z**4 + 13*z**3 + 2*z**2 - 8*z + 5. Let g(t) = -3*t**4 + 6*t**3 + t**2 - 4*t + 2. Let a(o) = -15*g(o) + 6*x(o). Determine i, given that a(i) = 0.
-1, 0, 1, 4
Let h(m) be the second derivative of -m**6/10 + 3*m**5/20 + m**4 - 2*m**3 - 2*m. Factor h(n).
-3*n*(n - 2)*(n - 1)*(n + 2)
Let x(z) be the second derivative of -2/45*z**5 + 5*z + 1/27*z**4 + 1/9*z**2 + 0 - 1/45*z**6 + 4/27*z**3. Determine q so that x(q) = 0.
-1, -1/3, 1
Let o = -190 + 1333/7. Let x(q) be the first derivative of -4/7*q + 2/21*q**3 + 3/14*q**4 - 1 - o*q**2 + 2/35*q**5. Factor x(f).
2*(f - 1)*(f + 1)**2*(f + 2)/7
Let q(z) be the first derivative of z**2 - 3 + 0*z + 1/4*z**4 - 1/10*z**5 + 1/60*z**6 - 1/3*z**3. Let k(w) be the second derivative of q(w). Factor k(v).
2*(v - 1)**3
Let k(a) be the second derivative of 0*a**2 - 1/20*a**5 + 3*a + 1/12*a**4 - 1/24*a**3 + 0. Let k(d) = 0. Calculate d.
0, 1/2
Suppose -2*g + 15 = 3*j, -9 = 2*j - j - 4*g. Suppose p - 7 = -u, -j*p + 4*p - 17 = -3*u. Solve -p*a**3 - 2*a**4 + 0*a**2 - 1/2*a**5 + 0 + 0*a = 0 for a.
-2, 0
Factor 1/2 + 5/2*u**2 - 2*u - u**3.
-(u - 1)**2*(2*u - 1)/2
Let r(x) be the first derivative of -2*x**3/39 - 3*x**2/13 + 6. Find a, given that r(a) = 0.
-3, 0
Let z(k) be the second derivative of k**6/105 - k**4/42 - 12*k. Factor z(h).
2*h**2*(h - 1)*(h + 1)/7
Factor -1/3*u**4 + 0*u + 0 + 0*u**3 + 4/3*u**2.
-u**2*(u - 2)*(u + 2)/3
Factor 3/2*d**2 + 2 + d**3 - 1/2*d**4 - 4*d.
-(d - 2)*(d - 1)**2*(d + 2)/2
Let s(u) be the third derivative of u**9/15120 - u**8/5040 + u**5/15 - 2*u**2. Let a(f) be the third derivative of s(f). Solve a(o) = 0 for o.
0, 1
Let k(t) be the second derivative of -t**5/20 - t**4/6 - t**3/6 + 16*t. Let k(j) = 0. Calculate j.
-1, 0
Suppose g - 3*g = -18. Suppose -5*c = j - 42, 2*c - 3*j + g = 36. Solve -c*l + l - 2*l**2 + 0*l**2 - 6 - 2 = 0.
-2
Let u be -2 + (11 - 3 - 4). Let y(h) be the first derivative of -5/8*h**4 + h + 2*h**3 - 1 - 9/4*h**u. Find l such that y(l) = 0.
2/5, 1
Let w(a) be the third derivative of 0*a**6 - 1/840*a**7 + 0*a**3 + 3*a**2 + 0*a + 0*a**4 + 1/240*a**5 + 0. Find j, given that w(j) = 0.
-1, 0, 1
Factor -1/3*d + 1/3*d**2 - 2/3.
(d - 2)*(d + 1)/3
Let a(m) be the second derivative of -5*m**7/14 + 17*m**6/10 - 63*m**5/20 + 11*m**4/4 - m**3 + 5*m. Let a(o) = 0. What is o?
0, 2/5, 1
Factor -2/9*w**5 + 2/3*w**4 + 2/9*w**2 + 0 - 2/3*w**3 + 0*w.
-2*w**2*(w - 1)**3/9
Let c = 6 + -8. Let u(n) = -n**3 + 5*n**2 + n - 2. Let q(x) = x**2. Let k(o) = c*u(o) + 6*q(o). Solve k(l) = 0.
-1, 1, 2
Let j(h) = h**2 + 3*h + 4. Let w be j(-3). Factor s**3 + s**2 + 11*s + 0*s**3 - 12*s - s**w.
-s*(s - 1)**2*(s + 1)
Let j(k) be the first derivative of k**5/270 - k**4/108 - 3*k**2/2 - 2. Let p(g) be the second derivative of j(g). Factor p(y).
2*y*(y - 1)/9
Factor -2*w**2 - 4 + 0*w**2 + 4*w**2 - 2*w.
