et h(q) be the third derivative of b(q). Factor h(c).
-c**2*(c + 1)*(5*c + 2)
Let q(w) be the second derivative of 5*w**5/18 + 5*w**4/6 + 8*w**3/9 + 4*w**2/9 - 17*w - 2. Suppose q(h) = 0. What is h?
-1, -2/5
Solve -2/11*g + 2/11*g**2 + 0 = 0.
0, 1
Solve 0*w + 1/4*w**2 - 1 = 0 for w.
-2, 2
Let i = 370/17 - -1100/51. Let m = i - 43. Determine j, given that 1/3*j + 0 - 1/3*j**3 + 1/3*j**2 - m*j**4 = 0.
-1, 0, 1
Let u(i) = -24*i**4 - 98*i**3 - 118*i**2 + 22*i + 36. Let t(d) = 8*d**4 + 33*d**3 + 39*d**2 - 7*d - 12. Let o(r) = 10*t(r) + 3*u(r). Factor o(a).
4*(a + 1)**2*(a + 3)*(2*a - 1)
Let 0 + 2/5*w**2 - 2/5*w = 0. Calculate w.
0, 1
Let h(x) = 2*x**2 + 8*x. Let k(o) be the second derivative of -o**4/3 - 17*o**3/6 - o**2/2 - 3*o. Let b(f) = -14*h(f) - 6*k(f). Factor b(p).
-2*(p + 3)*(2*p - 1)
Let l(y) be the third derivative of 1/480*y**6 - y**2 - 1/96*y**4 + 0*y + 0 + 1/24*y**3 - 1/240*y**5. Factor l(n).
(n - 1)**2*(n + 1)/4
Find a, given that -1/3*a + 0 + 1/3*a**2 = 0.
0, 1
Let x(y) be the first derivative of -14*y**5/5 - 9*y**4/2 - 4*y**3/3 + 3. Factor x(g).
-2*g**2*(g + 1)*(7*g + 2)
Let j(m) = 3*m**2 - 24*m + 9*m + 12*m. Let z(i) = -6*i**2 + 5*i + 1. Let s(h) = 5*j(h) + 3*z(h). Factor s(k).
-3*(k - 1)*(k + 1)
Let r(c) = 13*c**3 + 10*c**2 + 16*c + 8. Let q(s) = 7*s**3 + 5*s**2 + 8*s + 4. Let l(i) = -11*q(i) + 6*r(i). Factor l(w).
(w + 1)*(w + 2)**2
Let o(f) be the second derivative of 0*f**2 + 4*f - 1/20*f**5 + 1/6*f**3 - 1/12*f**4 + 1/30*f**6 + 0. Let o(s) = 0. Calculate s.
-1, 0, 1
Let q(s) = -24*s**4 - 143*s**3 - 89*s**2 + 25*s - 10. Let y(l) = 12*l**4 + 72*l**3 + 45*l**2 - 12*l + 6. Let n(k) = 3*q(k) + 5*y(k). Factor n(t).
-3*t*(t + 1)*(t + 5)*(4*t - 1)
Let q(r) be the third derivative of r**8/1512 + 2*r**7/945 - r**5/135 - r**4/108 + 41*r**2. Factor q(f).
2*f*(f - 1)*(f + 1)**3/9
Let y(o) be the second derivative of 0 + 0*o**2 - 1/3*o**3 + 3*o + 3/10*o**5 + 2/15*o**6 + 0*o**4. Find f such that y(f) = 0.
-1, 0, 1/2
Let v be 40/30 + (-3)/(1 - -2). Suppose -2/3*f**3 + v*f + 1/3*f**2 + 0 = 0. What is f?
-1/2, 0, 1
Let s(r) be the first derivative of 11 - 2/3*r**3 + 2*r**2 - 8/3*r + 1/12*r**4. What is h in s(h) = 0?
2
Suppose -6*t - 3*i = -2*t + 1, i - 1 = -2*t. Let g(y) = y**3 - 12*y**2 + y - 8. Let l be g(12). Factor -l*w + w**2 + 0*w**2 + w**2 + t.
2*(w - 1)**2
Let l(t) be the first derivative of t**6/12 + 11*t**5/10 + 17*t**4/4 + 23*t**3/3 + 29*t**2/4 + 7*t/2 + 40. Factor l(c).
(c + 1)**4*(c + 7)/2
Let a(v) = v**3 + 7*v**2 + 7*v + 3. Let k be a(-6). Let j = k + 18. Determine m, given that -21*m**3 - 4*m**2 + j*m**3 + m**2 - 3*m**4 = 0.
-1, 0
Factor -3/4*f + 3/4*f**3 + 9/4 - 9/4*f**2.
