)
Let w(r) = r**3 - 6*r**2 + r - 4. Let h be w(6). Suppose h*v - 4*v + 5*t = -6, -v = -t - 3. Factor -n**5 + 2*n**4 + 0*n**v + 2*n**5 + 0*n**5 + n**3.
n**3*(n + 1)**2
Let w be 30/(-4)*2/(-3). Let a = w - 3. Let a*m - 3*m + m**2 - m + m**3 = 0. Calculate m.
-2, 0, 1
Suppose -5*l - 3*v + 19 = 0, v - 4 = -1. Find w, given that 119 + w - 119 - w**l = 0.
0, 1
Let n = 23 + -17. Suppose 0 = x - 3*x + n. Factor -4/5*o**4 + 4/5*o**2 + 0 + 2/5*o**5 - 2/5*o + 0*o**x.
2*o*(o - 1)**3*(o + 1)/5
Let r(j) = -4*j**2. Let a(c) = -3*c - 3. Let k be a(-3). Let o(w) = 17*w**2. Let h(l) = k*o(l) + 26*r(l). What is i in h(i) = 0?
0
Solve 3/2 - 1/2*r**2 + r = 0.
-1, 3
Let w = -36455/84 + 434. Let h(r) be the third derivative of 0*r**3 + 0*r + 2*r**2 - 1/210*r**5 - w*r**4 + 0. Solve h(z) = 0 for z.
-1, 0
Let q = 277/411 - 1/137. Let n = -5/12 + q. Determine p, given that 1/4*p**4 + n*p + 0 + 3/4*p**3 + 3/4*p**2 = 0.
-1, 0
Let t(h) be the second derivative of -1/15*h**6 - 3*h + 1/21*h**7 + 0*h**2 + 0*h**3 + 0*h**5 + 0*h**4 + 0. Factor t(v).
2*v**4*(v - 1)
Let g(y) = 3*y**2 + 27*y + 39. Let f(k) = -3*k**2 - 26*k - 38. Let q(i) = 3*f(i) + 2*g(i). Factor q(d).
-3*(d + 2)*(d + 6)
Let n(r) be the first derivative of r**6/4 + 2*r**5/5 - 11*r**4/24 + r**3/9 + 31. Factor n(i).
i**2*(i + 2)*(3*i - 1)**2/6
Let z = -68 + 72. Let a(h) be the second derivative of -1/2*h**2 + 1/3*h**3 + 3*h + 0 - 1/12*h**z. What is v in a(v) = 0?
1
Find r such that 2/5*r + 0 + 1/5*r**2 = 0.
-2, 0
Let s(o) be the second derivative of -o**7/2100 - o**6/150 - o**5/25 - 2*o**4/15 - 2*o**3/3 + 3*o. Let v(d) be the second derivative of s(d). Factor v(z).
-2*(z + 2)**3/5
Find n, given that 0 + 0*n - 6/5*n**3 + 0*n**2 - 3/5*n**4 = 0.
-2, 0
Let q(b) = -b**2 - 24*b + 36. Let r(s) = -24*s + 36. Let u(o) = -o + 11. Let g be u(7). Let x(d) = g*q(d) - 5*r(d). Factor x(z).
-4*(z - 3)**2
Let h(r) = r**3 - r. Let w(y) = -4*y**3 - 2*y**2 + 3*y. Let j(z) = -3*h(z) - w(z). Factor j(f).
f**2*(f + 2)
Let y(v) = -v + 3. Let x be y(-1). Suppose -15 + 7 = -x*z. Factor 4/3*c + 2*c**3 + 14/3*c**z + 0.
2*c*(c + 2)*(3*c + 1)/3
Let u(d) be the second derivative of 0*d**2 + 0*d**3 + 0 + 1/70*d**5 + 1/42*d**4 + 8*d. Suppose u(s) = 0. What is s?
-1, 0
Let u = -31 - -94/3. Suppose 8*x + 4*j = 5*x - 14, -x - j - 3 = 0. What is s in 0 + 0*s + 1/3*s**3 + u*s**x = 0?
-1, 0
Suppose -c - 4*c + 10 = 0. Determine i so that 18*i**2 - 9*i + 8 - 2*i**3 - 8*i**c - 7*i = 0.
1, 2
Let z(k) = 60*k**3 - 111*k**2 + 9*k + 21. Let a(q) = 6*q**3 - 11*q**2 + q + 2. Let g(s) = -21*a(s) + 2*z(s). Factor g(m).
-3*m*(m - 1)*(2*m - 1)
Let b(m) be the third derivative of -m**8/336 - m**7/30 - 19*m**6/120 - 5*m**5/12 - 2*m**4/3 - 2*m**3/3 + 7*m**2. Determine n so that b(n) = 0.
