- r + 0*r**3. Factor f(a).
2*a**2*(a + 1)**3/9
Let i(p) = 24*p - 94. Let f be i(4). Factor -1/5*l**5 - 8/5*l + 4/5 + l**3 - 1/5*l**4 + 1/5*l**f.
-(l - 1)**3*(l + 2)**2/5
Let f(n) be the second derivative of -2*n**6/15 + n**4/3 - 3*n. Factor f(w).
-4*w**2*(w - 1)*(w + 1)
Let u(y) = -y**2 + y - 1. Let t(d) = d**3 - 11*d**2 + 10*d - 9. Let f(a) = -4*t(a) + 36*u(a). Factor f(n).
-4*n*(n - 1)**2
Suppose -22/17*k + 10/17 + 14/17*k**2 - 2/17*k**3 = 0. Calculate k.
1, 5
Let j(l) be the third derivative of l**6/540 + l**5/45 + l**4/12 + 4*l**3/27 + 4*l**2 - 6*l. Solve j(u) = 0.
-4, -1
Let r(h) be the first derivative of 7*h**6/6 + 2*h**5/5 - 7*h**4/4 - 2*h**3/3 - 7. Factor r(q).
q**2*(q - 1)*(q + 1)*(7*q + 2)
Let j(q) be the first derivative of -3*q**4/16 - 5*q**3/4 + 3*q**2/8 + 15*q/4 + 38. Find y such that j(y) = 0.
-5, -1, 1
Let l be (2/(-3))/((-17)/102). Determine m, given that 0 + 2/3*m + 0*m**3 - 1/3*m**l + m**2 = 0.
-1, 0, 2
Let i(r) = r**3 + 9*r**2 - r - 3. Let d(n) be the first derivative of 3*n**4/2 + 46*n**3/3 - 2*n**2 - 16*n - 3. Let g(m) = 3*d(m) - 16*i(m). Factor g(q).
2*q*(q - 2)*(q - 1)
Factor 4*k + 0 + 2/3*k**2.
2*k*(k + 6)/3
Let i be ((-20 - -11)/(-9))/((-9)/(-2)). Suppose -i*g**5 - 8/9*g**2 + 0 + 8/9*g**4 + 8/9*g - 2/3*g**3 = 0. What is g?
-1, 0, 1, 2
Factor -2/3*r**3 + 0*r + 0 - 1/3*r**2.
-r**2*(2*r + 1)/3
Let t(y) = 10*y**5 + y**4 - 3*y**3 + 7*y**2 + 9*y + 8. Let p(i) = -i**5 - i**2 - i - 1. Let x(l) = 40*p(l) + 5*t(l). Determine h, given that x(h) = 0.
-1, 0, 1/2, 1
Factor -17*p**3 + p**2 - 11*p**3 + 3*p**2 + 0*p**3 + 49*p**4.
p**2*(7*p - 2)**2
Let d(n) = 4*n**2 + 5*n + 4. Let i(s) = -7*s**2 - 9*s - 7. Let t = 4 - 0. Let j = -1 + t. Let l(m) = j*i(m) + 5*d(m). Factor l(k).
-(k + 1)**2
Let z be (-3)/((-27)/(-48))*-3. Suppose 5*l - 24 = z. Factor -l*u**3 - 3*u + 9*u**3 + 2*u.
u*(u - 1)*(u + 1)
Let o(k) = -k**3 - 8*k**2 - 8*k - 3. Let q be o(-7). Let v(f) = 1. Let i(r) = -4*r**2 - 2*r - 4. Let j(u) = q*v(u) + i(u). Factor j(d).
-2*d*(2*d + 1)
Let u(y) = -y + 2. Let q be u(0). Determine v, given that -2 + 1 + 2*v**2 - q*v**4 + 1 = 0.
-1, 0, 1
Let r(i) be the third derivative of 0*i + 1/8*i**4 + 0 + 0*i**3 + 1/20*i**5 + 7*i**2. Suppose r(p) = 0. Calculate p.
-1, 0
Let w(i) = -i**3 + 4*i**2 + 2*i - 4. Let o(f) = f**3 - f**2 + f + 4. Let k be o(0). Let r be w(k). Solve 1/4*y + y**r + 0 - 1/4*y**3 - y**2 = 0.
-1, 0, 1/4, 1
Factor 10/3*t + 2/3*t**3 - 4/3 - 8/3*t**2.
2*(t - 2)*(t - 1)**2/3
Suppose -2*n + 115 = -7*n. Let w = n + 25. What is d in 1/2*d**w + 1/2*d**3 - 1/2*d - 1/2 = 0?
-1, 1
Factor -14/5*h**2 - 6/5*h**3 - 2*h - 2/5.
-2*(h + 1)**2*(3*h + 1)/5
Find j such that 192/7 - 48/7*j + 3/7*j**2 = 0.
