) = n**2 + n. Let q(w) = -g(w) + 5*r(w). Suppose q(t) = 0. Calculate t.
-2, -1, 0, 1
Let i(o) be the second derivative of o**8/4200 - o**7/1050 + o**6/900 - o**3/3 - 4*o. Let n(c) be the second derivative of i(c). Solve n(g) = 0.
0, 1
Let y = 25/12 + -23/12. Factor 0*v + 0 - 1/6*v**4 + 1/6*v**5 + 1/6*v**2 - y*v**3.
v**2*(v - 1)**2*(v + 1)/6
Let s(n) be the second derivative of 5*n**4/12 - 5*n**3/6 - 12*n. Factor s(z).
5*z*(z - 1)
Let d be (-1 + 3)*50/150. Determine p, given that 0 + d*p + 2/9*p**2 = 0.
-3, 0
Let h(q) be the second derivative of q**4/42 - 8*q**3/21 + 16*q**2/7 + 10*q. Suppose h(o) = 0. Calculate o.
4
Let u = 8 - 4. Factor 2 - 10*l**2 + 4*l**3 - 5*l**5 + l**4 + l**u + l + 6*l**4.
-(l - 1)**3*(l + 1)*(5*l + 2)
Let w(j) be the first derivative of 49*j**5 - 385*j**4/4 - 110*j**3 + 130*j**2 - 40*j + 32. Factor w(b).
5*(b - 2)*(b + 1)*(7*b - 2)**2
Suppose 0 = z + 2*g + 2, 0 = -5*z - 2*g + 6. Suppose 0 = -h + z, 0*k + 3*h = 2*k + 2. Determine v, given that 8/3*v - 8/3 - 2/3*v**k = 0.
2
Let h = -1 - -13. Factor -h*g - 7 + 4*g**2 - 8 - 1.
4*(g - 4)*(g + 1)
Suppose 0 = s - 210 - 1192. Let o = s - 6986/5. Suppose -6/5*l**3 - 14/5*l**5 - o*l**4 + 0*l + 4/5*l**2 + 0 = 0. What is l?
-1, 0, 2/7
Let t(y) = -2*y**4 + 4*y**3 - 6*y**2 - 4*y + 2. Let z(r) = -9*r**4 + 17*r**3 - 25*r**2 - 17*r + 8. Let a(s) = -26*t(s) + 6*z(s). Factor a(i).
-2*(i - 1)**2*(i + 1)*(i + 2)
Let g(s) = -s**3 + s + 1. Let l(y) = y**4 - 5*y**3 + 6*y**2 - 3*y + 2. Let h(u) = 5*g(u) - 5*l(u). Factor h(d).
-5*(d - 1)**4
Determine d so that 2*d**3 - 5*d**3 + 7*d**5 - 3*d**5 - d**3 = 0.
-1, 0, 1
Let v(w) be the second derivative of 1/42*w**4 + 0 - 2/21*w**3 - 2*w + 1/7*w**2. Factor v(z).
2*(z - 1)**2/7
Let o = 2607 - 547469/210. Let r(m) be the third derivative of 0*m + 0*m**3 + o*m**5 + 0*m**4 + 0*m**6 + 3*m**2 + 0 - 1/735*m**7. Suppose r(l) = 0. Calculate l.
-1, 0, 1
Suppose 3*k + 3*v - 18 = 0, -5*v = k - 21 - 1. Suppose -4/3 - k*w**2 + 14/3*w = 0. Calculate w.
1/3, 2
Suppose -23*w + 2 - 2 = 0. Factor w + 0*y - 1/2*y**2 + 1/2*y**4 + 0*y**3.
y**2*(y - 1)*(y + 1)/2
Let t(q) be the second derivative of -q**5/210 + q**4/84 - q**2 + q. Let g(k) be the first derivative of t(k). Factor g(j).
-2*j*(j - 1)/7
Let r = -429 - -1717/4. Find f, given that r*f**2 + 1/4*f - 1/2 = 0.
-2, 1
Let l(j) be the second derivative of 8*j**4/15 + 8*j**3/15 + j**2/5 + 2*j. Factor l(t).
2*(4*t + 1)**2/5
Let h(r) be the third derivative of -r**8/1008 + r**6/180 - r**4/72 + 5*r**2. Factor h(c).
-c*(c - 1)**2*(c + 1)**2/3
Let i(f) = -2*f**2 + 14*f + 3. Let z be i(7). Factor -1/4*d + 1/4 + 1/4*d**z - 1/4*d**2.
(d - 1)**2*(d + 1)/4
Factor -3/7*q**2 - 3/7*q**3 + 0 + 6/7*q.
-3*q*(q - 1)*(q + 2)/7
Let x(f) be the second derivative of -f**4/4 + 5*f**3/2 - 6*f**2 + 16*f. Factor x(n).
