uppose a + w = 3*u + 5, -u - 3*a = 12. Factor -4/7*r**2 - 2*r**4 + 0 - 18/7*r**u + 0*r.
-2*r**2*(r + 1)*(7*r + 2)/7
Suppose 4*j + 0*j = 2*i + 26, -2*j = 5*i + 5. Suppose -3*l + 13 = -u, 3*l = 2*u - j*u + 21. Factor -4*a + 2*a + 27*a**2 - 25*a**u.
2*a*(a - 1)
Suppose 2*m + 4*c = 2*c, -4*m = 2*c - 6. Determine i, given that 12/7*i**4 + 34/7*i**m + 2*i + 34/7*i**2 + 2/7 = 0.
-1, -1/2, -1/3
Let i(t) be the first derivative of -t**5/90 + t**4/36 + 2*t**3/9 - 2*t**2 + 2. Let r(k) be the second derivative of i(k). What is g in r(g) = 0?
-1, 2
Let t(x) = x - 5. Let r be t(7). Suppose 5*v = -z + 28, -2*v = -4*v - r*z + 16. What is d in 6*d**3 + d**4 + 3*d**5 - v*d**3 - 2*d**5 + d**4 = 0?
-1, 0
Let z = -98 + 100. Factor -9/2*w - 3/2 - 3*w**z.
-3*(w + 1)*(2*w + 1)/2
Factor -1/2*c**2 - 5*c + 0.
-c*(c + 10)/2
Let w = 10 + -8. Solve b - 3*b + 2*b + 3*b**w = 0 for b.
0
What is a in 8*a**4 - 32*a**2 - 16*a**3 + 1 - 1 - 1184*a**5 + 1188*a**5 = 0?
-2, 0, 2
Suppose 3*h + 3*w - 6 = 0, h = -10*w + 13*w + 2. Factor -2/3*x - 2/3*x**h + 0.
-2*x*(x + 1)/3
Let s(d) = -9*d**5 + 10*d**4 - 2*d**2 - d. Let k = 0 + 6. Let o(b) = -18*b**5 + 19*b**4 - b**3 - 3*b**2 - 2*b. Let v(p) = k*o(p) - 15*s(p). Factor v(a).
3*a*(a - 1)**2*(3*a + 1)**2
Let j = -4 - 6. Let x be -2*(j/(-4) + -3). Factor x + 5*k + 2*k + 0 - 3*k + 3*k**2.
(k + 1)*(3*k + 1)
Let t be 4/(-14) + (-128)/(-56). Solve 3*b**4 - 6*b - 2*b**3 - 9*b**2 + t*b**3 + 12*b = 0 for b.
-2, 0, 1
Let b = -58/21 - -24/7. Solve -f + b + 1/3*f**2 = 0 for f.
1, 2
Let x(w) be the first derivative of -4*w**5/5 + 3*w**4 - 4*w**3 + 2*w**2 + 6. Factor x(i).
-4*i*(i - 1)**3
Let p = 3 + -1. Let u(i) = i**3 - i**2 - i + 2. Let a be u(0). Factor -3*f - 2*f**a + f - p*f.
-2*f*(f + 2)
Let d(l) = l**3 + 4*l**2 + 3*l. Let o be d(-2). Let p be (-96)/(-6) + o/(-2). Factor 2*i**2 + p*i + 2*i**3 - 15*i.
2*i**2*(i + 1)
Solve -3*p**2 - p - p**4 + p - 3*p**3 - 5*p + 4*p = 0 for p.
-1, 0
Let u = -1 + 1. Let n be 2 + (1 - 0) + u. Determine r so that -n + r**2 + 4*r - 2*r**2 + 0 = 0.
1, 3
Solve -4/5*n**2 + 0*n + 2/5 + 0*n**3 + 2/5*n**4 = 0.
-1, 1
Let j(l) be the first derivative of 3 - 1/6*l**3 + 0*l**2 + 0*l. Solve j(n) = 0.
0
Let n(k) be the third derivative of -k**6/600 + k**5/75 - k**4/40 - 16*k**2. Factor n(o).
-o*(o - 3)*(o - 1)/5
Factor 0*i**2 + 0*i**3 - 4*i**3 - 4*i**2.
-4*i**2*(i + 1)
Let m(t) be the second derivative of -t**6/480 - t**5/240 + t**4/96 + t**3/24 - 3*t**2/2 - 5*t. Let p(z) be the first derivative of m(z). Solve p(q) = 0 for q.
-1, 1
Let q(r) = 6*r**4 - 2. Let h(k) = 7*k**4 - k**3 + k - 2. Let y(u) = -4*h(u) + 5*q(u). Solve y(j) = 0.
-1, 1
Factor 12/7*n**2 - 36/7*n + 4/7*n**3 + 20/7.
4*(n - 1)**2*(n + 5)/7
Suppose 0 = 3*l - 91 + 28. Let d be 1/2*56/l. Factor 1/3*s**3 + 2/3 + 5/3*s + d*s**2.
