*d**2.
-2*d*(d + 1)**2
Suppose 4*l = -0*l + 20. Determine x, given that x**2 + x**2 - 8*x**4 + 3*x**l + x**3 + 2*x**5 + 0*x**3 = 0.
-2/5, 0, 1
Let u(x) be the third derivative of 1/60*x**5 + 0*x + 0 - 4*x**2 + 1/12*x**4 + 1/6*x**3. Find h, given that u(h) = 0.
-1
Determine f so that 6/7*f + 3/7*f**3 + 0 + 9/7*f**2 = 0.
-2, -1, 0
Let -5/2 - 5/4*d + 5/4*d**2 = 0. Calculate d.
-1, 2
Factor -10*m**2 + 1077*m - 5*m**3 - 1077*m.
-5*m**2*(m + 2)
Let d = 43/105 - -9/35. Suppose 0*l**2 + 0 + 2/3*l**5 + 0*l - 4/3*l**3 - d*l**4 = 0. Calculate l.
-1, 0, 2
Let d = -1 + 4. Suppose -d - 9 = -3*y. Let 3*z**2 + 0*z**3 - 2*z**y + 0*z**3 - z**2 = 0. What is z?
-1, 0, 1
Let o = 3 + 0. Factor 7 + 0*u**2 - 8*u**2 + 12*u - o - u**2 - 7*u**3.
-(u - 1)*(u + 2)*(7*u + 2)
Let u = -38 + 13. Let n be ((-2)/u)/((-8)/(-40)). Suppose 0*v - 3/5*v**4 - v**3 - n*v**2 + 0 = 0. What is v?
-1, -2/3, 0
Let z be (-3 - (-57)/9)*-6. Let q = 74/3 + z. Factor q*p**2 - 4/3*p - 16/3*p**3 + 0 + 2*p**4.
2*p*(p - 1)**2*(3*p - 2)/3
Let l(g) = -8*g**3 + g**2. Let r be l(1). Let v = -3 - r. Factor 4*t**2 + t - 5*t**2 + t**v + 4*t**3 - 5*t**3.
t*(t - 1)**2*(t + 1)
Let l be -2 - -2 - (-30)/2. Let b be (-3)/20 + 6/l. Find c such that -1/4*c**2 + b*c + 0 - 1/4*c**3 + 1/4*c**4 = 0.
-1, 0, 1
Let d(y) = y**4. Let j(t) = -8*t**4 + 15*t**3 + 75*t**2 + 125*t. Let k(w) = 18*d(w) + 2*j(w). Factor k(g).
2*g*(g + 5)**3
Let y(v) be the first derivative of -1/270*v**5 + 3/2*v**2 - 1/54*v**4 + 3 + 1/540*v**6 + 0*v + 0*v**3. Let c(s) be the second derivative of y(s). Factor c(a).
2*a*(a - 2)*(a + 1)/9
Let 30*f**3 + 3/4*f**4 + 7500 + 3000*f + 450*f**2 = 0. Calculate f.
-10
Suppose -2*z + 3*x + 1 = 0, -5*z - 8 + 13 = -5*x. Factor -3/4*m + 1/4*m**3 - 1/2 + 0*m**z.
(m - 2)*(m + 1)**2/4
Let y be (-2)/((-81)/84 + 1). Let m = 282/5 + y. Factor 0 + 0*r**4 - m*r**3 + 2/5*r**5 + 0*r**2 + 0*r.
2*r**3*(r - 1)*(r + 1)/5
Let k(q) = -q**3 - q + 80. Let h be k(0). Let f be 16/h - 0/(-2). Factor 1/5*l**2 + 1/5*l - 1/5*l**4 + 0 - f*l**3.
-l*(l - 1)*(l + 1)**2/5
Let r be (6/(-14))/(2/(-7)). Suppose -r*w - 1/2*w**2 + 1/2 + 3/2*w**3 = 0. What is w?
-1, 1/3, 1
What is v in -99*v**3 - 3*v**5 + 18*v + 120*v**2 + 18*v + 30*v**4 - 84*v = 0?
0, 1, 4
Let d(t) be the third derivative of -t**5/210 - 5*t**4/84 - 2*t**3/7 - 36*t**2. Factor d(k).
-2*(k + 2)*(k + 3)/7
Let q(z) be the first derivative of -z**6 - 9*z**5/5 + 3*z**4 + 3*z**3 - 3*z**2 - 30. Let q(b) = 0. Calculate b.
-2, -1, 0, 1/2, 1
Suppose y - 161 + 42 = -2*s, -3*s + 183 = 3*y. Factor 2*u - u**2 + u**4 - 2*u**3 + 0*u**2 + 58 - s.
u*(u - 2)*(u - 1)*(u + 1)
Let c(z) be the first derivative of 1/3*z**3 + 1/24*z**4 - 4 + z**2 - 3*z. Let y(o) be the first derivative of c(o). Factor y(w).
(w + 2)**2/2
Suppose 3*p - 8 - 4 = 0. Let r = -2 + p. Factor r*l - 6*l**3 + l - 6*l**2 + 3*l**5 + 3*l**4 + 0 + 3.
3*(l - 1)**2*(l + 1)**3
Suppose 4*h - 4*c - 8 = 0, 0 = -4*h - 3*c + 6 + 2. What is k in k + 6*k**h - 2*k**2 + k - k**2 = 0?
-2/3, 0
Factor -z**3 + 25*z**4 + 11*z**3 + 69*z**2 - 69*z**2.
5*z**3*(5*z + 2)
Let f(d) be the second derivative of -d**4/72 - d**3/18 - d**2/12 + 3*d. Determine w so that f(w) = 0.
-1
Let k(s) be the third derivative of s**8/1680 - s**7/525 + s**6/600 + 4*s**2. Factor k(m).
m**3*(m - 1)**2/5
Let b(p) = -2*p**3 - 4*p**2 + 3*p + 1. Let a(i) = 3*i**3 + 6*i**2 - 5*i - 2. Let g(h) = 5*a(h) + 8*b(h). Let y be g(-2). Factor 2/3*q - q**2 + y.
-q*(3*q - 2)/3
Let m(j) be the third derivative of j**6/360 + j**5/90 + j**4/72 + 12*j**2. Let m(c) = 0. Calculate c.
-1, 0
Factor -8/5*x**2 + 0 + 2/5*x.
-2*x*(4*x - 1)/5
Let s(a) be the first derivative of -5*a**6/18 - a**5 + 20*a**3/9 - 69. Find f, given that s(f) = 0.
-2, 0, 1
Let b = 3 + 1. Suppose f + 4*h - 16 = 0, 3*h - 4*h = 5*f - b. Factor 2*i**3 - 4*i**2 + 4*i + 0*i**2 + f*i**3 - 2*i**2.
2*i*(i - 2)*(i - 1)
Let s(p) be the first derivative of -5*p**5 - 15*p**4/4 + 110*p**3/3 + 30*p**2 - 40*p - 18. Suppose s(f) = 0. What is f?
-2, -1, 2/5, 2
Let w(v) be the third derivative of v**7/630 - v**6/360 + 2*v**2. Factor w(x).
x**3*(x - 1)/3
Factor 0*b**2 + 5/3*b + 0 - 5/3*b**3.
-5*b*(b - 1)*(b + 1)/3
Let x be 1/2*0/6. Let