- 18*q**3 + 3*q**4 - 51*q**4 + p*q**5 = 0.
-1, -1/4, 0
Let x(u) be the second derivative of -1/90*u**6 + 1/60*u**5 + 0*u**3 + 0*u**4 + 0*u**2 + 4*u + 0. Factor x(b).
-b**3*(b - 1)/3
Let x(w) be the third derivative of w**6/660 + w**5/110 + w**4/44 + w**3/33 - 5*w**2. Factor x(b).
2*(b + 1)**3/11
Let o(n) be the second derivative of 0*n**3 + 0*n**2 - 3*n + 0 - 1/24*n**4. Factor o(m).
-m**2/2
Let a(y) be the second derivative of 0*y**4 + 0*y**2 + 5*y + 0*y**5 + 0 + 1/105*y**6 + 0*y**3. What is l in a(l) = 0?
0
Let n be (5 + 0)*(-2)/(-5). Let z(s) = s**2 - 4. Let k be z(-3). Factor n*x**3 - k*x + 5*x.
2*x**3
Let n(h) = 7*h**2 + 11*h - 2. Let r(c) = c**2 + c + 1. Let g(z) = -n(z) + 6*r(z). Let d be g(-6). Let 7*a + 5*a**2 - 6*a - 4*a**2 + 0*a**d = 0. What is a?
-1, 0
Let b(x) be the second derivative of x**6/135 - x**5/90 - x**4/54 + x**3/27 + 8*x. Factor b(y).
2*y*(y - 1)**2*(y + 1)/9
Let h = -14 - -59/4. Find q, given that -1/4*q**4 + 0 + h*q**2 - 1/2*q + 0*q**3 = 0.
-2, 0, 1
Let x(p) be the second derivative of p**5/4 + 10*p**4/3 + 50*p**3/3 + 40*p**2 + 18*p. Factor x(f).
5*(f + 2)**2*(f + 4)
Let w(k) be the first derivative of 3*k**6/5 + 9*k**5/5 + 11*k**4/6 + 2*k**3/3 - k - 3. Let u(v) be the first derivative of w(v). Determine r so that u(r) = 0.
-1, -2/3, -1/3, 0
Let m(w) be the second derivative of -w**5/4 - 5*w**4/4 + 5*w**3/6 + 15*w**2/2 + 5*w. What is h in m(h) = 0?
-3, -1, 1
Suppose -2*k**2 - 3*k**2 + k**2 + 5*k**2 + 2*k = 0. What is k?
-2, 0
Factor 1/9 - 2/9*f + 1/9*f**2.
(f - 1)**2/9
Let v(j) be the third derivative of -j**5/270 - j**4/54 + j**3/9 + 2*j**2. Let v(z) = 0. What is z?
-3, 1
Suppose -2*h = -7*h + 60. Let d be (-20)/(-15)*h/14. Factor 6/7*n**2 - d - 8/7*n.
2*(n - 2)*(3*n + 2)/7
Factor 10*o**2 - 3*o**5 - 2*o**5 - 44 + 5*o + 44 - 10*o**4.
-5*o*(o - 1)*(o + 1)**3
Let t = 6 - 5. Suppose -2*o + 3 = -t. Factor -25*n**3 - 2*n + 0*n - o*n - 20*n**2.
-n*(5*n + 2)**2
Suppose 14*j**5 + 13*j**3 - 7*j**3 - 16*j**2 + 8*j + 5*j**4 - j**4 - 16*j**5 = 0. Calculate j.
-2, 0, 1, 2
Suppose -l = 5*a + 2*l - 21, -4 = -4*a + 4*l. Let b be (a/9)/(2/18). Solve -b*o**3 + 0*o**3 - 2*o**4 + 2*o**5 + 2*o**2 + o**3 = 0.
-1, 0, 1
Let x be (-18)/93*1/2. Let k = 89/279 + x. What is i in 4/9*i - k*i**2 - 2/9 = 0?
1
Suppose 784/5*k**4 + 136/5*k + 686/5*k**5 - 268/5*k**2 - 322/5*k**3 - 16/5 = 0. What is k?
-1, 2/7
Let g(n) be the second derivative of -n**6/21 - 4*n**5/35 - n**4/42 + 2*n**3/21 + 6*n. Factor g(c).
-2*c*(c + 1)**2*(5*c - 2)/7
Let n(c) be the second derivative of -c**5/10 - c**4/6 + 4*c**3/3 + 4*c**2 + 3*c. Factor n(i).
-2*(i - 2)*(i + 1)*(i + 2)
Suppose 4*z + 11*z = 2*z. Factor 2/9*m**4 - 4/9*m**2 + 0*m + 2/9 + z*m**3.
2*(m - 1)**2*(m + 1)**2/9
Solve 1/6*u**2 - 5/6*u + 2/3 = 0 for u.
