*h**3 - 3*h**5 - 2*h - 3*h**3 + 9*h**3 - h.
-3*h*(h - 1)**2*(h + 1)**2
Suppose -3*n + 5*c = -6, 3 = 5*n - c - 7. Find x, given that -4*x**3 - 4*x**2 + x**2 + 12*x**n - 8*x**4 - 7*x**4 - 2*x = 0.
-1, 0, 1/3, 2/5
Let r be (10/(-70))/(12/(-14)). Let n(g) be the second derivative of 0*g**2 + 1/30*g**6 - 3*g + 0 + 1/4*g**4 - r*g**3 - 3/20*g**5. Find o such that n(o) = 0.
0, 1
Let m(t) be the second derivative of -5*t**4/4 - 35*t**3/6 - 5*t**2 - t. Factor m(l).
-5*(l + 2)*(3*l + 1)
Find n, given that 2/3*n**2 + 0 - n**3 + 0*n = 0.
0, 2/3
Let w(b) = -b**2 - 4*b - 1. Let q be w(-3). What is z in 2*z**4 - 3*z**2 + 6*z**3 + 7*z**2 + 2*z + 2*z**q = 0?
-1, 0
Let k(b) be the third derivative of b**7/210 + b**6/48 - b**5/40 + 8*b**2. Find v, given that k(v) = 0.
-3, 0, 1/2
Let w be 2/(-4) + 7/6. Let a(r) be the first derivative of -2 + 0*r + 2/7*r**2 + 5/14*r**4 - w*r**3. Factor a(f).
2*f*(f - 1)*(5*f - 2)/7
Let l be (-87)/(-90) + (-23)/10 + 2. Factor -4/3*c + 1/3*c**3 + 8/3 - l*c**2.
(c - 2)**2*(c + 2)/3
Let z = 20 + -18. Let l(q) be the second derivative of 1/12*q**4 + 0*q**z + 1/6*q**3 + 0 + q. Factor l(u).
u*(u + 1)
Let f(a) = -2*a**2 - 2*a + 4. Let r(w) = 6*w**2 + 5*w - 11. Suppose 55 = 4*u + u. Let o(x) = u*f(x) + 4*r(x). Factor o(l).
2*l*(l - 1)
Let q be (3 + -4 + (-1)/(-2))/(-1). Factor -q*j**2 + 0*j + 1/2*j**3 + 0.
j**2*(j - 1)/2
Let o = -7 + 5. Let x be (1/(-3))/(1/o). Factor 2/3 + x*k**2 - 4/3*k.
2*(k - 1)**2/3
Let d(p) be the first derivative of 1/6*p**4 + 1 + 8/9*p**3 + 4/3*p**2 + 0*p. Determine c so that d(c) = 0.
-2, 0
Let h(k) be the third derivative of -k**7/735 + k**6/105 - 2*k**5/105 + 4*k**2. What is r in h(r) = 0?
0, 2
Let b = 6041/20 - 302. Let s(l) be the first derivative of 1/4*l**4 + 1/2*l**2 - 1/2*l**3 - b*l**5 - 2 - 1/4*l. Factor s(c).
-(c - 1)**4/4
Let s(u) be the second derivative of 4/7*u**2 + 13/42*u**4 + 1/105*u**6 - u + 4/7*u**3 + 3/35*u**5 + 0. Factor s(o).
2*(o + 1)**2*(o + 2)**2/7
Let y(s) be the first derivative of s**6/360 - s**4/72 - s**2 + 2. Let x(h) be the second derivative of y(h). Factor x(d).
d*(d - 1)*(d + 1)/3
Let k(s) = s**3 - 3*s**2 + 4*s - 2. Suppose -2*j - 5*n = 16, -5*j = -4*n + 2 - 28. Let y be k(j). Solve -p**3 - 16/3*p - 13/3*p**y - 4/3 = 0.
-2, -1/3
Let x = 555/14 + -77/2. Suppose 2/7*o**2 + 6/7 + x*o = 0. Calculate o.
-3, -1
Let d = -9 + 15. Let p = d - 4. Let 3*i**2 - 4*i**p + 0*i**2 + 2 - 4*i + 3*i**2 = 0. What is i?
1
Factor -f + 1/2 - 1/8*f**3 + 5/8*f**2.
-(f - 2)**2*(f - 1)/8
Let n(v) be the third derivative of 0*v**3 + 1/30*v**5 + 0*v**4 - v**2 + 0 + 0*v. Find w, given that n(w) = 0.
0
Determine q, given that -20*q**4 + 0 - 2/3*q**3 + 8*q + 56/3*q**2 - 6*q**5 = 0.
-3, -2/3, 0, 1
Let s(m) be the first derivative of m**6/12 + 3*m**5/10 + m**4/4 - m**3/3 - 3*m**2/4 - m/2 - 10. Factor s(o).
