 + 2)
Suppose 36*g = 105 + 3. Factor -20/3*i**g - 28/3*i + 4/3*i**4 + 8/3 + 12*i**2.
4*(i - 2)*(i - 1)**3/3
Let x = 28 + -20. Suppose 0*n**3 + 3*n**3 + 6*n**2 - x + 8 = 0. What is n?
-2, 0
Suppose -o - o = 2. Let t = -6 - -11. Let y(b) = b**4. Let u(n) = 4*n**4 - 2*n**3 + 2*n + 1. Let f(m) = o*u(m) + t*y(m). Factor f(s).
(s - 1)*(s + 1)**3
Find n, given that 2/13*n - 6/13*n**2 + 4/13 + 2/13*n**4 - 2/13*n**3 = 0.
-1, 1, 2
Let p be -5 + (-8)/(-4) - -4. Let w be (p + -2)*(-5)/10. Determine f, given that w*f**3 + 0 + 0*f + 1/2*f**2 - f**4 = 0.
-1/2, 0, 1
Let h be -3*2/1*5/(-45). Let n(r) be the first derivative of 4*r - 2 + h*r**3 - 3*r**2. Factor n(a).
2*(a - 2)*(a - 1)
Solve 4/7*b**3 + 0*b**2 - 2/7*b**4 - 2/7*b**5 + 0*b + 0 = 0 for b.
-2, 0, 1
Let f = -5/79 + 415/316. Factor -7/4*r + 1/4*r**4 + 1/2 - f*r**3 + 9/4*r**2.
(r - 2)*(r - 1)**3/4
Let x be ((-1)/5)/(3/(-5)). Factor 0 - 1/3*k**5 + x*k**3 + 0*k - 1/3*k**2 + 1/3*k**4.
-k**2*(k - 1)**2*(k + 1)/3
Let 14*m**3 + 2*m + m**2 - 23*m**3 + 10*m**3 + 2*m**2 = 0. What is m?
-2, -1, 0
Suppose -1 + 5/3*o + 2/3*o**2 + 1/3*o**5 + 1/3*o**4 - 2*o**3 = 0. Calculate o.
-3, -1, 1
Let s be (8/(-42))/(7 - (-55)/(-7)). Let v = 1 - -2. Factor 0 + 2/9*n - 4/9*n**2 + s*n**v.
2*n*(n - 1)**2/9
Let f = -11/31 - -179/155. Let a(p) be the first derivative of -f*p - 2 + 0*p**2 + 1/20*p**4 + 1/5*p**3. Solve a(i) = 0 for i.
-2, 1
Factor 12*r**2 - 3*r**3 + 3*r + 0*r**3 - 3*r**4 - 9*r**2.
-3*r*(r - 1)*(r + 1)**2
Suppose 3*s - 7 = -1. Let 2*m - 3*m + m**s - m + 3 - 2*m**2 = 0. What is m?
-3, 1
Factor 0*l**3 - 3/4*l + 0 - 3/2*l**2 + 3/4*l**5 + 3/2*l**4.
3*l*(l - 1)*(l + 1)**3/4
Let p(k) = 12*k**5 + 16*k**4 - 24*k**3 + 16*k**2 + 12*k - 16. Let l(g) = -4*g**5 - 5*g**4 + 8*g**3 - 5*g**2 - 4*g + 5. Let v(d) = 16*l(d) + 5*p(d). Factor v(m).
-4*m*(m - 1)**2*(m + 1)**2
Let w(u) be the second derivative of -u**5/20 - 11*u**4/12 + 2*u**3 + u**2 + 9*u. Let k be w(-12). Factor 4/3*g + 0 + 2/3*g**k.
2*g*(g + 2)/3
Factor -9 + 56*f**2 + 4*f**4 + 14*f + 10*f**5 - 3 - 60*f**3 - 12*f.
2*(f - 1)**3*(f + 3)*(5*f + 2)
Suppose x + 0*x = -9. Let y be (x/6)/((-9)/30). Solve -3*k**4 - 2*k**3 + 4*k**3 + y*k**4 = 0 for k.
-1, 0
Let s(q) be the first derivative of q**6/21 - 2*q**5/35 - 5*q**4/14 + 2*q**3/21 + 8*q**2/7 + 8*q/7 - 10. What is x in s(x) = 0?
-1, 2
Let y = -1377/5 - -277. Suppose 22/5*k**2 - 24/5*k + y - 6/5*k**3 = 0. What is k?
2/3, 1, 2
Let j(n) = 8*n**5 - 21*n**4 - 8*n**3 + 21*n**2 + 5*n. Let k(o) = 4*o**5 - 11*o**4 - 4*o**3 + 11*o**2 + 3*o. Let u(x) = 3*j(x) - 5*k(x). Factor u(r).