8
Let h(v) = v**2 - 10*v + 4. Let b be h(10). Factor 3 - l**4 + 4*l**3 - 5 + 3*l**4 - b*l.
2*(l - 1)*(l + 1)**3
Let h(l) = 45*l**3 - 54*l**2 + 51*l. Let y(m) = 9*m**3 - 11*m**2 + 10*m. Let n(f) = -4*h(f) + 21*y(f). Determine c so that n(c) = 0.
0, 2/3, 1
Let r(i) = i**2 + i - 2. Let g be r(2). Factor 4*p**5 - 9*p**4 + p**3 - g*p**5 + p**5 + 11*p**4.
p**3*(p + 1)**2
Suppose 20 = -4*z - 5*g, -8*z + 5*g + 20 = -13*z. What is k in -3/2*k**2 + 3/2*k**4 + k**3 + z - k = 0?
-1, -2/3, 0, 1
Let n = -567 - -569. Solve 1/5*c**n + 4/5*c + 4/5 = 0.
-2
Let -1/9 + 1/9*l**2 - 1/9*l + 1/9*l**3 = 0. What is l?
-1, 1
Let r(w) be the second derivative of 1/36*w**5 + 0 + 0*w**3 - 1/36*w**4 + 1/2*w**2 + 2*w. Let t(c) be the first derivative of r(c). Factor t(s).
s*(5*s - 2)/3
Let n(o) be the first derivative of 2 - 3/2*o**4 - 7/10*o**5 - 1/2*o**3 + 0*o + 1/2*o**2. Factor n(g).
-g*(g + 1)**2*(7*g - 2)/2
Let h(l) = 2*l**2 - 2. Suppose 0 = p - 3*w + 8, 0 = 2*p + 6*w - 5*w - 12. Let d(v) = -3*v**2 + v + 2. Let j(i) = p*h(i) + 3*d(i). Factor j(t).
-(t - 2)*(t - 1)
Factor -2/3*c**5 + 0*c**2 + 0 + 0*c**4 + 0*c + 8/3*c**3.
-2*c**3*(c - 2)*(c + 2)/3
Let b(z) be the second derivative of -4*z + 0 + 1/2*z**4 + 2*z**2 - 5/3*z**3. Find w such that b(w) = 0.
2/3, 1
Suppose 2*v - 10 = -2*k, 4*k - 5*k - 3*v + 11 = 0. Suppose k*a**2 - 14 - 18*a - 13 - 5*a**2 = 0. Calculate a.
-3
Let i(f) be the first derivative of 2*f**3/27 + 2*f**2/9 + 2*f/9 + 13. Determine z so that i(z) = 0.
-1
Let f(p) be the second derivative of -p**5/20 + 3*p**4/4 - 2*p**3 - 5*p**2 + 5*p. Let c be f(7). Factor 0 + 4/7*q**3 + 2/7*q**c + 2/7*q**2 + 0*q.
2*q**2*(q + 1)**2/7
Let z(m) be the second derivative of m**5/70 - m**4/21 + m**3/21 - 5*m. Factor z(y).
2*y*(y - 1)**2/7
Suppose 0*d + 1/2 - 27*d**3 - 27/2*d**2 = 0. Calculate d.
-1/3, 1/6
Let p = 6 + -5. Suppose 0 = -f - 0 + p. Suppose k + f - 2*k**3 + 2*k**3 + k**3 - 2*k**3 - k**2 = 0. Calculate k.
-1, 1
Let v = -11 - -11. Let b(t) be the second derivative of 1/75*t**6 + 0*t**2 + 0*t**4 - 1/50*t**5 + 2*t + 0*t**3 + v. Factor b(k).
2*k**3*(k - 1)/5
Let n(f) be the third derivative of -f**6/180 + f**5/270 - 9*f**2. Factor n(t).
-2*t**2*(3*t - 1)/9
Let u = -46 + 140/3. Suppose 0 = d - 4*v - 10, 5*v - 3 = -13. Factor 0 + u*m**3 - 4/3*m - 2/3*m**d.
2*m*(m - 2)*(m + 1)/3
Let t(b) be the second derivative of b**6/30 + b**5/20 - b**4/4 - b**3/6 + b**2 + 10*b. Factor t(o).
(o - 1)**2*(o + 1)*(o + 2)
Factor 6/13*l**2 + 10/13*l - 2/13*l**4 + 4/13 - 2/13*l**3.
-2*(l - 2)*(l + 1)**3/13
Let f(w) be the first derivative of -4/3*w - w**2 - 10 + 0*w**3 + 1/6*w**4. Solve f(d) = 0 for d.
-1, 2
Let b(y) = 3*y**3 - 2*y**2 + 2*y - 1. Let q be b(1). What is t in -4/3*t**3 - 3*t + 4*t**q + 2/3 = 0?
1/2, 2
Let x(s) be the third derivative of -s**6/180 - s**5/15 - s**4/3 - 2*s**3/3 - 4*s**2. Let m(b) be the first derivative of x(b). Factor m(i).
