*g**6/6 - 12*g**5 + 125*g**4/4 + 110*g**3/3 - 90*g**2 + 40*g + 14. Suppose i(n) = 0. Calculate n.
-2, 2/7, 1
Factor 1 + 4/3*t + 1/3*t**2.
(t + 1)*(t + 3)/3
Let v(o) be the third derivative of 7*o**5/75 - o**4/15 + o**2. Factor v(g).
4*g*(7*g - 2)/5
Let w(q) = -3*q**3 + 11*q**2 + 8*q. Let p(j) = 2*j**3 - 7*j**2 - 5*j. Let g(l) = -8*p(l) - 5*w(l). What is a in g(a) = 0?
0, 1
Let x be (24/(-9))/((-2)/(-24)). Let c be ((-3)/(-2))/((-132)/x). What is b in c - 10/11*b + 4/11*b**2 = 0?
1/2, 2
Let t(j) = 21*j**2 - 111*j + 90. Let k(y) = -3*y**2 + 16*y - 13. Let z(l) = 27*k(l) + 4*t(l). Let z(b) = 0. What is b?
1, 3
Let l(i) be the first derivative of 8/7*i + 54/7*i**3 - 36/7*i**2 - 3. Let l(r) = 0. What is r?
2/9
Let i be 0/(0/(-2) + -3). Factor 1/3*j + 0 + i*j**3 - 2/3*j**2 + 2/3*j**4 - 1/3*j**5.
-j*(j - 1)**3*(j + 1)/3
Solve 0*g**2 + 4*g**4 + 0*g**2 + 1414*g**5 + 2*g**3 - 1412*g**5 = 0.
-1, 0
Suppose 4*u = 9 - 1. Factor -5 + u*z**3 + 6*z + 6*z**2 + 0*z**3 + 7.
2*(z + 1)**3
Let k(u) be the third derivative of u**6/24 - u**5/12 - 5*u**4/6 + 10*u**3/3 - 9*u**2. Factor k(w).
5*(w - 2)*(w - 1)*(w + 2)
Factor -17*n**2 - 20*n**3 + 3*n**4 - 33*n + 44*n**2 + 12*n + 5*n**3 + 6.
3*(n - 2)*(n - 1)**3
Suppose 0*d = -4*d + 5*o - 73, d + 16 = 2*o. Let w = 40 + d. Suppose -18 + f**2 - f + w = 0. What is f?
0, 1
Let c(k) = k + 16. Let r(s) = s + 15. Let x(m) = -2*c(m) + 3*r(m). Let a be x(-13). Factor a - 2/7*w + 2/7*w**2.
2*w*(w - 1)/7
Let b(k) be the first derivative of 5*k**4/4 + 5*k**3 + 5*k**2 + 1. Suppose b(q) = 0. What is q?
-2, -1, 0
Let h(i) be the third derivative of 1/6*i**4 + 5/24*i**6 + 0*i**3 + 0*i - 1/3*i**5 + 0 + 6*i**2. Factor h(u).
u*(5*u - 2)**2
Let c be (-112)/6 + (-11)/33. Let o = c - -22. Factor -2/3*y**o - 2/3*y**2 + 0 + 4/3*y.
-2*y*(y - 1)*(y + 2)/3
Let v(o) = -6*o**2 + 3*o - 9. Let i(x) = 23*x - 14*x - 1 - x**2 - 9*x. Let m(l) = -9*i(l) + v(l). Solve m(r) = 0.
-1, 0
Suppose -4*q = 5 + 3. Let f be 0 - ((-1)/q + -1). Find t such that -f*t - 1/2*t**2 + 0 = 0.
-1, 0
Let d(j) be the first derivative of 1 + 0*j**2 + 0*j - 21/16*j**4 - 1/2*j**3. Let d(h) = 0. What is h?
-2/7, 0
Let b(c) = -c**4 + c - 1. Let q(k) = 6*k**4 - 3*k**3 + 3*k**2 - 6*k + 5. Let w(z) = 10*b(z) + 2*q(z). Factor w(l).
2*l*(l - 1)**3
Let g(l) = -l**5 + l**3 + l**2 + l + 1. Let q = -12 - -6. Let r(k) = 4*k**5 + 2*k**4 - 4*k**3 - 8*k**2 - 6*k - 6. Let t(f) = q*g(f) - r(f). Factor t(h).
2*h**2*(h - 1)**2*(h + 1)
Let w(k) = k**2 - 10*k + 2. Let n be w(10). Suppose 12 = n*y - 0*y. Factor 5*s + s**3 + 4 - 4 - y*s.
s*(s - 1)*(s + 1)
Let p(j) be the first derivative of -j**4/24 + j**3/6 + 3*j**2/4 - 9*j/2 - 17. Factor p(i).