3*(f - 3)*(f - 1)*(f + 1)/4
Let p(g) be the first derivative of -1 + 5/12*g**4 + 0*g + 0*g**2 + 7/15*g**5 + 1/9*g**3 + 1/6*g**6. Factor p(y).
y**2*(y + 1)**2*(3*y + 1)/3
Let n(i) = 3*i**3 - 6*i**2 + 3*i - 3. Let w be n(4). Factor w*g - 8 + 2*g**2 - 105*g.
2*(g - 2)*(g + 2)
Factor 162/5 + 2/5*d**2 - 36/5*d.
2*(d - 9)**2/5
Let k(j) = j**4 + 1. Let q(r) = 4*r**4 + 2*r**3 - 2*r**2 - 2*r + 2. Let u(p) = 2*k(p) - q(p). Factor u(a).
-2*a*(a - 1)*(a + 1)**2
Let b(z) be the second derivative of z**6/10 + 9*z**5/10 + 13*z**4/4 + 6*z**3 + 6*z**2 + 7*z. Solve b(u) = 0.
-2, -1
Factor 0 - 2*v**2 - 8/3*v**3 + 2/3*v**4 + 12*v.
2*v*(v - 3)**2*(v + 2)/3
Let g = -3091 - -49473/16. Let n = 247/112 - g. Find f such that 0 + 18/7*f**3 + n*f**4 + 2/7*f + 12/7*f**2 = 0.
-1, -1/4, 0
Suppose 0 = 9*y - y - 24. Suppose 2*c + 0 - 2 = -5*h, -3*c = y*h + 6. Determine g so that -3/5*g + 12/5*g**h - 3/5*g**5 + 6/5*g**3 - 6/5*g**4 - 6/5 = 0.
-2, -1, 1
Let n(f) be the first derivative of 1 + 2*f + 5/6*f**3 - 1/4*f**4 - f**2. Let a(i) be the first derivative of n(i). Factor a(l).
-(l - 1)*(3*l - 2)
Determine n, given that -3/2 - 3/2*n**3 - 9/2*n - 9/2*n**2 = 0.
-1
Let s(g) be the second derivative of 2/15*g**6 - 2*g**2 + 0 + 0*g**4 + 2/5*g**5 + g - 4/3*g**3. Suppose s(h) = 0. What is h?
-1, 1
Let r be 3*3/3 - -1. Let n be (-10)/(-4) - (-2)/r. Factor 1/4*s**2 - 1/4*s + 1/4*s**n - 1/4.
(s - 1)*(s + 1)**2/4
Let f be ((7 + -5)*1)/11. Find o, given that 0 - f*o**2 + 0*o = 0.
0
Let h(t) be the third derivative of -t**6/420 - t**5/105 - t**4/84 - 30*t**2. Factor h(s).
-2*s*(s + 1)**2/7
Let i(p) be the second derivative of -p**7/21 + 2*p**6/15 - 17*p. Factor i(s).
-2*s**4*(s - 2)
Let b(q) be the second derivative of -q**10/45360 + q**8/5040 - q**6/1080 - q**4/12 - q. Let x(c) be the third derivative of b(c). Let x(n) = 0. What is n?
-1, 0, 1
Let c(k) be the second derivative of -k**4/21 - 2*k**3/21 - 3*k. Suppose c(d) = 0. What is d?
-1, 0
Let i(u) = -u**2 + 4*u - 1. Let z(p) = -2*p - 7. Let q be z(-5). Let v be i(q). Let 2/5*m**v + 0*m + 0 = 0. What is m?
0
Suppose y + 0*y = -5*b - 15, 5*b = y - 25. Let z = 15 - 13. Factor y*g - 3*g - 3*g + z*g**3 - g**5.
-g*(g - 1)**2*(g + 1)**2
Suppose -x = 4 + 4. Let s be ((-4)/(-24))/((-2)/x). Suppose -4/9*o**2 + 2/9*o**5 - 2/9 + 4/9*o**3 - s*o + 2/3*o**4 = 0. What is o?
-1, 1
Let n be -6*((-6)/(-4) + -2). Suppose 0 = n*d - 0 - 6. Determine m so that m**2 + 2*m - 2*m**3 - 4*m + 3*m**d = 0.
0, 1
Factor 2/3*v**3 + 2/9*v**4 - 4/9 + 2/9*v**2 - 2/3*v.
2*(v - 1)*(v + 1)**2*(v + 2)/9
Let j(a) be the first derivative of a**8/168 + a**7/420 - a**6/60 - a**5/120 - a**2 - 5. Let f(k) be the second derivative of j(k). Suppose f(r) = 0. What is r?
-1, -1/4, 0, 1
Let w be 6/(-20)*(-20)/72. Let p = w - -5/12. Determine y, given that 1/2 - p*y**2 + 0*y = 0.
-1, 1
Suppose 2*r - 10 = -z, -5*r - 6 + 1 = -5*z. Solve -1/4*p**r - 3/4*p - 3/4*p**2 - 1/4 = 0.
