4*w**4 + 1 + 0*w + 0*w**2. Factor y(k).
-k**2*(k + 2)/6
Let o = 92 - 60. Let f(z) = z + 4. Let i be f(0). Factor -o*x**2 + 2 + 18*x**3 + 2 + 6*x + i*x.
2*(x - 1)**2*(9*x + 2)
Let j(r) be the second derivative of -r**6/10 + 3*r**5/10 + r**4/4 - r**3 + 45*r. What is d in j(d) = 0?
-1, 0, 1, 2
Let h be (10 + -1)*1 + -2. Factor -2*q**2 - 5*q + h*q - 4*q.
-2*q*(q + 1)
Let p be 1/(-2) - (-25)/10. Factor o**4 + 5*o**p - 5*o**3 - 2*o + 2*o**3 + 0*o**3 - o**3.
o*(o - 2)*(o - 1)**2
Let y(m) = -m**3 + 1. Let h(i) = -4*i**3 - 14*i**2 - 49*i + 3. Let d(k) = -2*h(k) + 6*y(k). Factor d(o).
2*o*(o + 7)**2
Suppose 0 - 15/4*c**2 + 3/2*c + 3*c**3 - 3/4*c**4 = 0. Calculate c.
0, 1, 2
Let b(g) = -g - 1. Let f(t) = 6*t + 11. Let q(k) = -4*b(k) - f(k). Let y be q(-5). Suppose -128*p**3 - p**2 + 1 - 95*p**2 - y - 24*p = 0. What is p?
-1/4
Let p(x) be the second derivative of -x**4/30 - x**3/3 - 6*x**2/5 - 19*x. Suppose p(y) = 0. What is y?
-3, -2
Let p = -70 - -214/3. Factor -2 - 2/9*d**2 - p*d.
-2*(d + 3)**2/9
Let x(q) = q**2 - q. Let l be (-8)/(-6)*9/6. Let d be x(l). Factor 6/7*o + 2/7*o**d + 4/7.
2*(o + 1)*(o + 2)/7
Let k be (-2)/(-4)*9/540. Let s(l) be the second derivative of 0*l**3 + 0*l**4 + 0 - k*l**6 - 2*l + 0*l**2 + 0*l**5. Suppose s(i) = 0. Calculate i.
0
Let h(x) be the second derivative of -x**6/135 + x**5/45 - 2*x**3/27 + x**2/9 - x. Factor h(l).
-2*(l - 1)**3*(l + 1)/9
Let v(m) = -6*m**2 - 8*m + 5. Let i be v(5). Let u = i + 1297/7. Determine l, given that -4/7 - u*l + 2/7*l**3 + 4/7*l**2 = 0.
-2, -1, 1
Let v(c) be the second derivative of c**5/30 - 17*c**4/54 + 10*c**3/27 + 25*c. Factor v(f).
2*f*(f - 5)*(3*f - 2)/9
Let l be ((-14)/196)/(1/(-96)). Factor -l*p + 10*p**2 + 8/7.
2*(5*p - 2)*(7*p - 2)/7
Let q(c) = 8*c**2 + 100*c - 80. Let p(l) = l**2 + 11*l - 9. Let h(x) = -28*p(x) + 3*q(x). Suppose h(u) = 0. What is u?
-3, 1
Let r(z) be the first derivative of 0*z**2 + 3 + 1/3*z**3 - z. Factor r(d).
(d - 1)*(d + 1)
Let c = -212 - -215. Let g(j) be the third derivative of 0*j**4 + 0*j**c - 4/35*j**7 + 3/112*j**8 + 0 - 5*j**2 - 1/10*j**5 + 0*j + 7/40*j**6. Factor g(s).
3*s**2*(s - 1)**2*(3*s - 2)
Let t(o) = -o**3 - 10*o**2 + o + 13. Let y be t(-10). Let k(s) be the second derivative of 1/42*s**4 + 0*s**3 + 0 - 1/7*s**2 + y*s. Factor k(a).
2*(a - 1)*(a + 1)/7
Let u = 3/5 + -1/10. Factor 0 - u*w - 1/4*w**2.
-w*(w + 2)/4
Suppose 3*i = 2*f + i - 10, 4*i + 8 = -2*f. Factor f*v**3 + v + 3*v**3 - 2*v + 0*v**4 + 3*v**4 + v**2.
v*(v + 1)**2*(3*v - 1)
Let o = -15 - -18. Factor o*s**4 + 3*s**3 + 0*s**4 - 7*s**2 + 2*s**2 - s**2.
3*s**2*(s - 1)*(s + 2)
Suppose -l = 1 - 2, u - l + 16 = 0. Let a(o) = -o**2 + o - 1. Let d(c) = 4*c**2 - 5*c + 6. Let h(t) = u*a(t) - 3*d(t). Factor h(w).