-2, -1
Let x(k) = -k**2 + 9*k - 8. Let a be x(6). Suppose -3*s = -2*b - 5*s + a, b - 1 = s. Find m, given that -2*m**b + 0 + 7/4*m**2 - 1/2*m + 3/4*m**4 = 0.
0, 2/3, 1
Let x(w) = -w**2 + 3*w. Let n be x(4). Let m = n + 6. Suppose 0*j**m - 4*j + 3*j + 2*j**2 + j**3 + 2*j = 0. Calculate j.
-1, 0
Suppose 0 = 3*t - 1 - 8. Factor 0*w**t + w**3 - 2*w + 6*w + 2*w**2 - 3*w.
w*(w + 1)**2
Let w(m) be the third derivative of -11/40*m**6 - 2*m**3 + 0*m + 1/2*m**4 - 8*m**2 + 3/112*m**8 + 0 + 9/20*m**5 - 1/70*m**7. Find f, given that w(f) = 0.
-2, -2/3, 1
Suppose 0 = -5*m - 3*p - 14, m = 2*p + 2 - 10. Let q = m - -9. Factor 28/3*y**3 + 2/3*y**q + 4/3 + 32/3*y**2 + 4*y**4 + 6*y.
2*(y + 1)**4*(y + 2)/3
Let f(m) = -9*m**4 - 11*m**3 + 7*m**2 - 3*m + 2. Let b(k) = 8*k**4 + 10*k**3 - 6*k**2 + 2*k - 2. Let h(c) = 7*b(c) + 6*f(c). Let h(s) = 0. Calculate s.
-1, 1
What is q in 4*q**2 + 2/5*q**5 + 2/5*q**3 - 8/5*q - 16/5 - 8/5*q**4 = 0?
-1, 2
Suppose -18 = 4*x - k - 31, -2*x - k = 1. Let 2/9 + 2/9*q**x - 4/9*q = 0. What is q?
1
Let o(n) be the first derivative of 10*n**5/3 - 5*n**4 + 2*n**3/3 + 2*n**2/3 - 5. Determine b, given that o(b) = 0.
-1/5, 0, 2/5, 1
Let r(t) be the first derivative of t**3 + 0*t + 0*t**4 - 1 + 1/210*t**5 + 0*t**2 - 1/1260*t**6. Let v(y) be the third derivative of r(y). Factor v(j).
-2*j*(j - 2)/7
Let c(j) = -6*j**2 + 12*j - 15. Suppose -f + 12 = -3*v, v - 2 = -f + 2*v. Let x(m) = -5*m**2 + 12*m - 14. Let u(k) = f*x(k) + 2*c(k). Solve u(q) = 0 for q.
2
Let 8/9*h**2 - 8/9*h**4 - 2/3*h**3 + 8/9*h + 0 - 2/9*h**5 = 0. Calculate h.
-2, -1, 0, 1
Let w(k) = -k**3 - 4*k**2 - 2*k + 4. Let o be w(-2). Let -1/7*u**3 + 0 + 1/7*u + o*u**2 = 0. What is u?
-1, 0, 1
Let b(f) be the first derivative of -f**3/3 - 3*f**2/2 + 3*f - 6. Let z(x) = -8*x**2 - 20*x + 20. Let v(w) = -20*b(w) + 3*z(w). Find n, given that v(n) = 0.
0
Suppose 57 = -3*i + 63. Let y(s) be the second derivative of 0 - 8/27*s**3 - 1/90*s**5 + 4/9*s**i + 5/54*s**4 + 3*s. What is t in y(t) = 0?
1, 2
Let l(w) be the first derivative of -w**4/12 - w**3 - 9*w**2/2 + 2*w + 1. Let f(a) be the first derivative of l(a). Factor f(h).
-(h + 3)**2
Let j = -4 + 8. Let x(o) = -o**3 + o**2 - o - 1. Let f be x(-1). Solve 9/2*h + h**f + 1 - 2*h**j - 9/2*h**3 = 0.
-2, -1, -1/4, 1
Let y be -8 - -4 - 213/(-46). Let i = y + -3/23. Factor -i*b**2 + 2*b - 2.
-(b - 2)**2/2
Let s(h) = -h**3 - 6*h**2 - 2*h - 6. Let m be s(-6). Factor 0*t + 5*t - t - m*t**2 - 10*t**3.
-2*t*(t + 1)*(5*t - 2)
Suppose 4*l + 5*b - 10 = 2, 5*l - 3*b = 15. Factor -4*f**4 + 2*f**4 + 10*f**l + 4*f**2 - 6*f**2 - 6*f**4.
-2*f**2*(f - 1)*(4*f - 1)
Suppose 16*w - 18*w + 8 = 0. Factor -2/5*n**3 + 0 - 6/5*n**w + 4/5*n**2 + 0*n.