-3*(n - 4)*(n - 1)
Let k(v) be the third derivative of 0 + v**2 - 1/3*v**4 + 0*v**3 + 0*v - 1/60*v**6 - 2/15*v**5. Factor k(m).
-2*m*(m + 2)**2
Let u(w) be the second derivative of w**6/165 - w**5/11 + w**4/2 - 40*w**3/33 + 16*w**2/11 + 3*w. Determine r so that u(r) = 0.
1, 4
Let z be 7/((-21)/36) + -2. Let l = z - -100/7. What is u in -8/7*u**2 - 12/7*u**3 + 0 - l*u**5 - 2/7*u - 8/7*u**4 = 0?
-1, 0
Let c be -21 + 9 - -11 - -1. Solve -2/7*u**3 + c + 4/7*u + 2/7*u**2 = 0.
-1, 0, 2
Let z be (3/6)/((-3)/(-12)). Factor -3 + 4*v - 4*v**2 + 11*v**2 - 5 - 3*v**z.
4*(v - 1)*(v + 2)
Let g(y) be the third derivative of -y**7/105 + y**6/30 - y**5/30 + 3*y**2. Factor g(z).
-2*z**2*(z - 1)**2
Let z = 6279/25 + -251. Let k(h) be the first derivative of 0*h**4 + z*h**5 + 0*h - 4/15*h**3 + 1/5*h**2 - 1/15*h**6 - 4. Find x, given that k(x) = 0.
-1, 0, 1
Let p = 103/3 - 34. Suppose -p*o + 0 + 1/3*o**2 = 0. What is o?
0, 1
Let w(x) be the third derivative of x**8/20160 + x**7/3780 - x**4/6 - 6*x**2. Let z(c) be the second derivative of w(c). Let z(m) = 0. Calculate m.
-2, 0
Let c be (-5 + 4)*(5 + 1). Let b be (-22)/(-33)*c/(-8). Factor -7/4*v**2 - 1/2*v**3 + 7/4*v**4 + b*v + 0.
v*(v - 1)*(v + 1)*(7*v - 2)/4
Let n(d) be the first derivative of -1/3*d + 1 - 1/9*d**3 + 1/3*d**2. Find h, given that n(h) = 0.
1
Suppose 3*j - 9 = 3. Let m(w) be the first derivative of 2/7*w**2 - j + 2/21*w**3 + 2/7*w. Factor m(u).
2*(u + 1)**2/7
Let p be (15/(-9) + 3)*-3. Let b be (-5 - -11)/(-2 - p). Solve 2/9*l**b + 4/9*l**2 - 4/9 - 2/9*l = 0.
-2, -1, 1
Let t(c) = -13*c**2 + 11*c - 12. Let n(g) = -9*g**2 + 7*g - 8. Let h(k) = -7*n(k) + 5*t(k). Solve h(p) = 0.
1, 2
Let m(l) be the second derivative of l**4/54 + 5*l**3/27 + 2*l. What is y in m(y) = 0?
-5, 0
What is v in -12/5*v**3 + 48/5*v + 2/5*v**2 + 2/5*v**4 + 32/5 = 0?
-1, 4
Suppose 0 = 2*o + 2*p - 6, o = 2*o + 3*p - 3. Factor -2*m**5 - 3*m**3 - 4*m**2 + 2*m + 5*m**4 + o*m**3 - m**4.
-2*m*(m - 1)**3*(m + 1)
Let k be 79*(3 - 30/9). Let q = k + 27. Factor 2/3*p + 2/3*p**2 - q - 2/3*p**3.
-2*(p - 1)**2*(p + 1)/3
Let k(x) be the first derivative of -x**6/6 - 3*x**5/25 + 3*x**4/5 - 4*x**3/15 + 2. Determine c so that k(c) = 0.
-2, 0, 2/5, 1
Let c(h) be the second derivative of h**7/10080 - h**6/2880 - h**4/4 + 2*h. Let y(t) be the third derivative of c(t). Find q such that y(q) = 0.
0, 1
Let h be 0 - -3 - 51/18. Let -1/6*t**2 + h*t**3 + 0 + 0*t = 0. Calculate t.
0, 1
Let d be (-186)/(-66) - (-2)/11. Factor -103*o**2 + 24 - 105*o**d - 2*o - 119*o**2 - 10*o.
-3*(o + 2)*(5*o + 2)*(7*o - 2)
Find v, given that 0*v**4 - 108 - v**4 - 111*v**2 - 6*v**3 + 180*v - 2*v**4 + 36*v**3 = 0.
2, 3
Let w = 9/40 + -1/8. Let v(m) be the second derivative of -2*m + 1/6*m**4 - m**2 + 0 + 1/3*m**3 - w*m**5. Factor v(r).
-2*(r - 1)**2*(r + 1)
Suppose -4*j + 0*j + 60 = 0. Factor 2*p + p + 5*p**4 + j*p**3 + p**4 - p**2 + 13*p**2.