3*(w - 1)*(w + 1)
Let c(t) be the second derivative of -t**6/75 + t**4/30 - 6*t. Determine x, given that c(x) = 0.
-1, 0, 1
Let k = -158/3 - -1762/33. Let r = -3314/33 - -304/3. Determine m, given that -r*m**5 + 0 + 30/11*m**3 + k*m - 32/11*m**2 + 4/11*m**4 = 0.
-2, 0, 2/5, 1
Let q(w) = -4*w**3 - 14*w**2 - 48*w - 32. Let d(f) = 10*f**3 + 36*f**2 + 120*f + 80. Let i(z) = 5*d(z) + 12*q(z). Solve i(k) = 0 for k.
-2
Let s = 16 + -12. Let g(d) be the second derivative of -1/90*d**5 + 0 - 2*d + 0*d**2 + 0*d**3 + 1/54*d**s. Factor g(w).
-2*w**2*(w - 1)/9
Let s(r) be the second derivative of -r**7/8 - 5*r**6/12 - 13*r**5/40 + r**4/4 + 7*r**3/24 - r**2/4 - 16*r. Determine x, given that s(x) = 0.
-1, 2/7, 1/3
Solve 3/5*i**2 - 3/5*i + 0 = 0.
0, 1
Let j be 9/(2/4*-3). Let z be 10/j*(-42)/35. What is h in -z*h**2 - h + 21/4*h**3 + 0 = 0?
-2/7, 0, 2/3
Let a = -35/2 - -73/4. Factor -1/2 - 1/4*y**2 + a*y.
-(y - 2)*(y - 1)/4
Suppose -2*m - 47 = 2*r - 185, -m - 351 = -5*r. Let a be r/15 - 2 - 2. Find h such that 2*h - 2*h**2 + 2/3*h**3 - a = 0.
1
Let z(h) be the second derivative of 0*h**2 + 0*h**5 + 4*h + 0*h**3 + 0 + 1/24*h**4 - 1/60*h**6. Factor z(i).
-i**2*(i - 1)*(i + 1)/2
Let o(y) be the first derivative of -4*y**5/15 + 2*y**4/3 + 4*y**3/9 - 4*y**2/3 + 21. Find f, given that o(f) = 0.
-1, 0, 1, 2
Let o = -58 + 408/7. Let t(v) be the first derivative of 1 + 2/7*v**3 + 1/14*v**4 + o*v**2 + 0*v. Factor t(p).
2*p*(p + 1)*(p + 2)/7
Let h be 3*15/(-50)*20/(-36). Find d, given that 0 - d**2 + d**4 + 0*d**3 - 1/2*d**5 + h*d = 0.
-1, 0, 1
Suppose 2*m - 2 = -4*f - m, -6 = -f + 2*m. Let j(q) = -q + 2. Let p be j(f). Factor -1/4*w**4 - 3/4*w**2 + p + 1/4*w + 3/4*w**3.
-w*(w - 1)**3/4
Let l be -2 - -4 - (-4)/(-3). Factor -1/3*n**2 - 1/3 - l*n.
-(n + 1)**2/3
Suppose 0*t + 64 = 4*t. Suppose 4*o - t = 4*y, 12 = -2*o - 4*y - 4. Factor 20*g + 8 + 0*g**4 + 7*g**3 + 18*g**2 + g**4 + o*g**4.
(g + 1)*(g + 2)**3
Let a(l) be the third derivative of -l**8/3696 + l**7/2310 + 3*l**6/440 - l**5/132 - 2*l**4/33 + 2*l**3/11 + 40*l**2. Find w such that a(w) = 0.
-2, 1, 3
Suppose -u + 3*q - 4*q = 0, 5*q = -u - 12. Suppose -u*s + 6 = -6. Factor -12*t**3 + 12*t + 0 - 2 - 9*t**s + 6 + 0 + 5*t**2.
-(t - 1)*(t + 1)*(3*t + 2)**2
Factor 2/11*o**2 - 6/11 + 4/11*o.
2*(o - 1)*(o + 3)/11
Factor 0 + 1/3*s**2 - 1/3*s**3 + 0*s.
-s**2*(s - 1)/3
Let l be 4/5*-20*1/(-4). Let u(t) be the first derivative of -2/9*t**3 - 7/12*t**l + 2/3*t + 7/6*t**2 - 1. Determine c so that u(c) = 0.
-1, -2/7, 1
Find o, given that -2/3*o**2 + 4/3*o - 2/3 = 0.
1
Suppose 0 = 2*s - 4 - 14. Suppose -4*h**3 + 2*h**2 + s - 9 + 2*h**4 + 0*h**4 = 0. What is h?
0, 1
Let b(v) = -9*v**4 + 3*v**3 - 5*v - 5. Let p(u) = 14*u**4 - 4*u**3 + 8*u + 8. Let m(s) = 8*b(s) + 5*p(s). Factor m(g).