(o - 1)*(o + 1)**4/2
Let w(i) be the second derivative of -i**8/1680 - i**7/420 - i**6/360 + i**3/2 - 3*i. Let u(h) be the second derivative of w(h). Let u(s) = 0. What is s?
-1, 0
Let c(g) = g + 2. Let b be c(-1). Let t be (-12)/30*(-4 - b). Factor 2/3*z + 8*z**3 + 2*z**5 - 20/3*z**4 - 4*z**t + 0.
2*z*(z - 1)**3*(3*z - 1)/3
Let t(r) = 6*r**4 + 6*r**3 + 8*r**2 - 6*r - 7. Let b(p) = -5*p**4 - 5*p**3 - 7*p**2 + 5*p + 6. Let q(n) = -7*b(n) - 6*t(n). Factor q(g).
-g*(g - 1)*(g + 1)**2
Let h(r) be the third derivative of -r**5/300 + r**4/120 + 22*r**2. Suppose h(b) = 0. What is b?
0, 1
Let x(s) be the first derivative of 2*s**5/75 - 2*s**4/15 - 4. Factor x(d).
2*d**3*(d - 4)/15
Find d, given that 4/3*d**2 - 4*d + 8/3 = 0.
1, 2
Factor 34*z**2 - 15*z**2 + 3*z + 3*z**4 - z**5 - 21*z**2 - 2*z**3 - 1.
-(z - 1)**4*(z + 1)
Let -3/7*k + 3/7*k**3 + 2/7 - 1/7*k**2 - 1/7*k**4 = 0. What is k?
-1, 1, 2
Let u = -9 + 5. Let f = 7 + u. Solve 2*w + 6 - 3*w**f + 10*w - 3*w + 0*w = 0.
-1, 2
Let l(k) = 105*k**2 - 33*k + 3. Let r(j) = -9*j**2 - 5*j. Let h(i) = 5*i**2 + 3*i. Let q(s) = 7*h(s) + 4*r(s). Let v(c) = -l(c) + 3*q(c). Factor v(m).
-3*(6*m - 1)**2
Let p(x) = -x**2 - 3*x + 5. Let q be p(-4). Suppose 5 = 3*a - 1. Determine d, given that -q - 2*d**2 + 0*d + d**2 - a*d = 0.
-1
Factor -5 - 33*i**2 - 16*i - 11 + 29*i**2.
-4*(i + 2)**2
Let y(j) = j - 8. Let q be y(6). Let o be 4 - -3*q/6. Factor 3*c**2 + 2*c + 8*c**3 - 6*c**o + c**2.
2*c*(c + 1)**2
Let m(u) be the first derivative of 3 + 1/10*u**5 + 1/8*u**4 + 0*u + 0*u**3 + 0*u**2. Factor m(j).
j**3*(j + 1)/2
Suppose 6*x = 1 + 35. Factor 18*y**3 - 2/3 - 18*y**2 + x*y.
2*(3*y - 1)**3/3
Let r be -11 - -9 - 4*2. Let v be 14/10 + (-6)/r. Determine z so that 2/3*z**3 + v*z + 2/3 + 2*z**2 = 0.
-1
Let i = 11/2 - 21/4. What is p in -1/4*p**5 + 0*p + 1/4*p**2 + 0 - i*p**4 + 1/4*p**3 = 0?
-1, 0, 1
Suppose -2*z = -0*z - 5*z. What is o in z*o + 0 + 1/2*o**5 - 5/2*o**4 - 2*o**2 + 4*o**3 = 0?
0, 1, 2
Let v(r) be the third derivative of -r**6/1260 + r**4/84 - r**3/6 + 3*r**2. Let k(z) be the first derivative of v(z). Factor k(q).
-2*(q - 1)*(q + 1)/7
Let t be 0 + 2/1 + 0. Let n = 4 - t. Find h such that -6*h**2 + 2*h - n*h**2 + 7*h**2 = 0.
0, 2
Suppose -36 = 41*z - 118. Find u, given that 14/3*u**5 + 0*u**z - 10/3*u**4 + 0 - 4/3*u**3 + 0*u = 0.
-2/7, 0, 1
Let a = 34 + -28. Let g(r) be the third derivative of -1/42*r**4 - 1/42*r**5 + 0*r + 0*r**3 + 0 + 1/60*r**a + r**2. Factor g(f).
2*f*(f - 1)*(7*f + 2)/7
Factor -m + m**3 - 2*m**3 - 2*m - 2*m + 4*m**2 + 2.
-(m - 2)*(m - 1)**2
Let j(s) = -81*s**2 - 321*s - 399. Let i(p) = 5*p**2 + 20*p + 25. Let h(a) = 33*i(a) + 2*j(a). Solve h(v) = 0 for v.
-3
Let n be ((-14)/(-27))/(-1 - 8/(-6)). Suppose 10/9*m**4 - 2*m**2 - 8/9*m - 2/3*m**5 + n*m**3 + 8/9 = 0. What is m?