-1
Let j(q) be the first derivative of -6*q**5/85 + 2*q**4/17 + 2*q**3/51 - 2*q**2/17 + 12. What is r in j(r) = 0?
-2/3, 0, 1
Let r(o) be the second derivative of o**4/66 - 7*o**3/33 + 6*o**2/11 + 17*o. Factor r(z).
2*(z - 6)*(z - 1)/11
Let q = -253 - -256. Determine d, given that 2/5*d**q - 54/5 - 18/5*d**2 + 54/5*d = 0.
3
Let q(k) = -10*k**2 + 2*k. Let x(b) = 18*b**2 - 3*b. Let o(z) = -11*q(z) - 6*x(z). Find r, given that o(r) = 0.
0, 2
Suppose 4*h + 4 = 20. Let z(w) = -w**2 + 6*w. Let i be z(5). Factor 2*s**i - h*s - 6*s**4 + 6*s**3 + 4*s - 2*s**2.
2*s**2*(s - 1)**3
Solve 6*w**3 + 9*w**4 + 5*w - 18*w**2 + 3*w**5 - 12*w**3 + 9 - 2*w = 0.
-3, -1, 1
Let m(o) be the first derivative of 2*o**3/27 + 4*o**2/9 + 8*o/9 + 10. Factor m(g).
2*(g + 2)**2/9
Factor -6*z**2 + 6*z - 3 + 4*z**3 - 2*z - z**4 + 2.
-(z - 1)**4
Factor -2/5*j**3 + 0 + 0*j**2 - 2/5*j**4 + 0*j.
-2*j**3*(j + 1)/5
Factor 0*c + 0*c**2 + 14/3*c**4 + 0 - 2/3*c**5 - 4*c**3.
-2*c**3*(c - 6)*(c - 1)/3
Let j(u) be the first derivative of u**3/27 - 5*u**2/18 - 2*u/3 + 44. What is z in j(z) = 0?
-1, 6
Factor -3/2*w + 0 - 3*w**2 - 3/2*w**3.
-3*w*(w + 1)**2/2
Suppose 2*g = 3*y - 8*y + 24, 2 = 2*y - 3*g. Let m(p) be the first derivative of 4/9*p**2 + 8/27*p**3 + 2 + 1/18*p**y + 0*p. Let m(t) = 0. Calculate t.
-2, 0
Let g(x) be the second derivative of 1/56*x**7 + 0*x**2 - 1/8*x**4 + 0 - 1/8*x**3 + 7*x + 0*x**5 + 1/20*x**6. Factor g(v).
3*v*(v - 1)*(v + 1)**3/4
Solve -6/7 + 3/7*w**2 + 3/7*w = 0 for w.
-2, 1
Let c(r) = -r - 7. Let n be c(-7). Let h(m) be the second derivative of 1/54*m**4 - 1/27*m**3 + m + 0*m**2 + n. Determine i, given that h(i) = 0.
0, 1
Let k = 35/6 - 23/4. Let a(p) be the third derivative of -1/20*p**5 - k*p**6 - p**2 + 1/2*p**4 + 0 + 2/3*p**3 - 1/70*p**7 + 0*p. Let a(t) = 0. What is t?
-2, -1/3, 1
Factor 72*h**4 + 22*h**3 - 5*h**5 - 125*h**2 - 8*h**4 - 97*h**3 - 19*h**4.
-5*h**2*(h - 5)**2*(h + 1)
Let n be (-50)/(-15) + 1 + -4. Let i(c) be the second derivative of 0 + 1/10*c**5 - 3*c - 1/3*c**4 + n*c**3 + 0*c**2. Suppose i(d) = 0. What is d?
0, 1
Let d = 0 + 7. Suppose 2 + d = 3*s. Factor 6 + 2 - s - 7 - 2*j**2 + 4*j.
-2*(j - 1)**2
Suppose 3*m - 8 = m - v, -3*v + 9 = m. Let -12/5*i**2 + 3/5*i**3 + m*i - 6/5 = 0. What is i?
1, 2
Factor 0 + 2/13*r**4 - 8/13*r**3 + 8/13*r - 2/13*r**2.
2*r*(r - 4)*(r - 1)*(r + 1)/13
Let y(v) be the third derivative of -1/15*v**5 + 0*v + 2/3*v**3 - 2*v**2 + 1/60*v**6 + 0 - 1/12*v**4. Factor y(h).
2*(h - 2)*(h - 1)*(h + 1)
Let y(c) be the second derivative of c**6/30 + c**5/8 + c**4/8 - c**3/12 - c**2/4 - 3*c. Factor y(x).
(x + 1)**3*(2*x - 1)/2
Let z(q) = -q**3 - 9*q**2 - q - 7. Let c be z(-9). Suppose 5*b = c*b. Let -1/2 + b*h + 1/2*