1, 4
Suppose 1 = 2*a - 3. Let v = -127/2 + 643/10. Solve -1/5*x**3 - 4/5*x + 0 - v*x**a = 0.
-2, 0
Let f = -47263 + 1654024/35. Let o = 39/7 + f. Factor -o*w**2 - 8/5*w - 8/5.
-2*(w + 2)**2/5
Let y = -33 + 33. Let d(p) be the second derivative of 1/9*p**4 + y + 0*p**2 + 1/30*p**5 - 2*p + 1/9*p**3. Factor d(f).
2*f*(f + 1)**2/3
Let a(o) be the first derivative of o**4/8 - o**3/6 - o**2/2 - 4. Determine m, given that a(m) = 0.
-1, 0, 2
Let c(z) be the third derivative of z**7/350 - z**6/200 - 3*z**5/100 + z**4/40 + z**3/5 - 3*z**2. What is u in c(u) = 0?
-1, 1, 2
Let a be (12/9)/((-4)/42). Let i be 7/a*8/(-2). Factor 4*y**i - y - y - 2*y**3 + 0*y.
-2*y*(y - 1)**2
Let w(h) be the first derivative of -h**7/14 - h**6/5 + h**4/2 + h**3/2 + 4*h - 1. Let m(b) be the first derivative of w(b). Solve m(o) = 0 for o.
-1, 0, 1
Factor 10/3 + 2*s**2 + 6*s - 2/3*s**3.
-2*(s - 5)*(s + 1)**2/3
Let -4*h**2 + 9*h**2 - 3*h**2 - 4 - 2*h = 0. Calculate h.
-1, 2
Let u(z) be the third derivative of -2*z**2 - 1/420*z**5 + 0*z**3 + 0*z + 0 - 1/84*z**4. Factor u(l).
-l*(l + 2)/7
Suppose -4*j = 2*g - 12, -4 = 3*j - 2*g - 3*g. Let s = 13 + -4. Solve j + s*q**2 + 4*q + 5*q + 3*q**3 + 1 = 0 for q.
-1
Suppose 4*i - 3*z = 11, i - 2*z + 7 = 2*z. Suppose -i*h - 2*t = -16, -5*h - 5*t = -7 - 3. Solve s**h + 0*s**4 + 2*s**2 - s**3 - 4*s**2 = 0.
-1, 0, 2
Let u = -441 + 443. Suppose 1/4*q**u + 9/4 + 3/2*q = 0. Calculate q.
-3
Let l(s) = -s**4 - 3*s**3 + 3*s**2 + 5*s + 2. Let i(c) = -c**4 - c**3 - c**2. Let k(o) = -2*i(o) - l(o). Factor k(v).
(v - 1)*(v + 1)**2*(3*v + 2)
Let i be (1/(-6) + 9/(-27))*0. Factor 0*s + i + 1/5*s**2.
s**2/5
Let d(l) = l**2 + 5*l + 7. Let n be d(-4). Let g = n + -5/2. Factor -1/2*b - g*b**2 + 0.
-b*(b + 1)/2
Let k(v) = -2*v - v**2 + 5*v - 2*v. Let l(p) = 3*p**2 - p - 2. Let w(r) = 4*k(r) + l(r). Factor w(n).
-(n - 2)*(n - 1)
Let z(m) = -m**3 - 7*m**2 - 3*m + 3. Let g be (-1)/((-3)/(-21) + 0). Let k(a) = -2*a**3 - 13*a**2 - 6*a + 5. Let w(q) = g*z(q) + 4*k(q). Factor w(r).
-(r + 1)**3
Let f be (-11)/(-33)*(-1 + 1). Let b = f - -3. Factor -2/9*u + 0 + 4/9*u**2 - 2/9*u**b.
-2*u*(u - 1)**2/9
Let m(r) be the first derivative of r**6/15 + 6*r**5/25 - r**4/10 - 14*r**3/15 + 8*r/5 + 2. Let m(y) = 0. What is y?
-2, -1, 1
Let r = -1 - -3. Let w be (-3)/(-6) + r/(-8). Factor w*p**2 + 0*p - 1/2*p**3 + 0 + 1/4*p**4.
p**2*(p - 1)**2/4
Find v such that -8/7 - 16/7*v + 166/7*v**3 + 102/7*v**2 + 8*v**4 = 0.
-2, -1, -1/4, 2/7
Let a = -173/2 + 88. Let -3/2*b**4 + 0 - 5/2*b**5 + 7/2*b**3 + a*b**2 - b = 0. What is b?
-1, 0, 2/5, 1
Let q be (4/6)/(8/18). Factor q*a + a**2 + 1/2.
(a + 1)*(2*a + 1)/2
Factor -7 + 3*j**2 + 3*j**3 + 16 - 9.