-2*g**3*(g - 2)
Let i be (0/2)/(1 + -4). Let u(c) be the first derivative of 3 + 2/15*c**3 + i*c - 1/5*c**2. Factor u(n).
2*n*(n - 1)/5
Let m(v) = -v**3 + v**2 + v - 1. Let b(i) = -4 - 31*i**2 + 4 + 3 - 3*i - 4*i - 46*i**3. Let k(z) = 2*b(z) + 6*m(z). Determine t, given that k(t) = 0.
-2/7, 0
Let v(x) = -3*x - 1. Let o(m) = -m - 1. Let d(w) = 4*o(w) - v(w). Let n be d(-5). Suppose -3*p**2 + n*p**2 + 0*p - p = 0. Calculate p.
-1, 0
Let g(n) be the first derivative of n**3/9 - 2*n**2/3 + 4*n/3 + 7. Suppose g(c) = 0. Calculate c.
2
Find x, given that 0 - 1/5*x**2 + 0*x = 0.
0
Determine z so that -2 - z + 2*z**2 - 2*z**3 - 2*z + 5*z = 0.
-1, 1
Let i be (11 + -8)/((-3)/4). Let l be (-11)/i + (-15)/20. Solve 0 + 2/3*a**l - 2/3*a**4 + 0*a**3 + 0*a = 0.
-1, 0, 1
Factor -1/3*b**2 - 2*b + 0.
-b*(b + 6)/3
Let g(o) be the first derivative of 1/2*o**4 + o**2 - 8/3*o**3 + o + 7/5*o**5 - 2/3*o**6 - 2. Solve g(d) = 0.
-1, -1/4, 1
Let n(t) = -3*t + 3. Let s be n(11). Let c be (s/96)/(2/(-8)). Determine h, given that -3/4*h**3 - c*h**2 + 0 - 1/2*h = 0.
-1, -2/3, 0
Let o(w) be the first derivative of w**6/240 + w**5/40 - w**3/3 - 3*w**2/2 - 3. Let h(l) be the second derivative of o(l). Factor h(i).
(i - 1)*(i + 2)**2/2
Let b(n) be the first derivative of n**5/75 - n**4/120 - n**2/2 - 1. Let p(j) be the second derivative of b(j). Factor p(o).
o*(4*o - 1)/5
Let g be 7/(-14)*(-2 - -2). Determine i, given that g*i - 2 - i**2 - 4*i + i = 0.
-2, -1
Factor -1/5*g**3 + 1/5*g**5 + 0*g - 1/5*g**4 + 0 + 1/5*g**2.
g**2*(g - 1)**2*(g + 1)/5
Factor 3*k**3 + 36*k - 2*k**2 + 14 - 22*k**2 - 30 + k**3.
4*(k - 4)*(k - 1)**2
Suppose -3/4*j**3 - 15/4*j**2 - 21/4*j - 9/4 = 0. Calculate j.
-3, -1
Let c(q) be the first derivative of 2/5*q**5 + 0*q**2 - 4/3*q**3 + 2*q - 4 + 0*q**4. Suppose c(m) = 0. Calculate m.
-1, 1
Let a(y) be the second derivative of -y**5/120 - y**4/48 + y**3/6 + 3*y**2/2 + 5*y. Let x(z) be the first derivative of a(z). Factor x(t).
-(t - 1)*(t + 2)/2
Let x(s) be the third derivative of -s**5/12 + 25*s**4/12 - 125*s**3/6 + 11*s**2. Factor x(w).
-5*(w - 5)**2
Factor 3/8*z**4 - 7/8*z**2 + 0 - 1/4*z**3 - 1/4*z.
z*(z - 2)*(z + 1)*(3*z + 1)/8
Solve 0*o**2 - 4*o**4 - 3*o**2 + 7*o**4 + 6*o**3 - 6*o**4 = 0 for o.
0, 1
Let x(t) be the second derivative of 4*t**7/21 - 2*t**6/3 + 4*t**5/5 - t**4/3 - 8*t. Factor x(p).
4*p**2*(p - 1)**2*(2*p - 1)
Let b(f) = f - 11. Let j be b(9). Let u = j + 2. Factor 2/7*c + 6/7*c**2 + 0*c**3 + u - 8/7*c**4.
-2*c*(c - 1)*(2*c + 1)**2/7
Suppose -28 = -5*h - 8. Let b(p) be the second derivative of 0*p**2 + 3*p + 0 + 3/20*p**5 - p**3 - 1/4*p**h. Determine t so that b(t) = 0.
-1, 0, 2
Let p(d) be the first derivative of -d**6/12 + d**5/5 - d**4/8 - 10. Factor p(n).
-n**3*(n - 1)**2/2
Let t(r) = r**3