*2 + 4*a. Let d(n) = 2*n**4 + 9*n**3 + 7*n**2 + 9*n + 9. Let o(z) = -4*d(z) + 9*s(z). Factor o(p).
p**2*(p - 1)*(p + 1)
Let g(t) = -4*t**5 + 2*t**4 + 2*t**3 - t. Let l(o) = o**5 - o**3 + o. Let v be -1 - (-2 - (-2 - 1)). Let j(w) = v*l(w) - 2*g(w). Factor j(m).
2*m**3*(m - 1)*(3*m + 1)
Suppose 3*f = 4*f. Suppose -5*y + 4*y + 4*h = f, 2*y - 2*h = 0. Factor 0*a - 1/2*a**3 + 0 + y*a**2.
-a**3/2
Factor -3/8*g**3 + 1/8*g**4 - 1/8*g + 0 + 3/8*g**2.
g*(g - 1)**3/8
Suppose 3*i - 2 = -l + 2, 4 = -3*i - 5*l. Let b(g) be the first derivative of -3 - 2/21*g**3 + 1/7*g**i + 4/7*g. Factor b(c).
-2*(c - 2)*(c + 1)/7
Let v(c) be the second derivative of 0 + 0*c**2 - 1/6*c**3 + 7*c + 1/12*c**4. Factor v(t).
t*(t - 1)
Let k(m) be the first derivative of -1/4*m**3 + 15/8*m**2 + 2 - 3/16*m**4 - 9/4*m. Let k(v) = 0. Calculate v.
-3, 1
Factor 4/15*q - 2/15*q**2 + 0.
-2*q*(q - 2)/15
Let f = -7 - -13. Let p = f + -4. Let 1/2 + 1/2*x**p - x = 0. Calculate x.
1
Let i(w) be the third derivative of 0 + 8*w**2 + 2/105*w**7 - 1/168*w**8 + 0*w**6 + 0*w + 1/12*w**4 + 0*w**3 - 1/15*w**5. Factor i(j).
-2*j*(j - 1)**3*(j + 1)
Let m(d) be the second derivative of -d**4/72 + d**3/18 - d**2/12 - 9*d. Find s, given that m(s) = 0.
1
Let u(b) = -2*b**2 + 12*b + 18. Let s be u(7). Let 1/4*m**2 + 0*m + 0 + 0*m**3 - 1/4*m**s = 0. What is m?
-1, 0, 1
Let a(n) = 2*n + 7. Let c be a(-8). Let g = c - -12. Factor -2*k**5 - k**g + 3*k**3 + 0*k**5.
-2*k**3*(k - 1)*(k + 1)
Suppose 5*g + 0*z = -z + 20, 5*z + 50 = 5*g. Suppose 0 = -g*j - v - 5, 10 = 4*j - 4*v - 10. Let -2/5*o**4 + 0 + j*o**2 + 0*o - 2/5*o**3 = 0. Calculate o.
-1, 0
Let v(t) be the third derivative of -8*t**2 + 0 + 0*t + 1/24*t**4 + 1/18*t**3 + 0*t**5 - 1/90*t**6. Factor v(k).
-(k - 1)*(2*k + 1)**2/3
Suppose 0*i = -i. Suppose i = -3*o + 5*o - 4. Suppose -2/5*y**5 + 4/5*y**3 + 0 + 0*y**4 - 2/5*y + 0*y**o = 0. Calculate y.
-1, 0, 1
Let p = 43 + -41. Factor 0 + 6*u**2 - p*u - 9/2*u**3.
-u*(3*u - 2)**2/2
Let q = -34 - -21. Let j = q + 13. Find b such that -4/5*b**2 + 2/5*b**4 + j*b + 2/5 + 0*b**3 = 0.
-1, 1
Let w(q) = 5*q**2 + q - 1. Let p(h) = -h. Let t(g) = -12*p(g) + 4*w(g). Factor t(z).
4*(z + 1)*(5*z - 1)
Suppose -k + w + 1 = 0, -k = 3*k + 2*w - 28. Suppose -4*t = 3*j + 1 - 6, -k*j = 3*t - 1. Determine h, given that -2/5*h + 0 + 3/5*h**t = 0.
0, 2/3
Let i(o) = -15*o**3 + 23*o**2 + 7*o - 23. Let s(a) = 5*a**3 - 8*a**2 - 2*a + 8. Let v(p) = 3*i(p) + 8*s(p). Suppose v(y) = 0. What is y?
-1, 1
Let 32 + 16*p**3 + 2*p**4 + 6*p**4 + 48*p**2 - 6*p**4 + 64*p = 0. What is p?
-2
Determine a so that 1/6*a**3 + 0 - 1/3*a**4 - 1/6*a + 1/3*a**2 = 0.
-1, 0, 1/2, 1
Suppose 5*o + 0*o - 44 = 4*s, 4*o = -5*s - 14. Let f be ((-40)/165)/4*s. Factor -2/11*h**5 + 4/11*h**2 + 0*h**3 + 0 + 2/11*h - f*h**4.
