 2/9*h**2 + 0.
-2*h*(h - 1)/9
Solve 44*d**2 - 139*d**2 - 40 + 6*d**3 + 125*d + 4*d**3 = 0 for d.
1/2, 1, 8
Let c(o) be the third derivative of -o**6/60 + o**5/10 - o**4/4 + o**3/3 - 7*o**2. Factor c(f).
-2*(f - 1)**3
Let i(h) be the third derivative of h**6/480 - h**4/96 - 4*h**2. Suppose i(t) = 0. What is t?
-1, 0, 1
Let g(y) be the first derivative of 24*y**2 + 4*y**3 + 1/4*y**4 - 5 + 64*y. Factor g(z).
(z + 4)**3
Let v(m) be the first derivative of 2 - 32*m**6 + 528/5*m**5 + 73*m**3 - 21*m**2 + 3*m - 129*m**4. What is t in v(t) = 0?
1/4, 1
Factor -2/9*j**2 + 8/9*j - 8/9.
-2*(j - 2)**2/9
Factor 1/4*b**4 + 5/4*b**2 - b**3 - 1/2*b + 0.
b*(b - 2)*(b - 1)**2/4
Let r(g) be the second derivative of 0*g**4 + 0 - 1/3*g**2 - 2/9*g**3 - 5*g + 1/45*g**6 + 1/15*g**5. Factor r(l).
2*(l - 1)*(l + 1)**3/3
Let t = -198 + 200. Factor 0 + 2/3*f**3 + 4/3*f - 2*f**t.
2*f*(f - 2)*(f - 1)/3
Let t(a) be the first derivative of -a**6/10 + 6*a**5/25 - 2*a**3/5 + 3*a**2/10 + 35. Let t(j) = 0. Calculate j.
-1, 0, 1
Let q(d) = 2*d**3 + d. Let l be q(1). Factor 3*r**4 + 0*r**3 + 6*r**3 - 7*r - l + 0*r + r.
3*(r - 1)*(r + 1)**3
Let n = -1 - -6. Suppose 5*w - 4*f - 12 = 0, 0*w + 4*w - n*f - 15 = 0. Solve -2*c + 2 - 1 - 2 + w - c**2 = 0.
-1
Factor 12*j - 1 + 0 - 2 - 1 - 8*j**2.
-4*(j - 1)*(2*j - 1)
Let f = 311 - 1237/4. Suppose -k + 21/4*k**3 + 1/2*k**4 + 2*k**2 - f*k**5 + 0 = 0. Calculate k.
-1, 0, 2/7, 2
Let p(a) = a**2 - 4*a - 7. Let v be p(5). Let j(h) = -h**2 - 4*h - 1. Let z be j(v). Factor -1/2*k**2 + 1/2*k + 1/2 - 1/2*k**z.
-(k - 1)*(k + 1)**2/2
Let w(o) be the second derivative of -o**7/168 - o**6/60 + 3*o**5/80 + o**4/12 - o**3/6 + 14*o. Find b such that w(b) = 0.
-2, 0, 1
Let i(h) be the second derivative of -h + 1/8*h**2 + 1/2*h**4 + 0 - 1/5*h**5 - 3/8*h**3. Suppose i(f) = 0. Calculate f.
1/4, 1
Let v(k) be the second derivative of k**6/15 + k**5/5 + k**4/6 - 6*k. Solve v(g) = 0 for g.
-1, 0
Let t(u) be the first derivative of u**4/30 - u**3/15 - 2*u**2/5 - 6*u + 5. Let a(h) be the first derivative of t(h). Factor a(c).
2*(c - 2)*(c + 1)/5
Suppose 5*b - 2*b = x + 12, -x = 2*b - 8. Suppose 2 + b = 3*a. Factor -5*l**a + 13*l**2 + 11*l**4 + 12*l**3 + 2*l**5 - 3*l**4 + 2*l.
2*l*(l + 1)**4
Suppose -37*f + 138 + 47 = 0. Determine o so that 4/5*o**4 - 2/5*o**3 + 0*o + 0*o**2 - 2/5*o**f + 0 = 0.
0, 1
Let g be (-6)/4*(-12)/(-99). Let l = g + 4/11. Find t, given that 2/11 + l*t**2 - 4/11*t = 0.
1
Let y(h) be the third derivative of -1/6*h**4 + 1/30*h**6 + 0 + 2/15*h**5 - 1/3*h**3 + 0*h - 1/35*h**7 + 2*h**2. Suppose y(q) = 0. What is q?
-1, -1/3, 1
Let k(w) = -5*w + 12. Let y be k(4). Let p be y/(-12) - 4/6. Suppose -6/7*x**3 + p*x + 2/7*x**4 + 0 + 4/7*x**2 = 0. Calculate x.