2*(w - 2)*(w + 1)
Let t(y) = -y**3 + 6*y**2 + y - 2. Let v be t(6). Suppose 54 = -3*w + v*w. Factor 46*l**4 + 4*l + w*l**3 + 0*l + 14*l**5 + 17*l**2 + 9*l**2.
2*l*(l + 1)**3*(7*l + 2)
Let q be 9 + (-6 - (3 + -6)). Suppose 3*f**2 - 1 - q*f - 6*f + 13 = 0. What is f?
2
Let k(t) = t**2 + 7*t + 2. Let x be (5 - -4)/(-3) - 4. Let n be k(x). Factor -18/5 + 12/5*z - 2/5*z**n.
-2*(z - 3)**2/5
Let t(o) be the third derivative of -o**7/8820 + o**6/2520 + o**4/12 - o**2. Let a(k) be the second derivative of t(k). Factor a(w).
-2*w*(w - 1)/7
Let a(q) = -8*q**3 + 4*q**2 + 20*q + 12. Let b(r) = -9*r**3 + 6*r**2 + 21*r + 11. Let i(w) = 5*a(w) - 4*b(w). Solve i(u) = 0 for u.
-2, -1, 2
Let p = -6 + 8. Let g(q) = q + 2*q**p + q + q + 0 + 1. Let i(r) = -2*r**2 - 4*r - 2. Let f(h) = -2*g(h) - 3*i(h). Factor f(l).
2*(l + 1)*(l + 2)
Suppose 4*r = -8, 0*k + 18 = 5*k + r. Let n(y) be the third derivative of 4*y**2 + 0 - 1/24*y**k + 0*y - 1/120*y**5 - 1/12*y**3. Factor n(v).
-(v + 1)**2/2
Let u(v) be the third derivative of -v**8/448 + v**7/56 - v**6/16 + v**5/8 - 5*v**4/32 + v**3/8 + 2*v**2. Find q such that u(q) = 0.
1
Let i(r) = r**4 - r**3 - r**2 - r + 1. Let t(a) = -2*a**5 + 10*a**4 - 34*a**3 + 54*a**2 - 28*a + 4. Let f(u) = -4*i(u) - t(u). Factor f(v).
2*(v - 2)**2*(v - 1)**3
Suppose -3*d = t - 2*t - 6, -6 = -3*d + 5*t. Factor n**2 - d*n + n + 1 - 1.
n*(n - 1)
Let 1/4*m**2 + 1/4*m + 0 = 0. What is m?
-1, 0
Let j(q) be the first derivative of q**3 - 9*q**2/2 - 24. Find r, given that j(r) = 0.
0, 3
Suppose -1/10*b**4 - 1/5*b**3 + 0 - 1/10*b**2 + 0*b = 0. Calculate b.
-1, 0
Let h = 307408/5 - 60987. Let b = h + -493. Factor -8/5 - 2/5*x**2 + b*x.
-2*(x - 2)**2/5
Factor 1/2*f**3 - f**4 + 0 + 0*f + 0*f**2 + 1/2*f**5.
f**3*(f - 1)**2/2
Suppose v + 0 = 4. Suppose v*u = 8*u. Factor 0*j + 0 + u*j**2 - 1/2*j**3.
-j**3/2
Let h be (3/21)/((-16)/(-196)). Factor -15/4*x**2 - 19/4*x**3 - h*x**4 - 1/4*x + 1/2.
-(x + 1)**3*(7*x - 2)/4
Let m = 826/5 - 164. Let b be 28/30 + (-4)/(-6). What is y in 2/5 - b*y**2 - m*y = 0?
-1, 1/4
Let b(r) = -3 - 2 - 4 - 11*r - 15*r**2 - 2*r**3 - 2. Let l(i) = -5 - i**3 + 0*i**3 - 5*i - 11*i**2 + 4*i**2. Let j(h) = 6*b(h) - 13*l(h). Factor j(o).
(o - 1)*(o + 1)**2
Find t such that 0*t - 2/5*t**2 + 0 + 2/15*t**3 = 0.
0, 3
Let l(u) be the first derivative of -8/5*u - 16/5*u**2 - 2*u**3 + 2. Factor l(c).
-2*(3*c + 2)*(5*c + 2)/5
Solve -5 + k**2 + 4 - 4 + 4 = 0 for k.
-1, 1
Let p(s) be the first derivative of s**6/21 + 4*s**5/35 - 4*s**3/21 - s**2/7 + 13. Let p(g) = 0. Calculate g.
-1, 0, 1
Let d be 2/4*(18 - 6). Suppose 0 = -3*b + z + d, -z - 4 = -2*b - 0*z. What is s in 2/5*s**3 - 2/5*s**5 + 0 + 0*s**b + 0*s**4 + 0*s = 0?