-2*h*(h - 1)*(h + 1)**3/11
Let f(p) be the second derivative of -p**6/50 - 9*p**5/100 + 2*p**3/5 - 6*p. Solve f(r) = 0.
-2, 0, 1
Let d(c) = -c**2 - 5*c + 3. Let u(b) be the first derivative of 4*b**3/3 + 12*b**2 - 14*b - 3. Let z(m) = -14*d(m) - 3*u(m). Factor z(n).
2*n*(n - 1)
Let f = -7/4 + 39/20. Factor -1/5*k**3 + f - 1/5*k**2 + 1/5*k.
-(k - 1)*(k + 1)**2/5
Let i(w) be the second derivative of -w**8/630 + w**7/180 - w**6/270 - w**5/180 + w**3/6 + 2*w. Let q(k) be the second derivative of i(k). Factor q(u).
-2*u*(u - 1)**2*(4*u + 1)/3
Let k be 2/1 + (216/30)/(-6). Let 0*y**2 - 2/5*y**5 - 2/5*y + 0*y**4 + k*y**3 + 0 = 0. What is y?
-1, 0, 1
Let k(l) = 78*l**2 + 20*l - 8. Let i(q) be the second derivative of -13*q**4/6 - 7*q**3/6 + 3*q**2/2 + 4*q. Let x(c) = 8*i(c) + 3*k(c). Factor x(n).
2*n*(13*n + 2)
Suppose -4*o = 3*v - 24, o + 2*v - 11 = -0*o. Factor 0 - 1/4*f**2 - 1/4*f**4 + 0*f - 1/2*f**o.
-f**2*(f + 1)**2/4
Suppose -2*d = -6*z + 3*z + 23, -2*z - 3*d = 2. Determine w, given that 0 + 4/3*w**4 - 1/3*w + 4/3*w**2 - 2*w**3 - 1/3*w**z = 0.
0, 1
Solve -28*i**3 + 36*i**2 - 954 + 479 + 475 - 8*i = 0.
0, 2/7, 1
Suppose u + 8 = 5*u. Let x = 19 + -131/7. Factor -x*l + 4/7*l**u + 0 - 2/7*l**3.
-2*l*(l - 1)**2/7
Let p = -10 - -18. What is y in -2 + 4*y + y**5 - p*y**2 - 2*y**3 - 11*y - 2*y**4 + 4*y**4 = 0?
-1, 2
Let j(b) = 3 - 10 - 7*b + b**2 + 4. Let n(h) = h**2 - 3*h - 1. Let t(u) = -3*j(u) + 5*n(u). Solve t(l) = 0.
-2, -1
Let w = 2 + 0. Factor 2*f**4 + 58 - 58 + 12*f**3 + 18*f**w.
2*f**2*(f + 3)**2
Let v(u) = 8*u**3 - 6*u**2 + 10*u + 6. Let c(g) = -23*g**3 + 18*g**2 - 29*g - 17. Let l(b) = -6*c(b) - 17*v(b). Factor l(a).
2*a*(a - 2)*(a - 1)
Let l(n) = -n**2 + 5*n + 3. Let m be l(5). Solve 3*o**2 - 2*o**2 - 2*o**2 + o**m = 0 for o.
0, 1
Let a(z) = z**3 - 22*z**2 - 5*z + 114. Let l be a(22). Solve -1/3*o**5 + 1/3*o**l + 0*o**2 + 0*o**3 + 0*o + 0 = 0 for o.
0, 1
Let d(y) be the third derivative of 7*y**2 + 1/1848*y**8 + 0*y + 0*y**4 + 1/330*y**5 + 0*y**3 + 0 - 1/660*y**6 - 1/1155*y**7. Find a, given that d(a) = 0.
-1, 0, 1
Let t(w) be the third derivative of w**5/12 - 5*w**3/6 + 11*w**2. What is j in t(j) = 0?
-1, 1
Solve -2*t**2 + 2*t + 4/7*t**3 - 4/7 = 0.
1/2, 1, 2
Let a(w) be the first derivative of 3*w**5/20 - w**4/2 + 4*w + 3. Let x(t) be the first derivative of a(t). Factor x(s).
3*s**2*(s - 2)
Let c(x) be the third derivative of 7*x**8/72 - 31*x**7/45 + 11*x**6/180 + 101*x**5/18 + 22*x**4/3 + 4*x**3 - 9*x**2. Determine p so that c(p) = 0.
-1, -2/7, 3
Suppose -d - 5*y - 18 = -2*d, -3 = -5*d - 4*y. Determine q, given that 0 + 2/3*q**2 + 2/3*q**d + 0*q = 0.
-1, 0
Let s(j) be the first derivative of -7*j**5/15 + 37*j**4/12 - 59*j**3/9 + 35*j**2/6 - 2*j - 36. Solve s(o) = 0 for o.