-(i - 3)**2*(i + 3)/6
Let w(t) be the third derivative of t**10/30240 - t**9/5040 + t**8/3360 + t**4/8 - 2*t**2. Let r(g) be the second derivative of w(g). Factor r(d).
d**3*(d - 2)*(d - 1)
Factor 0 + 3/4*q**3 + 3/4*q - 3/2*q**2.
3*q*(q - 1)**2/4
Suppose 3*y + 0*p - 10 = p, 3*y = 5*p - 10. Suppose -13*o**2 - y*o**3 - 5*o + o + 4 + 0 = 0. Calculate o.
-2, -1, 2/5
Let n(w) = 3*w - 25. Let a be n(9). Factor 0 + 2/3*y + 4/3*y**a + 2/3*y**3.
2*y*(y + 1)**2/3
Let f(j) = -j**5 + j**4 - j**3 - j**2 + j + 1. Let g(y) = -5*y**5 + 17*y**4 - 23*y**3 + 7*y**2 + 2*y + 2. Let p(m) = -2*f(m) + g(m). Solve p(o) = 0 for o.
0, 1, 3
Let x be (-100)/350*(-42)/8. Solve 9/4*t + 3/2*t**2 - 3/4*t**5 + 3/4 - 9/4*t**4 - x*t**3 = 0 for t.
-1, 1
Factor -1 + 15*l + 17 - 36*l**2 - 79*l.
-4*(l + 2)*(9*l - 2)
Suppose 9/4*z**2 + 3/2*z**3 + 3/8*z**4 + 3/2*z + 3/8 = 0. What is z?
-1
Suppose 9*n - 6*n = 75. Let g = n + -25. Solve 0*x - 3/4*x**3 + g - 3/4*x**2 = 0.
-1, 0
Let n(u) be the third derivative of -u**7/1470 - u**6/420 + u**5/140 + 2*u**2. Determine a, given that n(a) = 0.
-3, 0, 1
Factor -2/17*t**2 + 0 - 20/17*t.
-2*t*(t + 10)/17
Let w(a) be the first derivative of 0*a**3 + 0*a**4 - 1/75*a**6 + 0*a**2 - a + 1/50*a**5 - 2. Let h(u) be the first derivative of w(u). Factor h(d).
-2*d**3*(d - 1)/5
Determine f, given that -1/3*f - 2/3*f**2 + 0 - 1/3*f**3 = 0.
-1, 0
Let v(g) be the second derivative of g**7/525 - g**5/150 - 3*g**2/2 + 3*g. Let q(l) be the first derivative of v(l). Factor q(m).
2*m**2*(m - 1)*(m + 1)/5
Let a = 45 - 68. Let f be ((-1)/2)/(2/a). Factor -13/4*n + 27/4*n**2 + 1/2 - f*n**3 + 7/4*n**4.
(n - 1)**3*(7*n - 2)/4
Factor 12*z**2 + 4*z - 2*z**4 - 17*z**3 - 8 - 2*z**4 + 13*z**3.
-4*(z - 1)**2*(z + 1)*(z + 2)
Let o(n) be the third derivative of 0*n**6 + 10*n**2 + 0*n + 0 - 1/180*n**4 + 0*n**3 + 2/1575*n**7 + 1/2520*n**8 - 1/225*n**5. Factor o(h).
2*h*(h - 1)*(h + 1)**3/15
Factor 2/11*d**5 + 112/11*d**2 + 32/11 + 96/11*d + 64/11*d**3 + 18/11*d**4.
2*(d + 1)*(d + 2)**4/11
Let m(b) be the first derivative of 7*b**4 + 76*b**3/3 - 12*b**2 + 33. Factor m(p).
4*p*(p + 3)*(7*p - 2)
Suppose 0 = -3*r + 92 - 86. What is c in -7/4*c + 9/4*c**r - 5/4*c**3 + 1/4*c**4 + 1/2 = 0?
1, 2
Let m(d) be the second derivative of 0*d**2 + 0 - 9*d - 8/3*d**3 - 1/5*d**5 + 4/3*d**4. Factor m(b).
-4*b*(b - 2)**2
Let g be (2/7)/(-34 + 35). Suppose 4*b - d - 12 = 0, d = -d. Factor -g*y - 2/7*y**b + 0 - 4/7*y**2.
-2*y*(y + 1)**2/7
Let c(w) = 4*w**3 - 12*w + 21. Let s(l) = -l**3 + 3*l - 5. Let z(a) = 2*c(a) + 9*s(a). Let t(r) be the first derivative of z(r). Factor t(x).
-3*(x - 1)*(x + 1)
Let x(d) be the third derivative of -d**7/735 + d**6/210 - d**5/210 + 2*d**2. Suppose x(u) = 0. Calculate u.
0, 1
Let a be (1/(-6))/(-1) + (-238)/(-408). Factor -a*x**2 - 1/2*x - 1/4*x**3 + 0.