0, 1, 2
Let z(g) = -g**3 + g**2. Let j(b) = -4*b**3 + 6*b**2. Let p = 13 - 14. Let w(n) = p*j(n) + 5*z(n). Suppose w(d) = 0. What is d?
-1, 0
Let j(z) = -z**2 - z. Let f(s) = s + 9*s + 2*s + 0*s + 12*s**2. Let b(k) = f(k) + 15*j(k). Factor b(l).
-3*l*(l + 1)
Let k(u) = 6*u**3 - 15*u**2 + 20*u + 23. Let f(j) = -2*j**3 + 5*j**2 - 7*j - 8. Let m(l) = 17*f(l) + 6*k(l). Factor m(t).
(t - 2)*(t - 1)*(2*t + 1)
Let b(s) be the first derivative of 16/39*s**3 + 2/13*s**4 + 2/13*s + 5/13*s**2 - 1. Factor b(g).
2*(g + 1)*(2*g + 1)**2/13
Let h = -36 + 46. Let b be -5*(-2)/h + 1. Let -3/7*z - 3/7*z**3 - 6/7*z**b + 0 = 0. What is z?
-1, 0
Determine f, given that 13*f**3 + 3*f**2 - 22*f**3 + 15*f**3 + 3*f**4 = 0.
-1, 0
Factor t**3 - 2*t**2 + 8*t**3 - 3*t**4 + 5*t**5 + t**4 - 10*t**4.
t**2*(t - 1)**2*(5*t - 2)
Let f be 1/7*(-21 - -22). Let k(x) be the third derivative of 0*x + 0 + 8/21*x**3 - 1/420*x**6 + x**2 - f*x**4 + 1/35*x**5. Let k(b) = 0. Calculate b.
2
Let j = 21 + 0. Let r be 10/6 - (-7)/j. Factor 2/3*d + d**r - 1/3.
(d + 1)*(3*d - 1)/3
Let z(m) be the third derivative of m**6/420 - m**4/28 - 2*m**3/21 - 6*m**2. Factor z(a).
2*(a - 2)*(a + 1)**2/7
Let j(i) = -2*i**3. Let c(q) = -q**5 - q**4 + 2*q**2 - q - 1. Let u(d) = -2*c(d) + 2*j(d). Find y, given that u(y) = 0.
-1, 1
Let f(m) = -8*m**2 - 5*m + 7. Let r(k) = -105*k**2 - 65*k + 90. Let q(b) = -40*f(b) + 3*r(b). Determine z, given that q(z) = 0.
-2, 1
Suppose 2*j - 3*j = -5. Let -j + 3 - 2 + 4*a**2 = 0. Calculate a.
-1, 1
Let o(c) be the third derivative of -c**5/90 - c**4/9 - 24*c**2. Factor o(r).
-2*r*(r + 4)/3
Let n(l) be the first derivative of l**5/10 - l**4/2 + 2*l**3/3 + l - 3. Let q(u) be the first derivative of n(u). Factor q(k).
2*k*(k - 2)*(k - 1)
Let l(h) = -h**2 + 12*h - 11. Let f be l(11). Suppose -5*t + 4 + 6 = f. Determine u so that u**2 - t*u + 2*u**2 - u + 2*u = 0.
0, 1/3
Let n(r) be the third derivative of -r**6/240 - r**5/60 - r**4/48 + 4*r**2. Factor n(c).
-c*(c + 1)**2/2
Let c(l) be the second derivative of l**7/4200 - l**6/900 + l**5/600 - l**3/2 - 2*l. Let q(v) be the second derivative of c(v). What is i in q(i) = 0?
0, 1
Suppose 0 = -2*q - 3*f - 81, -2*f = -2*q - 0*f - 56. Let x be 6/q - 4/(-22). Solve 0*r**2 - 1/4*r + 0*r**4 + 1/2*r**3 + x - 1/4*r**5 = 0.
-1, 0, 1
Let t = -91/4 - -23. Factor -t*g + 3/4*g**2 + 1/4*g**4 - 3/4*g**3 + 0.
g*(g - 1)**3/4
Let k be 6*(3 - 32/12). Let m(i) be the first derivative of -4/5*i**3 + 2/5*i**4 - k - 2/25*i**5 + 4/5*i**2 - 2/5*i. Find j such that m(j) = 0.
1
Let z(f) be the first derivative of 1/5*f**5 + 0*f**4 - 2*f - 1/3*f**3 + 0*f**2 + 3 + 0*f**6 - 1/21*f**7. Let m(s) be the first derivative of z(s). Factor m(l).
-2*l*(l - 1)**2*(l + 1)**2
Let m(d) = 7*d**2 - d + 5. Let p(a) = -6*a**2 - 4. Let y(q) = 4*m(q) + 5*p(q). Factor y(g).