4*r**2*(r - 2)*(r - 1)*(r + 1)
Let r(k) be the third derivative of 49*k**6/144 + 35*k**5/36 - 65*k**4/36 + 10*k**3/9 + 14*k**2. Factor r(f).
5*(f + 2)*(7*f - 2)**2/6
Factor 3*g**3 + 9*g + 3*g**3 - 3 - g**2 - 3*g**3 - 8*g**2.
3*(g - 1)**3
Let y(z) be the first derivative of -1/3*z + 0*z**2 + 1/9*z**3 + 3. Let y(s) = 0. What is s?
-1, 1
Let q(z) be the third derivative of -z**9/3024 - z**8/840 - z**7/840 - z**3/2 + 3*z**2. Let f(p) be the first derivative of q(p). Find d such that f(d) = 0.
-1, 0
Let l(d) be the first derivative of d**5/30 - d**4/6 + d**2/2 - 3. Let b(a) be the second derivative of l(a). Factor b(o).
2*o*(o - 2)
Suppose -117*p = -126*p + 36. Factor -2/5*x + 0 + 1/5*x**5 - x**2 - 3/5*x**3 + 1/5*x**p.
x*(x - 2)*(x + 1)**3/5
Let v(q) be the first derivative of -4*q**5/5 - q**4 + 21. Factor v(d).
-4*d**3*(d + 1)
Let 3*a**2 + 3/2*a**3 - 3 - 3/2*a = 0. Calculate a.
-2, -1, 1
Let r(f) = 2*f**5 + 12*f**3 + 8*f**2 - 6*f - 4. Let b(x) = -5*x**5 - 35*x**3 - 23*x**2 + 18*x + 12. Let m(n) = 4*b(n) + 11*r(n). Find c such that m(c) = 0.
-1, 1, 2
Let m(s) = -23*s**3 + 3*s**2 + 7*s + 7. Let l(j) = -11*j**3 + j**2 + 3*j + 3. Let a(u) = 7*l(u) - 3*m(u). Factor a(w).
-2*w**2*(4*w + 1)
Factor -9/4*i + 27/8*i**2 + 3/8.
3*(3*i - 1)**2/8
Solve 9 + 2 + 12*g + 4*g**2 - 11 = 0.
-3, 0
Let d(i) = i**2 + 3*i + 5. Let u be 1 + 1 - 8/(-8). Let j(p) = 4*p**2 + 14*p + 24. Let w(x) = u*j(x) - 14*d(x). Solve w(h) = 0 for h.
-1, 1
Suppose -11*b + 16*b + 3*j = 25, 20 = 4*j. Let q(s) be the third derivative of 1/6*s**4 - b*s**2 + 0*s**3 + 1/10*s**5 + 0 + 1/60*s**6 + 0*s. Factor q(l).
2*l*(l + 1)*(l + 2)
Suppose 0 = 2*n + 16 - 26, -2*n + 16 = 2*v. Find a, given that -16/9*a - 2/9*a**4 + 0 + 8/9*a**2 + 4/9*a**v = 0.
-2, 0, 2
Let d = 29/2 + -13. Solve 1/2 - q + 2*q**3 + 2*q**4 - d*q**2 = 0.
-1, 1/2
Let x(q) = 4*q**2 - q**3 + 0*q**3 - 2*q + 0*q**3 + 1. Let c be x(3). Let 2*p**3 + 3*p**c - p**4 + 0*p**3 - 2*p**2 - 2*p**5 = 0. What is p?
-1, 0, 1
Let p(r) be the second derivative of r**8/6720 - r**7/2520 - r**6/720 + r**5/120 - r**4/3 + 3*r. Let a(q) be the third derivative of p(q). Factor a(w).
(w - 1)**2*(w + 1)
Suppose -2*f = -10*f + 16. Factor 0*d + 0 - 2/7*d**f.
-2*d**2/7
Suppose -4*w + 12 = -j, 0*j - j + 12 = 4*w. Let k(b) be the second derivative of -1/15*b**5 + 1/45*b**6 + 1/18*b**4 - w*b + 0 + 0*b**2 + 0*b**3. Factor k(r).
2*r**2*(r - 1)**2/3
Let u(l) be the second derivative of l**7/105 + l**6/75 - l**5/50 - l**4/30 - 17*l. Factor u(d).
2*d**2*(d - 1)*(d + 1)**2/5
Let c be 28/21*2/8 - 0. Factor c*u + 0 - 1/3*u**2.
-u*(u - 1)/3
Find c such that -12*c + 4*c**3 + 6*c**3 - 3*c**3 - 8 - 3*c**3 = 0.
-1, 2
Let v(h) be the third derivative of h**8/1344 - h**6/160 - h**5/120 + 16*h**2. Suppose v(f) = 0. What is f?
-1, 0, 2
Factor -1/2 + 0*b + 1/8*b**2.
(b - 2)*(b + 2)/8
Factor 0 - 1/4*s - 1/4*s**2.