-x*(x + 1)*(x + 2)/4
Let d(u) be the second derivative of -u**8/13440 - u**7/1680 - u**6/480 - u**5/240 + u**4/6 + u. Let l(r) be the third derivative of d(r). Factor l(f).
-(f + 1)**3/2
Let p(c) = 22*c**5 + 232*c**4 + 528*c**3 + 352*c**2 - 34. Let d(v) = -2*v**5 - 21*v**4 - 48*v**3 - 32*v**2 + 3. Let b(q) = -68*d(q) - 6*p(q). Factor b(k).
4*k**2*(k + 1)*(k + 4)**2
Let v(h) = -h**3 - 7*h**2 - 11*h - 2. Let b be v(-5). Let o be 1/b + -3 + 3. Determine t so that t**2 - 1/3*t + o*t**4 - t**3 + 0 = 0.
0, 1
Let 101*v**3 - 14*v**2 - 105*v**3 - 2*v**2 - 12*v = 0. Calculate v.
-3, -1, 0
Let q(d) be the second derivative of -49*d**6/15 + 21*d**5/10 + 4*d**4 + 4*d**3/3 - 7*d. Determine p so that q(p) = 0.
-2/7, 0, 1
Let t(j) be the second derivative of -j**7/315 + j**5/150 - 10*j. Factor t(n).
-2*n**3*(n - 1)*(n + 1)/15
Let o be (8/6)/(3/9). Suppose i = o*i - 6. Factor 4*s**2 + s**3 - 7*s**3 - i*s**5 - 2*s**2 + 6*s**4.
-2*s**2*(s - 1)**3
Let i(k) be the third derivative of 0*k + 0 - 1/60*k**4 + 0*k**3 + 1/150*k**5 - 2*k**2 + 1/300*k**6 - 1/525*k**7. Factor i(p).
-2*p*(p - 1)**2*(p + 1)/5
Let d be 1/(-1 + 9/6). Let t(i) be the second derivative of 1/3*i**3 + i - 1/10*i**5 + 1/6*i**4 + 0 - i**d. Factor t(p).
-2*(p - 1)**2*(p + 1)
Suppose -4*z + 116 = 1192. Let b = z + 1893/7. Factor 0*n + 4/7*n**2 - 6/7*n**3 - b*n**4 + 0.
-2*n**2*(n + 1)*(5*n - 2)/7
Let u(j) = j**3 + 2*j**2 + 1. Let l be u(-2). Let o be l - (6/8 - 0). Find s such that -o + 1/4*s**2 - 1/2*s + 1/2*s**3 = 0.
-1, -1/2, 1
Let i(s) be the third derivative of 0*s**3 + 1/210*s**5 + 0 + 1/735*s**7 + 0*s - 3*s**2 - 1/210*s**6 + 0*s**4. Let i(d) = 0. What is d?
0, 1
Factor 4/5*n**2 + 36/5 + 24/5*n.
4*(n + 3)**2/5
Let y = 521 + -1561/3. Factor y*v**2 - 4/3*v + 2/3.
2*(v - 1)**2/3
Let x(y) be the second derivative of -y**6/50 + 3*y**5/25 - 3*y**4/20 - 3*y. Suppose x(r) = 0. What is r?
0, 1, 3
Let t(f) = f**2 - 14*f + 42. Let r be t(10). Factor z**r + 0 + 2/3*z + 0*z**3 - 1/3*z**4.
-z*(z - 2)*(z + 1)**2/3
Let f(h) = h**2 - 4*h. Let x be f(5). Let 63*o**5 + o**4 - 65*o**x - 3*o**4 = 0. Calculate o.
-1, 0
Suppose -5*v + 19 = -1. Let 0*u**v - 2*u**3 - 6*u**3 - 4*u**4 + 8*u + 4 = 0. What is u?
-1, 1
Let w(n) = 5*n**2 - 7*n + 6. Let j(t) = -11*t**2 + 15*t - 13. Let h = 32 + -26. Let y(d) = h*j(d) + 13*w(d). Solve y(b) = 0.
-1, 0
Let s(w) = -w**3 - 7*w**2 - 5*w. Let r be s(-6). Let q be (4/r)/(1/(-3)). Factor -2 + 0*o**2 - q*o**2 + 0*o**2 - 4*o.
-2*(o + 1)**2
Let z = -34 + 30. Let m be (z/(-14))/(16/14). Determine i, given that m*i**2 + 5/4*i**3 - 1/4*i**5 - 1/4*i**4 - 2*i + 1 = 0.
-2, 1
Find z such that 0 + 4/7*z**5 - 24/7*z**3 - 12/7*z + 32/7*z**2 + 0*z**4 = 0.
-3, 0, 1
Suppose 16 = 3*k + k. Suppose 2*x - k*x + 4 = 0. Factor 2*a**3 + 0 + 0 + 2*a**4 - 2*a**x - 2*a.
2*a*(a - 1)*(a + 1)**2
What is w