2/7, 1, 3
Let s(w) be the second derivative of w**5/5 + 2*w**4/3 + 5*w**3/6 + w**2/2 + 2*w. Solve s(d) = 0.
-1, -1/2
Suppose 3*a = -a + 8. Let t(p) be the second derivative of 1/60*p**4 + 1/10*p**a + 0 - p + 1/15*p**3. Factor t(g).
(g + 1)**2/5
Let q(k) = 2*k**3 - 6*k**2 + 4*k. Suppose 0 = -2*d - 2*d - 12. Let t(y) = 2*y**3 - 7*y**2 + 5*y. Let r(l) = d*q(l) + 2*t(l). Factor r(z).
-2*z*(z - 1)**2
Let o(a) be the second derivative of -a**7/210 + 3*a**5/100 - a**4/30 - 2*a. Solve o(q) = 0.
-2, 0, 1
Let i(l) be the first derivative of -l**4/10 - 4*l**3/5 - 8*l**2/5 - 46. Factor i(x).
-2*x*(x + 2)*(x + 4)/5
Let z(y) = -22*y**2 - 7*y - 6*y + 21*y**2. Let d be z(-13). Suppose 3/2 - 3/2*w**2 + d*w = 0. What is w?
-1, 1
Suppose -w**2 + 6*w**2 - 26*w + 31*w = 0. What is w?
-1, 0
Suppose 2*s - 3*s + 7 = 0. Factor 9*d**5 + 22*d**3 + 3*d**2 - s*d**3 + 10*d**4 + 15*d**4 - 4*d**4.
3*d**2*(d + 1)**2*(3*d + 1)
Let h(x) be the first derivative of -x**4/5 - 4*x**3/15 + 4*x**2/5 - 2. Solve h(z) = 0 for z.
-2, 0, 1
Let w(p) be the second derivative of 3*p + 0*p**2 - 1/42*p**4 - 1/21*p**3 + 0. Solve w(k) = 0 for k.
-1, 0
Let b(g) be the first derivative of -g**5/10 + 3*g**4/8 - g**2 + 3. Factor b(a).
-a*(a - 2)**2*(a + 1)/2
Let i(a) = -a**2 + 2*a + 2. Let x be i(2). Factor r - r**2 + 2 - x*r**3 - r**2 + r**3.
-(r - 1)*(r + 1)*(r + 2)
Let i(v) = v**5 - v**4 + v**3 - v - 1. Let l(a) = -5*a**5 + 2*a**4 - 5*a**3 + 4*a + 4. Let u(x) = 12*i(x) + 3*l(x). Factor u(m).
-3*m**3*(m + 1)**2
Let w = -12 + 17. Suppose -m = -w*m. Factor x + m*x**3 + 0*x**2 + x**3 - 2*x**2.
x*(x - 1)**2
Solve 9*c + 3*c**3 - 3*c**2 - 9*c**2 + 3 - 3 = 0 for c.
0, 1, 3
Suppose 32 + 4 = 12*r. Let b(m) be the first derivative of 1/3*m**2 + 0*m - r - 2/9*m**3. Factor b(y).
-2*y*(y - 1)/3
Let b(f) be the second derivative of f**6/10 + 3*f**5/20 - 3*f**4/4 - 5*f**3/2 - 3*f**2 - 11*f. Factor b(a).
3*(a - 2)*(a + 1)**3
Let w(v) be the third derivative of 0*v**7 + 0*v + 1/120*v**6 + 0*v**5 + 0 + 0*v**3 - 1/672*v**8 - 1/48*v**4 - 4*v**2. Let w(a) = 0. What is a?
-1, 0, 1
Let l = 444 + -442. Find n, given that 2/17*n + 0 + 2/17*n**l = 0.
-1, 0
Suppose -6*j = -3*j - 6. Let u(x) be the second derivative of -1/35*x**5 + 0*x**2 - j*x + 0*x**4 + 1/21*x**3 + 0 + 1/147*x**7 + 0*x**6. Factor u(s).
2*s*(s - 1)**2*(s + 1)**2/7
Let w(h) be the first derivative of -h**3 + 3*h**2/2 + 6*h + 2. Factor w(o).
-3*(o - 2)*(o + 1)
Suppose 24 = 4*c + 4*y, -2*y = 3*c - 5*y. Suppose 5*v = w + 11, c*w + 3*v - v - 18 = 0. Factor -12*b**4 - 4*b**2 - 14*b**3 - b**w + 3*b**4.
-2*b**2*(b + 1)*(5*b + 2)
Let m(n) = 4*n - 5. Let l be m(2). Determine q, given that -2*q**3 - 2*q**5 + 2*q**5 + 4*q**5 - l*q**5 + q = 0.
-1, 0, 1
Let q(f) = f**3 + 4*f**2 - f - 2. Let l be q(-4). 