-1, 2/3, 1, 2
Factor 2/19*f**3 + 12/19*f**2 + 18/19*f + 8/19.
2*(f + 1)**2*(f + 4)/19
Factor 3*a - 2*a**2 - 9 + 3*a**4 - 2*a**3 - a**5 + 0*a**3 + 8.
-(a - 1)**4*(a + 1)
Suppose 3*j = 13 - 1. Find a such that 5*a**j + 65*a**5 - 67*a**5 - 3*a**4 = 0.
0, 1
Let y(g) = -g + 3. Let w be y(0). Let b = -81/2 - -41. Factor -z - b*z**w + 0 - 3/2*z**2.
-z*(z + 1)*(z + 2)/2
Let f(p) = 4*p**2 + 2*p - 6. Let r(m) = -m**2 + m. Let s(h) = f(h) + 2*r(h). Suppose s(t) = 0. What is t?
-3, 1
Let p(y) = y**5 + 4*y**3 + 2*y**2 - 3*y + 2. Let m(r) = -7*r**5 - 25*r**3 - 13*r**2 + 19*r - 13. Let h(q) = -6*m(q) - 39*p(q). Factor h(k).
3*k*(k - 1)**2*(k + 1)**2
Let t = 6 - 4. Factor -4*x - 33*x**3 - 2*x + 18*x**t + 21*x**2.
-3*x*(x - 1)*(11*x - 2)
Let l(n) be the second derivative of -n**6/120 - n**5/40 - 7*n. Factor l(g).
-g**3*(g + 2)/4
Suppose 4*m + k - 2 = 1, -20 = -5*m + 2*k. Let j = 44/5 - 42/5. Suppose -4/5 - j*a**m + 6/5*a = 0. What is a?
1, 2
Let n(c) be the second derivative of 2*c**6/45 - c**5/30 - c**3 - 5*c. Let j(d) be the second derivative of n(d). Let j(l) = 0. What is l?
0, 1/4
What is k in 1/6*k**2 + 0*k - 1/6 = 0?
-1, 1
Determine a, given that -2/7*a**4 + 4/7 - 10/7*a + 6/7*a**2 + 2/7*a**3 = 0.
-2, 1
Factor 56*x**2 - 60*x**3 - 45*x + 6*x**4 - 56 + 46*x**2 + 2 + 15*x**3.
3*(x - 3)**2*(x - 2)*(2*x + 1)
Let t(g) = -6*g**2 - 9*g - 9. Let u(q) be the third derivative of q**5/60 + q**3/6 + 3*q**2. Let v(c) = -t(c) - 3*u(c). Determine x, given that v(x) = 0.
-2, -1
Let m(d) be the second derivative of -1/21*d**3 + 0 - 4*d - 1/21*d**4 - 1/70*d**5 + 0*d**2. Let m(z) = 0. What is z?
-1, 0
Let q(u) be the first derivative of -u**6/180 + u**3/3 - 1. Let o(k) be the third derivative of q(k). Let o(v) = 0. Calculate v.
0
Let h = 2/2639 - -361313/303485. Let p = 1/115 + h. Factor 0 + 4/5*y - 24/5*y**3 - p*y**2 - 14/5*y**4.
-2*y*(y + 1)**2*(7*y - 2)/5
Suppose 5*x - 20 = -5*p, -4*p - 2*x + 16 - 4 = 0. Suppose p = 3*m - 4. Factor 0 + 1/3*i**m + 1/3*i**3 + 0*i.
i**2*(i + 1)/3
Let o(u) be the second derivative of 0 + 1/6*u**6 + 0*u**2 + 1/3*u**3 - 1/10*u**5 - 5/12*u**4 - 3*u. Suppose o(h) = 0. Calculate h.
-1, 0, 2/5, 1
Let y(t) = -t**2 - 6*t - 6. Let m be y(-3). Factor 10*l**3 - 14*l**m - 9*l - 7*l - 16*l**2.
-4*l*(l + 2)**2
Let l(c) = c**3 - 2*c**2 + c. Let i be l(2). Let p be ((-6)/5)/(-3) - (-3)/(-20). Factor 1/2*m - 1/4 - p*m**i.
-(m - 1)**2/4
Let r(m) = -m**5 - 12*m**4 - m**3 + 9*m**2 + 8*m + 3. Let b(u) = 4*u**5 + 60*u**4 + 4*u**3 - 44*u**2 - 40*u - 16. Let o(y) = 3*b(y) + 16*r(y). Solve o(p) = 0.
-2, -1, 0, 1
Let a be 2 + ((-6)/14 - 10/(-7)). Factor -1/4*o**2 + 0*o + 1/4*o**4 + 0 + 0*o**a.
o**2*(o - 1)*(o + 1)/4