-2*g*(g + 2)
Let f(v) be the third derivative of -v**7/63 + 37*v**6/180 - 7*v**5/45 + 40*v**2. What is c in f(c) = 0?
0, 2/5, 7
Factor 1/2*k**2 - 4*k + 6.
(k - 6)*(k - 2)/2
Let t(z) be the second derivative of z**5/100 + z**4/30 + z**3/30 + 6*z. Factor t(b).
b*(b + 1)**2/5
Let a(r) be the second derivative of r**6/90 - r**5/20 + r**4/12 - r**3/18 + 9*r. Factor a(c).
c*(c - 1)**3/3
Let m(k) be the second derivative of 0*k**2 + 0 - 3/40*k**5 - 6*k + 0*k**4 + 1/4*k**3. Find p, given that m(p) = 0.
-1, 0, 1
Factor -2/7*d - 3/7*d**2 + 0 - 1/7*d**3.
-d*(d + 1)*(d + 2)/7
Let b(d) = -d**4 + d**3 + d**2 + 1. Let o(p) = 3*p**5 - 9*p**4 + 6*p**3 + 9*p**2 + 9. Let r be (4 + -1)*(-1)/3. Let l(s) = r*o(s) + 9*b(s). Factor l(g).
-3*g**3*(g - 1)*(g + 1)
Let o(p) = -p**4 - p**2 - p. Let b(x) = -3*x**4 + 2*x**3 + x**2 - 10*x + 4. Let z(s) = -3*b(s) + 6*o(s). Solve z(r) = 0.
-2, 1, 2
Let w = 201 + -199. Find n, given that 2/5*n**w + 0*n - 2/5 = 0.
-1, 1
Suppose -2*i + 2 + 12 = 0. Factor 5*n**2 + n**2 - 2*n**2 - i*n**2 + 2*n.
-n*(3*n - 2)
Let a(n) be the first derivative of -4 + 1/2*n**6 - 9/4*n**4 + 6*n**2 + 6/5*n**5 + 0*n - 4*n**3. Factor a(y).
3*y*(y - 1)**2*(y + 2)**2
Factor 6 + 0*k - k**2 + 2*k**4 + 4*k - 7*k**2 - 4*k**3.
2*(k - 3)*(k - 1)*(k + 1)**2
Let z(k) be the second derivative of -k**7/2100 - k**6/1800 - k**4/12 + k. Let y(o) be the third derivative of z(o). Solve y(i) = 0.
-1/3, 0
Factor 0 + 1/4*c**2 + 1/8*c + 1/8*c**3.
c*(c + 1)**2/8
Let d = -10 - -20. Suppose -2*k - 2*a - d = -4*k, a = -2. Factor 0 + 2/7*h**4 - 2/7*h**k + 2/7*h - 2/7*h**2.
2*h*(h - 1)**2*(h + 1)/7
Let y(n) be the second derivative of n**6/480 - n**5/96 + n**4/48 - n**3/3 + 2*n. Let w(j) be the second derivative of y(j). Factor w(s).
(s - 1)*(3*s - 2)/4
Determine n so that -1/3*n**4 + 0 - 16/3*n**2 + 0*n + 8/3*n**3 = 0.
0, 4
Factor 16*g**2 + 9*g + 3*g + 8*g**3 - 4*g**3.
4*g*(g + 1)*(g + 3)
Let x(g) = -g**5 - 4*g**4 - 2*g**3 + 3*g. Let j(p) = -3*p**5 - 11*p**4 - 5*p**3 + 8*p. Let a(t) = -4*j(t) + 11*x(t). Determine s, given that a(s) = 0.
-1, 0, 1
Factor -9/2*f + 3/2*f**2 + 3.
3*(f - 2)*(f - 1)/2
Let h(q) be the first derivative of 1/7*q**2 - 6 + 4/21*q**6 - 8/35*q**5 - 3/14*q**4 + 4/21*q**3 + 0*q. Let h(g) = 0. Calculate g.
-1/2, 0, 1
Factor 3 + 1 - y**4 - 6 + 3*y**3 - y**2 - 3*y + 4.
-(y - 2)*(y - 1)**2*(y + 1)
Let l(w) be the second derivative of w**7/2100 - w**5/300 + 5*w**3/6 + 4*w. Let f(v) be the second derivative of l(v). Determine g, given that f(g) = 0.
-1, 0, 1
Factor 1/3*x**2 + 0*x + 0.
x**2/3
Let k = 3/14 - -16/7. Suppose -3*g - 5 - 1 = 3*p, -3*g = 4*p + 9. Factor 2*d**2 + g - 1/2*d**3 - k*d.
-(d - 2)*(d - 1)**2/2
Let r be -6*1/(-9) - 2/3. Factor 2/5*h**5 + 0 + r*h - 2/5*h**3 + 0*h**4 + 0*h**2