(s + 1)**2*(s + 2)/3
Suppose 0*a - a + 3 = 0. Suppose 3*q = -a*n, -2*q - n = -0*q - 5. Suppose -3*d**3 + 3*d**5 - 4*d**5 - d + q*d**3 = 0. What is d?
-1, 0, 1
Suppose 2/5*z - 1/5 - 1/5*z**2 = 0. Calculate z.
1
Let s(x) = x**2 - 31*x - 36. Let c(u) = -u**2 + 61*u + 71. Let v(o) = -6*c(o) - 11*s(o). Solve v(y) = 0.
-3, -2
Suppose 3*x = c - 3, -2*c + 2*x + 2 = c. Let h(v) be the second derivative of 1/15*v**3 + c*v**2 + 3*v + 1/30*v**4 + 0 - 1/25*v**5. Factor h(w).
-2*w*(w - 1)*(2*w + 1)/5
Let y(v) = -v**3 + 9*v**2 + v + 3. Let a(f) = -5*f**3 + 37*f**2 + 3*f + 13. Let s(p) = 6*a(p) - 26*y(p). Let s(q) = 0. What is q?
-2, -1, 0
Let q be (-2 - 1)*4/(-4). Suppose 2*n**2 + 2*n**4 - 27*n**3 + 23*n**q + 0*n**2 = 0. What is n?
0, 1
Let l be 4/30 - (-5)/(300/112). Determine t, given that -2*t**l - 2*t + t**4 + 0 - 1/2*t**5 + 3/2*t**3 = 0.
-1, 0, 2
Suppose -4*k + 1 = -7, -2*b + 20 = -k. Let -3*p**5 - 15*p**3 - 2*p - 4 + b*p**4 + 9*p**2 + 4 = 0. Calculate p.
0, 2/3, 1
Suppose -1 - 19 = -4*n. Let a(t) be the third derivative of 0*t + 0*t**4 - 1/360*t**6 + 0*t**3 - 1/630*t**7 + 0*t**n - 2*t**2 + 0. Let a(k) = 0. What is k?
-1, 0
Let x = 53 - 317/6. Let r(c) be the second derivative of 2*c + x*c**4 + 0*c**5 + 0*c**2 + 0 - 1/15*c**6 + 0*c**3. Find u, given that r(u) = 0.
-1, 0, 1
Let s be (-10)/4*8/(-10). Suppose 0 = -s*y + 4 - 0. Factor -2 + 5*u - y*u + u + 5*u - 9*u**2.
-(3*u - 2)*(3*u - 1)
Let d be -2 + 2 + 1/5. Let x(z) be the first derivative of 1/2*z**4 - z**2 - d*z**5 - 2 + 0*z**3 + z. What is g in x(g) = 0?
-1, 1
Let z(c) be the second derivative of -3*c**5/20 - 9*c**4/4 - 15*c**3/2 + 75*c**2/2 + 44*c. Let z(r) = 0. Calculate r.
-5, 1
Let j(r) be the second derivative of -1/80*r**5 + 0 - 5*r + 1/120*r**6 - 1/48*r**4 + 0*r**2 + 1/24*r**3. Factor j(f).
f*(f - 1)**2*(f + 1)/4
Let h(n) be the third derivative of -n**8/168 - n**7/35 - n**6/30 + n**5/15 + n**4/4 + n**3/3 - 14*n**2. Factor h(j).
-2*(j - 1)*(j + 1)**4
Let w(m) be the third derivative of 0*m + 5*m**2 + 1/8*m**4 + 1/10*m**5 + 0 + 1/40*m**6 + 0*m**3. Suppose w(y) = 0. Calculate y.
-1, 0
Let s(l) be the second derivative of l**5/20 + 7*l**4/60 + l**3/15 - 6*l. Factor s(k).
k*(k + 1)*(5*k + 2)/5
Let d be 1 - 2/(360/177). Let a(p) be the third derivative of 0*p**3 + 0 + d*p**5 + 0*p**4 + 1/120*p**6 + 0*p + p**2. Factor a(f).
f**2*(f + 1)
Let n(t) be the second derivative of t**4 - 2*t**3/3 + 9*t. Factor n(l).
4*l*(3*l - 1)
Determine d, given that 1/3*d**2 - 1/3*d - 1/3*d**4 + 1/3*d**3 + 0 = 0.
-1, 0, 1
Suppose 2/5*z + 0 - 2/5*z**3 + 2/5*z**2 - 2/5*z**4 = 0. Calculate z.
-1, 0, 1
Suppose 4*u = 7*u - 6. Factor 0*v + 1/5*v**u - 1/5.
(v - 1)*(v + 1)/5
Let p(b) be the third derivative of b**5/300 - b**3/30 + 11*b**2. Factor p(j).