3*j**2*(j + 1)
Let y(h) be the second derivative of -3/10*h**5 + 2*h - 1/15*h**6 + 0 + 0*h**2 - 1/2*h**4 - 1/3*h**3. Find i, given that y(i) = 0.
-1, 0
Let j(m) = -m**4 + m**2 + 1. Let z(h) = 72*h**4 - 30*h**3 - 40*h**2 - 2*h - 22. Let p(d) = -44*j(d) - 2*z(d). Factor p(w).
-4*w*(w - 1)*(5*w + 1)**2
Let j(y) be the third derivative of y**9/13440 - y**8/1680 + y**7/840 + y**5/20 - 3*y**2. Let n(u) be the third derivative of j(u). Let n(a) = 0. Calculate a.
0, 2/3, 2
Let j(b) = b + 9. Let z be j(-7). Let f(g) be the first derivative of 2/3*g**z + 1/3*g**3 + 1/3*g - 2. Factor f(l).
(l + 1)*(3*l + 1)/3
Let i(z) = 2*z - 26. Let b be i(15). Let d(s) be the third derivative of 1/15*s**3 + 0*s**b - 2*s**2 - 1/150*s**5 + 0*s + 0. Determine u, given that d(u) = 0.
-1, 1
Let j(c) be the second derivative of -1/10*c**5 + 2*c - 1/8*c**4 - 1/40*c**6 + 0*c**3 + 0 + 1/2*c**2. Let z(b) be the first derivative of j(b). Factor z(y).
-3*y*(y + 1)**2
Let a = -27 + 29. Let l(j) be the first derivative of -4/9*j**3 + 0*j**2 + 0*j + 3/2*j**4 - a. Factor l(t).
2*t**2*(9*t - 2)/3
Factor 0*r**3 + 3/8*r**4 + 3/4*r + 0 - 9/8*r**2.
3*r*(r - 1)**2*(r + 2)/8
Let k = -53 + 53. Factor 2/9*g**4 + 2/9*g**3 - 2/9*g**2 + k*g - 2/9*g**5 + 0.
-2*g**2*(g - 1)**2*(g + 1)/9
Suppose 39*b = 40*b - 3. Let f(z) be the second derivative of 8/9*z**b - 4/3*z**2 + 0 - 1/6*z**4 - 2*z. Factor f(m).
-2*(m - 2)*(3*m - 2)/3
What is y in 1/3*y**2 + 16/3 - 8/3*y = 0?
4
Let g be 2/(-8) + (5/(-28) - -1). What is x in -2/7*x**3 + 6/7*x**2 - 6/7*x**4 + 0 - 2/7*x + g*x**5 = 0?
-1, 0, 1/2, 1
Suppose 0 = 5*o + 2*u - 9, -6*u - 9 = -o - 4*u. Let m(y) be the first derivative of 1 + 1/2*y**2 + 0*y - 1/6*y**o. Factor m(v).
-v*(v - 2)/2
Let k(n) = -2*n + n + 0*n - 6. Let z be k(-8). Let t(c) = -c. Let g(r) = -r**2 - 2*r - 4. Let i(o) = z*t(o) + g(o). Factor i(u).
-(u + 2)**2
Let y be 7/4 + (-11)/(-44). Suppose 0*l**2 + 5 - 1 - 7*l + 2*l**y + l = 0. What is l?
1, 2
Let h(b) be the third derivative of b**7/840 - b**6/160 + b**4/24 - 12*b**2. Factor h(z).
z*(z - 2)**2*(z + 1)/4
Let b(a) be the second derivative of 2*a**2 + 0*a**3 - 1/270*a**5 + 0*a**4 - 4*a + 0. Let y(n) be the first derivative of b(n). Find u, given that y(u) = 0.
0
Let w(q) = -q + 4. Let t be w(-2). Factor -2*k + 3*k**5 + k**5 - 12*k**3 + t*k + 4*k**3.
4*k*(k - 1)**2*(k + 1)**2
Let b(m) be the second derivative of m**6/72 - m**5/20 + m**4/24 - m**3/3 + m. Let r(l) be the second derivative of b(l). Find v such that r(v) = 0.
1/5, 1
Let t(w) = -3*w**3 - 35*w**2 - 43*w - 9. Let s(k) = 13*k**3 + 139*k**2 + 173*k + 37. Let h(l) = 6*s(l) + 22*t(l). Factor h(j).
4*(j + 2)*(j + 3)*(3*j + 1)
Solve 5/2*i**2 + 15/2 + 25/2*i - 5/2*i**3 = 0 for i.
-1, 3
Let o be -3 + 5 - 2 - -2. Determine w so that -12*w**o + 40*w**3 - 18*w**4 - 5*w**2 + 2*w + 2*w**4 = 0.
0, 1/4, 2
What is a in 2/