-s*(s + 1)/4
Let m(j) be the first derivative of j**4/6 - 10*j**3/9 + 7*j**2/3 - 2*j + 4. Factor m(g).
2*(g - 3)*(g - 1)**2/3
Factor -8 - 36*f**3 + 5*f**2 + 7*f**2 + 12*f**4 + 0*f**4 + 12*f + 8*f**3.
4*(f - 1)**3*(3*f + 2)
Let k(b) be the first derivative of b**4/2 - 14*b**3/3 + 11*b**2 - 10*b - 7. Find v, given that k(v) = 0.
1, 5
Let c(g) = -g**3 - 11*g**2 + 2*g + 25. Let z be c(-11). Suppose -2*y - 2/3*y**z + 2*y**2 + 2/3 = 0. Calculate y.
1
Suppose -2 + 28*r**3 + 8*r**2 - 4*r + 6*r**4 + 10*r**4 + 2 = 0. What is r?
-1, 0, 1/4
Let k(j) be the first derivative of -7*j**6/360 + j**5/60 + 4*j**2 + 4. Let m(o) be the second derivative of k(o). Determine h, given that m(h) = 0.
0, 3/7
Suppose 20*b + 12 = 23*b. Suppose 4*t - 3*m = 10, 9 + 7 = 2*t + b*m. Factor -2/11*y**t + 0*y + 2/11*y**3 - 2/11*y**5 + 0 + 2/11*y**2.
-2*y**2*(y - 1)*(y + 1)**2/11
Let l be (-2 - 2 - 1) + 9 + 0. Factor 0*y + 1/3*y**l + 0 - 1/3*y**3 - 2/3*y**2.
y**2*(y - 2)*(y + 1)/3
Let c(r) be the second derivative of r**5/10 - 4*r**4/3 + 13*r**3/3 - 6*r**2 + r - 28. Factor c(l).
2*(l - 6)*(l - 1)**2
Let g(r) = -r**3 + 3*r**2 - 6*r. Let k(d) = d**2 - d. Let s(l) = g(l) - 5*k(l). Factor s(n).
-n*(n + 1)**2
Let q(t) be the first derivative of t**6/6 + 2*t**5/5 + t**4/4 + 9. Let q(v) = 0. Calculate v.
-1, 0
Let j = 156/5 - 4987/160. Let o(d) be the third derivative of -1/48*d**5 + 0 - j*d**4 + 1/12*d**3 + 0*d - 2*d**2. Factor o(u).
-(u + 1)*(5*u - 2)/4
Let w = 6 + -8. Let z(h) = h**3 + 4*h**2 + 4*h + 3. Let v be z(w). Factor -2*o**v + 3*o**3 + o**2 + 0*o**3 - o - 1.
(o - 1)*(o + 1)**2
Let k(w) be the third derivative of w**6/360 - w**5/240 - w**4/48 + w**3/6 - 3*w**2. Let h(m) be the first derivative of k(m). Factor h(j).
(j - 1)*(2*j + 1)/2
Let v(h) be the first derivative of 1 - h**2 - 1/180*h**5 + 0*h**3 + 1/72*h**4 + 0*h. Let n(c) be the second derivative of v(c). Suppose n(r) = 0. Calculate r.
0, 1
Find w such that 45 + 5*w**2 + 5*w + 10*w + 24*w - 9*w = 0.
-3
Determine k, given that 63*k**4 - 4 + 49/2*k**5 - 59*k**2 + 11/2*k**3 - 30*k = 0.
-2, -1, -2/7, 1
Let y(z) be the third derivative of -z**6/24 - z**5/60 - 3*z**2. Let p be y(-1). Suppose -2*f**5 - f**p + 2*f**5 + 2*f**5 - f**4 = 0. Calculate f.
0, 1
Suppose 21*h - 16 - 47 = 0. What is c in 9*c**5 - 3*c + 78/7*c**h + 150/7*c**4 + 6/7 - 36/7*c**2 = 0?
-1, 2/7, 1/3
Suppose -6*v - 2*v = 0. Let l(g) be the second derivative of 2*g + 0*g**2 + 0*g**6 + 1/30*g**5 + 0*g**4 + v*g**3 + 0 - 1/63*g**7. Find w such that l(w) = 0.
-1, 0, 1
Let s(a) be the third derivative of a**8/21 - 44*a**7/105 + 29*a**6/24 - 19*a**5/30 - 13*a**4/6 - 4*a**3/3 - 2*a**2. Factor s(l).
(l - 2)**3*(4*l + 1)**2
Suppose 1/7*w**4 - 5/7*w**3 + 2/7 - w + 9/7*w**2 = 0. What is w?
1, 2
Let f be 2/4 - (-497)/(-966). Let g = 133/345 - f. Factor -1/5*l**3 + 0*l + g*l**4 - 1/5*l**5 + 0*l**2 + 0.
-l**3*(l - 1)**2/5
L