(j - 1)*(j + 1)/5
Let h(d) = -110*d**3 + 825*d**2 + 495*d - 395. Let w(s) = 10*s**3 - 75*s**2 - 45*s + 36. Let y(i) = -4*h(i) - 45*w(i). Factor y(g).
-5*(g - 8)*(g + 1)*(2*g - 1)
Let w be (-3*1)/((-9)/6). Solve -w*c**2 - 4*c + 6 + c + 5*c - 6*c = 0 for c.
-3, 1
Find y, given that -4/5*y**3 + 12/5*y + 0*y**2 + 8/5 = 0.
-1, 2
Let c(o) be the third derivative of o**9/2016 - o**8/560 + o**6/120 - o**5/80 - o**3/2 + 4*o**2. Let h(y) be the first derivative of c(y). Factor h(x).
3*x*(x - 1)**3*(x + 1)/2
Let g(l) = -l**2 - 6*l - 6. Let r be g(-4). Suppose x - r - 1 = 0. Factor -x*v**4 - 2*v**2 + 5*v**4 + 0*v**2.
2*v**2*(v - 1)*(v + 1)
Factor 10*h - 4*h**2 - 4 - 7 - 10*h**3 + 36 - h**4 - 20*h**2.
-(h - 1)*(h + 1)*(h + 5)**2
Let s(d) be the third derivative of -d**6/540 + d**5/135 + 8*d**2. Factor s(y).
-2*y**2*(y - 2)/9
Let w(f) = 3*f**3 + 2*f**2 - 4*f - 1. Let z(t) = -5*t + 0*t**3 + 3*t**2 + t - 2 + 3*t**3. Let k(d) = 2*w(d) - 3*z(d). Let k(y) = 0. What is y?
-2, -2/3, 1
Let d be 1*-14*1/(-2). Let n = -5 + d. Factor -2*j - 2*j**2 + 5*j**4 + 2*j**5 + 2*j**2 - j**4 - 4*j**n.
2*j*(j - 1)*(j + 1)**3
Let b(w) = w + 9. Let j be b(-5). Suppose -p + x - 3 = 6*x, -j*x = 2*p. Suppose 18*r + r**2 + r**p - 3 + 7 - 24*r**3 = 0. What is r?
-2/3, -1/4, 1
Let c(w) be the first derivative of 3*w**2/2 - w - 2. Let n be c(1). Factor 6/5*k**4 + 0 - 6/5*k**3 - 2/5*k**5 + 0*k + 2/5*k**n.
-2*k**2*(k - 1)**3/5
Let y(j) = 2. Let c(s) = -s**3 - s**2 - 5. Let x = 8 - 5. Let u be (-2)/2*(2 + x). Let w(m) = u*y(m) - 2*c(m). Factor w(i).
2*i**2*(i + 1)
Let k(u) = u**3 + 17*u**2 - u - 14. Let h be k(-17). Let l be 0*2*2/8. Factor l - 4/3*i**2 - 2*i**h - 4/3*i**4 - 1/3*i - 1/3*i**5.
-i*(i + 1)**4/3
Let a(o) = 4*o**3 - o + 3. Let x(n) = -4*n**3 - 4. Let w(l) = 4*a(l) + 3*x(l). Find y such that w(y) = 0.
-1, 0, 1
Suppose 2 = -q - 1. Let h = -3 - q. Factor 3*c - 3/2*c**2 + h.
-3*c*(c - 2)/2
Determine c, given that -7 - c**2 - 2*c**2 - 2*c**2 - 13 + 25*c = 0.
1, 4
Suppose 5 = 5*m - 10. Let c(i) = 23*i + 4 - 23*i + i**3 - m. Let l(j) = 17*j**3 - 32*j**2 + 22*j - 1. Let y(z) = 3*c(z) - l(z). Suppose y(v) = 0. Calculate v.
2/7, 1
Let k = 9209/7168 - -1/1024. Factor -6/7*w**2 - 3/7 + 9/7*w**4 + 6/7*w**3 - k*w + 3/7*w**5.
3*(w - 1)*(w + 1)**4/7
What is k in 15/2 - 3/8*k**4 + 3/2*k - 45/8*k**2 - 3*k**3 = 0?
-5, -2, 1
Let c(n) = 8*n**3 + 2*n**2 - 14*n - 8. Let k(w) = 9*w**3 + 2*w**2 - 15*w - 8. Let v(g) = 7*c(g) - 6*k(g). Factor v(h).
2*(h - 2)*(h + 1)*(h + 2)
Let t = 14 + -12. Suppose 3*k = -5*u + 10, t*k - 4*u + 8 = -2*k. Suppose 2/3*s**2 + s + 1/3*s**5 + k*s**4 - 2/3 - 4/3*s**3 = 0. What is s?
-2, -1, 1
Suppose r + 14 = f + 4*r, 0 = 5*f - 3*r + 2. Factor 7/2*l + 1 - 2*l**f.
-(l - 2)*(4*l + 1)/2
Suppose 0*n - 5*n + 10 = 0.