-2*(i + 2)**2
Let p(t) be the second derivative of 4*t - 1/20*t**5 + 1/6*t**3 + 1/10*t**6 - 1/4*t**4 + 0 + 0*t**2. Factor p(x).
x*(x - 1)*(x + 1)*(3*x - 1)
Let c be (2/(-5))/(126/(-2570)). Let w = 76/9 - c. Find u, given that -w*u**2 - 6/7*u - 4/7 = 0.
-2, -1
Suppose -2/9*o**2 + 0*o + 2/9 = 0. Calculate o.
-1, 1
Let g(x) be the second derivative of 1/6*x**4 - 1/6*x**3 - x - 1/15*x**6 + 0*x**2 + 1/20*x**5 + 0. Factor g(b).
-b*(b - 1)*(b + 1)*(2*b - 1)
Let k(r) = -r**2 - 6*r - 1. Let o be k(-5). Let m be o + (-2 - -3 - 1). What is f in 1/4*f**m + 1/4 + f + f**3 + 3/2*f**2 = 0?
-1
Factor 0*i**4 + 10*i**3 - 4*i + 5 + 10*i**2 - 5*i**5 - 5*i**4 - 10 - i.
-5*(i - 1)**2*(i + 1)**3
Suppose 5*s - 4 = 4*z - 7*z, 0 = -3*z - 6. Let w = 1 - -1. Factor 2*a + 3*a**s + 0*a**2 - a**w.
2*a*(a + 1)
Let b(y) = y**5 - y**2 - 1. Let q(w) = 3*w**5 - 2*w**4 + 3*w**3 + 4*w**2 + 4*w - 4. Let x(l) = -4*b(l) + q(l). Solve x(j) = 0 for j.
-2, -1, 0, 2
Let b be (-6)/(-3) + -2 - 5. Let o(c) = 4*c**4 + 7*c**3 + 3*c + 1. Let d(x) = 5*x**4 + 8*x**3 + 4*x + 1. Let f(q) = b*d(q) + 6*o(q). Solve f(i) = 0.
-1, 1
Suppose -1/4*y**3 + 1/4*y**2 + 0 + 0*y = 0. What is y?
0, 1
Let d be -3*1*3/9. Let g be 2/2*(d + 3). Factor -k**3 - k**4 + g*k**3 - k**3 - k**3.
-k**3*(k + 1)
Let f(q) = -q**3 + 2*q**2 + 4*q - 3. Let m be f(3). Suppose 5*d = -m*d + 15. Find a such that d*a**4 + 3*a**4 + 8*a**3 + 6*a**2 + 0*a**2 - 4*a**2 = 0.
-1, -1/3, 0
Let c be 27/(-18) - (-26)/12. Let p(l) be the first derivative of 5/4*l**2 - c*l**3 + 1 + 1/8*l**4 - l. Factor p(m).
(m - 2)*(m - 1)**2/2
Let m(k) be the third derivative of k**9/2268 + k**8/840 - k**6/540 - 2*k**3/3 - 3*k**2. Let v(d) be the first derivative of m(d). Factor v(u).
2*u**2*(u + 1)**2*(2*u - 1)/3
Let y(q) be the first derivative of 0*q + q**3 - 3/4*q**4 + 0*q**2 - 3*q**5 + 2 - 3/2*q**6. Factor y(p).
-3*p**2*(p + 1)**2*(3*p - 1)
Factor -44/5*v + 8/5 - 4/5*v**5 - 73/5*v**3 + 28/5*v**4 + 86/5*v**2.
-(v - 2)**3*(2*v - 1)**2/5
Let u(m) = -m**3 - 6*m**2. Let g(w) = -6*w**2. Let k(t) = -2*g(t) + 3*u(t). Factor k(r).
-3*r**2*(r + 2)
Let u = -2/89 + 97/356. Suppose 0*w + u*w**2 + 0 = 0. What is w?
0
Let j be ((-92)/(-18) + -5)*(6 - 0). Let f(d) be the second derivative of -1/9*d**3 - 1/18*d**4 + d + j*d**2 + 0. Solve f(s) = 0 for s.
-2, 1
Let q be (-4)/2*(-2)/2. Suppose 0 = -5*g + 2*z + 7, -2 + 0 = -q*g + z. Determine j so that -j**3 - j - j**3 + 3*j**g = 0.
-1, 0, 1
Let -4*h**2 - 3*h**2 - 30*h**3 - 12*h**4 - 17*h**2 + 4 - 2*h**3 = 0. What is h?
-1, 1/3
Determine l, given that -15/7 - 12/7*l + 3/7*l**2 = 0.
-1, 5
Let b(h) be the second derivative of h**7/21 - 2*h**6/5 + 11*h**5/10 - h**4 - 23*h. Solve b(m) = 0 for m.
0, 1, 2, 3
Let -t**2 - 8 + 5*t*