-1, 0, 1
Let c(g) be the first derivative of -1/6*g**3 + 1/8*g**4 - 1/2*g**2 + 2 + 0*g. Factor c(j).
j*(j - 2)*(j + 1)/2
Let a(j) be the first derivative of j**5/15 + j**4/4 + j**3/9 - j**2/2 - 2*j/3 - 5. Factor a(n).
(n - 1)*(n + 1)**2*(n + 2)/3
Suppose -97 = -5*q + 108. Factor 41 + 3*y - q - y**2.
-y*(y - 3)
Let 1/2*p**3 + 0*p**2 + 0*p - 1/2*p**4 + 0 = 0. Calculate p.
0, 1
Let m(o) be the third derivative of 11*o**6/210 + 8*o**5/35 + 5*o**4/14 + 4*o**3/21 - 17*o**2. Factor m(g).
4*(g + 1)**2*(11*g + 2)/7
Let i(g) = g**4 + g**3 - 1. Let l(o) = 10*o**4 + 12*o**3 + 3*o**2 - 5*o - 9. Let q(x) = -44*i(x) + 4*l(x). Let q(p) = 0. What is p?
-2, 1
Let p(w) be the third derivative of w**9/20160 - w**7/3360 - w**4/24 + 2*w**2. Let t(q) be the second derivative of p(q). Let t(f) = 0. What is f?
-1, 0, 1
Factor -3*a**2 - 11*a - 12*a**2 + 3*a**3 + 15 + 8*a.
3*(a - 5)*(a - 1)*(a + 1)
Let u(r) be the first derivative of r**6/48 - r**5/8 + 7*r**4/32 - r**3/8 + 8. Factor u(g).
g**2*(g - 3)*(g - 1)**2/8
Let j = 30/13 - 171/91. What is a in j - 3/7*a**2 + 0*a = 0?
-1, 1
Let s(o) = -o**3 + o. Let q(l) = 4*l**3 + 10*l**2 - 22*l + 8. Let f(m) = q(m) + 6*s(m). Let f(v) = 0. What is v?
1, 2
Solve 0 + 12/7*m - 4/7*m**3 + 8/7*m**2 = 0.
-1, 0, 3
Find a such that -3*a**2 + a - 1 + 2*a + 0*a**3 + a**3 + 0*a**3 = 0.
1
Let z(c) = -2*c - 6. Let t be z(-4). Factor 4 + 2*y - 2*y**3 + 6*y - 4*y - t*y - 4*y**2.
-2*(y - 1)*(y + 1)*(y + 2)
Let f(p) be the first derivative of -5*p**4/4 + 25*p**3 - 375*p**2/2 + 625*p - 19. Find h such that f(h) = 0.
5
Suppose -3*b = -36 - 0. Suppose 0 = 2*c + 2 - b. Factor 1/4*f**3 + 0*f**2 + 0*f + 0 + 0*f**4 - 1/4*f**c.
-f**3*(f - 1)*(f + 1)/4
Factor -72/5*s**2 - 27/5*s**3 - 48/5*s + 0 - 3/5*s**4.
-3*s*(s + 1)*(s + 4)**2/5
Let b(h) = -h + 7. Let y be b(5). Let c(t) be the second derivative of -y*t + 1/80*t**5 + 0 + 1/24*t**3 - 1/24*t**4 + 0*t**2. Factor c(f).
f*(f - 1)**2/4
Let s be -5*(-12)/405*2/32. Let b(z) be the third derivative of 0*z + 0*z**3 + 0 - 3*z**2 - 1/270*z**5 + s*z**4. Suppose b(w) = 0. Calculate w.
0, 1
Let j be (-3)/(-6)*(-8)/(-10). Let r = 6 - 3. Factor 4/5 - 2/5*t + j*t**4 - 6/5*t**2 + 2/5*t**r.
2*(t - 1)**2*(t + 1)*(t + 2)/5
Let l = 12/85 + 56/85. Determine s, given that 2/5*s**2 + 4/5*s**3 + 0 - 2/5*s**4 - l*s = 0.
-1, 0, 1, 2
Let f be 2 + -3 + (-1 - -11). Suppose 16 - 19 - f*l**2 - 3*l**3 - 5*l - 4*l = 0. Calculate l.
-1
Let c(h) be the third derivative of -h**5/240 + h**4/16 - 3*h**3/8 + 6*h**2. Find p such that c(p) = 0.
3
Let f(a) = -17*a**2 - 11*a + 6. Let o(n) = 6*n**2 + 4*n - 2. Let d(z) = 4*f(z) + 11*o(z). Factor d(s).
-2*(s - 1)*(s + 1)
Let l(w) be the third derivative of 1/540*w**6 + 0 - 1/108*w**4 - 1/270*w**5 + w**2 + 0*w + 1/27*w**3. Factor l(c).
2*(c - 1)**2*(c + 1