3*p*(p + 1)**2*(2*p + 1)
Factor -20*v + 20*v + 33*v**2 - 32*v**2.
v**2
Let r = 13 - 1. Let o be 11/4 + 3/r. Find x such that -2 - 2*x**2 + x + o*x**2 + 0 = 0.
-2, 1
Let o(v) = -v**4 - v**2 + v. Let y(z) = -8*z**4 + 20*z**3 - 8*z**2 - 27*z. Let b(p) = 3*o(p) - y(p). Factor b(t).
5*t*(t - 3)*(t - 2)*(t + 1)
Find u, given that -4*u - 4 + 4 - u**2 + 1 - 4 = 0.
-3, -1
Factor 0*l**2 - 9 - 6*l + 5 - 2*l**2.
-2*(l + 1)*(l + 2)
Let n = 388/995 - -2/199. Determine d so that -n*d**5 + 2/5*d**2 - 2/5*d**4 + 0*d + 2/5*d**3 + 0 = 0.
-1, 0, 1
Let -1 + 8*c + 10*c**2 - 7 + 2*c**5 + 137*c**4 - 10*c**3 - 139*c**4 = 0. Calculate c.
-2, -1, 1, 2
Factor 19 - 24*q - 16*q**2 - 10 + 11 - 4*q**4 + 24*q**3.
-4*(q - 5)*(q - 1)**2*(q + 1)
Let t(h) be the first derivative of 5*h**4/2 - 26*h**3/3 + 11*h**2 - 6*h - 14. Factor t(m).
2*(m - 1)**2*(5*m - 3)
Suppose -17*b = -97 + 12. Factor 1/2*c**2 - 1/4 - 1/4*c**4 + 1/4*c - 1/2*c**3 + 1/4*c**b.
(c - 1)**3*(c + 1)**2/4
Let r be -5 - (-8 + 2) - (-22)/8. Let k(u) be the first derivative of -1 - 1/3*u**3 - r*u**4 + u**2 + 0*u. Factor k(o).
-o*(3*o - 1)*(5*o + 2)
Let k be (-1 - -1 - 1) + 7. Suppose 4*b + k = 5*v, -4*v = -2*b - 0*b - 6. Factor 5*r**3 - r**3 - v*r**3 + 2*r**4.
2*r**3*(r + 1)
Let u(x) = x**2 + 3*x + 3. Let t be u(-3). Suppose -3*l = -t*n + 9, 3 + 3 = -3*n - 2*l. Find h such that n + 0*h**2 + 0*h + 2/7*h**3 = 0.
0
Suppose 5*p**2 - 3*p**2 - p - 7*p**2 + 10 - 4*p = 0. What is p?
-2, 1
Determine s, given that -5/4*s**2 + 0 + 1/4*s**4 + 3/4*s + 1/4*s**3 = 0.
-3, 0, 1
Let o(d) be the third derivative of 0*d + 0 + 0*d**4 + 1/240*d**5 + d**2 - 1/24*d**3. Factor o(v).
(v - 1)*(v + 1)/4
Determine a so that 4/7*a**3 - 4/7*a**4 - 4/7*a**5 + 0 + 0*a + 4/7*a**2 = 0.
-1, 0, 1
Let w(b) be the second derivative of -b**4/12 - b**3/3 - 18*b. Solve w(d) = 0 for d.
-2, 0
Factor 22*o**3 + 12*o**4 - 2*o**3 + 4*o**2 + 8*o - 12*o.
4*o*(o + 1)**2*(3*o - 1)
Let l be 1 + (-5)/(15/(-6)). Suppose -l = -2*g + u, 0*g + 3*u - 19 = -g. Factor -v**2 + 6*v - g*v - 4 + 2*v.
-(v - 2)**2
Let p(u) be the first derivative of -4*u**3/3 - 6*u**2 + 16*u - 66. Solve p(b) = 0 for b.
-4, 1
Suppose 2*m - 5 = -1. Suppose -m*f**4 - 4*f**3 - 99*f**2 + 99*f**2 = 0. Calculate f.
-2, 0
Let x(j) = j**3 - 2*j**2 - 3*j + 4. Let h be x(3). What is n in -8*n**4 + 21*n**h + n**3 - n - n**2 - 12*n**4 = 0?
-1, 0, 1
Let j(s) = 6*s**5 - s**4 + s**3 + 2*s. Let r(a) = 27*a - 24*a + 11*a**5 + 2*a**3 - 4*a**5. Let z(g) = -3*j(g) + 2*r(g). Factor z(o).
-o**3*(o - 1)*(4*o + 1)
Let h = -1 + 3. Factor 3*f**h + f - 4*f**2 - 3*f + f + 2.
-(f - 1)*(f + 2)
Let b(o) be th