-2*n**2*(n + 1)*(3*n - 2)/5
Suppose 3*z + 373 + 218 = 0. Let i = -1377/7 - z. Factor i*j - 6/7*j**4 + 2*j**3 - 10/7*j**2 + 0.
-2*j*(j - 1)**2*(3*j - 1)/7
Factor 3/5*w**2 + 3/5*w + 0.
3*w*(w + 1)/5
Let x(v) = -4*v**2 + 2*v. Suppose -5*i + 0*i + 39 = -4*k, -9 = 4*k + 5*i. Let a(r) = 9*r**2 - 4*r. Let t(p) = k*a(p) - 13*x(p). Factor t(o).
-2*o*(o + 1)
Let y(w) be the first derivative of w**3/3 + 3*w**2 + 9*w + 15. Factor y(x).
(x + 3)**2
Let h(b) = -7*b - b**2 + 19*b + 4*b**2 + 12. Let c(f) = -f**2 - 4*f - 4. Let z(x) = -11*c(x) - 4*h(x). Find n such that z(n) = 0.
-2
Let q be (7 - (2 - -8)) + 8. Solve 2/9*y**q - 2/3*y**3 + 2/9*y**2 + 0 - 2/9*y**4 + 4/9*y = 0.
-1, 0, 1, 2
Find z such that 1/4*z**3 + 5/4*z - z**2 - 1/2 = 0.
1, 2
Let n(a) be the first derivative of -1/14*a**4 + 0*a**2 - 4/21*a**3 + 0*a + 4. Factor n(h).
-2*h**2*(h + 2)/7
Factor -8/9*v + 14/9*v**3 + 0 - 8/3*v**2.
2*v*(v - 2)*(7*v + 2)/9
Factor 0*y**3 - 7*y**4 + 9*y**4 - 2*y**3.
2*y**3*(y - 1)
Let k(c) be the first derivative of -c**7/210 + c**6/120 + c**5/60 - c**4/24 + 3*c**2/2 - 4. Let i(y) be the second derivative of k(y). Factor i(n).
-n*(n - 1)**2*(n + 1)
Let f = 7 + -7. Let q = 3 + f. Suppose -b**3 - 8/3*b**2 + 0 + 4/3*b + q*b**4 = 0. What is b?
-1, 0, 2/3
Let j(m) be the first derivative of m**8/840 - m**6/180 + 4*m**3/3 - 3. Let v(l) be the third derivative of j(l). Factor v(u).
2*u**2*(u - 1)*(u + 1)
Let j(g) be the third derivative of g**8/2352 - 4*g**7/735 + g**6/70 + g**5/210 - 13*g**4/168 + g**3/7 + 5*g**2 + 1. Let j(s) = 0. What is s?
-1, 1, 6
Let t(c) be the third derivative of -c**6/36 - 11*c**5/180 - c**4/18 - c**3/6 - 2*c**2. Let f(s) be the first derivative of t(s). Factor f(v).
-2*(3*v + 1)*(5*v + 2)/3
Let f(i) be the first derivative of i**6/15 - 6*i**5/25 + 3*i**4/10 - 2*i**3/15 + 5. Solve f(u) = 0.
0, 1
Let p(b) be the first derivative of -b**9/4536 - b**8/1260 + b**6/270 + b**5/180 + b**3/3 + 5. Let h(n) be the third derivative of p(n). Factor h(x).
-2*x*(x - 1)*(x + 1)**3/3
Let w be (100/(-15))/(-5) - (1 + -1). Let l(z) be the second derivative of 7/12*z**4 + 0 - 1/4*z**5 - 2*z**2 + 4*z + w*z**3. Solve l(j) = 0.
-1, 2/5, 2
Let r = 1172 - 1169. Factor 0*v**2 + 0 + 2/7*v - 2/7*v**r.
-2*v*(v - 1)*(v + 1)/7
Find i such that -3/2*i**4 - 27*i**2 + 21/2*i**3 + 30*i - 12 = 0.
1, 2
Let c(y) be the second derivative of -y**5/20 - 5*y**4/12 - 4*y**3/3 - 2*y**2 + 6*y. Solve c(m) = 0.
-2, -1
Let n be (6/2)/(30/40). Factor 3*r**4 + 2*r**4 + 12*r**3 + 5*r**4 + 3*r**5 + 2*r**n.
3*r**3*(r + 2)**2
Let -6*b + 12*b - b**3 - 9*b**2 + 21*b**4 - 5*b**3 - 12*b**2 = 0. Calculate b.
-1, 0, 2/7, 1
Suppose 0 = 3*c + 2*c + 3*l - 13, -2*l = -c. Let j be ((-3)/5)/(c/(-10)). Find b, given that 3*b**3 + b**j - 2*b**3 = 0.
0
Let c = -14 + 17. Suppose -5*x + c*h + 5 = 0, 4*x + 7 = 4*h + 3. Find d such that -4/5 + 