**3 + 35*x**2 + 25*x - 23. Suppose v(m) = 0. Calculate m.
-1/3, 5
Let t = -4 - -8. Suppose h - 4*h = -5*o + 3, t*h = -o + 19. Solve 0*n**o - n**2 + 2*n**2 + 4*n**3 = 0 for n.
-1/4, 0
Suppose 0*s + 4*s = 28. Let t = -5 + s. Solve 3*w**2 - t - w**2 + 0*w**2 = 0.
-1, 1
Let z = 7 + -3. Let m(x) be the second derivative of -2*x + 0*x**6 + 1/18*x**3 + 0*x**2 + 0*x**z + 0 - 1/30*x**5 + 1/126*x**7. Factor m(y).
y*(y - 1)**2*(y + 1)**2/3
Find h, given that -37 - 125 + 27 - 29*h**3 - 135*h + 24*h**3 - 45*h**2 = 0.
-3
Let w be 120/144 + (-53)/78. Factor 0 + 0*d + 2/13*d**5 - 2/13*d**2 - w*d**3 + 2/13*d**4.
2*d**2*(d - 1)*(d + 1)**2/13
Let g be ((-1)/3)/(4/(-8)). Let t(c) = -c**2 + 12*c - 27. Let h be t(8). Factor 2/9*o**2 - 2/9*o**h - g*o**3 + 0*o + 0 + 2/3*o**4.
-2*o**2*(o - 1)**3/9
Let h - 4/5 - 1/5*h**2 = 0. Calculate h.
1, 4
Let k(v) = v**2 - 7*v + 3. Let x be k(7). Factor -2*f**2 + 2*f - x - 3*f + 3 - f**3.
-f*(f + 1)**2
Let j be 1/3 + 51/9. Let q(d) = 132*d**3 - 54*d**2 - 4*d + 4. Let o(h) = -395*h**3 + 161*h**2 + 13*h - 12. Let c(t) = j*o(t) + 17*q(t). Factor c(p).
-2*(3*p - 1)**2*(7*p + 2)
Let r(q) be the second derivative of -1/6*q**3 + 0 - 2*q + 1/3*q**4 - 7/60*q**6 - 1/4*q**2 - 1/20*q**5 + 1/21*q**7. What is a in r(a) = 0?
-1, -1/4, 1
Let y(f) be the second derivative of f**4/12 - f**3/6 - f**2 + 12*f. Factor y(i).
(i - 2)*(i + 1)
Let l be (-44)/(-28) + 6/14. Factor 2*a**2 - 2*a**2 + 4*a**2 - 3*a**l.
a**2
Let f(p) = -4*p**4 + 3*p**3 + 4*p**2 + 3*p + 3. Let y(t) = t**4 - t**3 - t**2 - t - 1. Let l(m) = f(m) + 3*y(m). Factor l(c).
-c**2*(c - 1)*(c + 1)
Let y(j) be the third derivative of -1/630*j**7 - j**2 + 1/72*j**4 + 0 + 0*j**3 - 1/60*j**5 + 0*j + 1/120*j**6. Determine h, given that y(h) = 0.
0, 1
Factor 12*i + 22 - 13*i**2 - 26 + 17*i**3 - i**4 - 11*i**3.
-(i - 2)**2*(i - 1)**2
Let g be 2/1*7/2. Let m = 10 - g. Determine j so that 0*j + 1/3*j**4 - 1/3*j**2 + 0*j**m + 0 = 0.
-1, 0, 1
Suppose 9 - 3 = 3*b. Suppose -k = b*k. Factor -m**2 + k*m - 1 + 0*m + 2*m.
-(m - 1)**2
Let l(r) be the second derivative of r**5/30 - r**4/6 + 4*r**2/3 + r. Determine q, given that l(q) = 0.
-1, 2
Suppose -2*x = -3*x. Suppose x = -5*b + 19 - 4. Factor -4*i + 2*i**b + 2*i**2 + 4*i.
2*i**2*(i + 1)
Let x = -598 + 600. Solve -4/11*t + 2/11*t**4 + 4/11*t**3 + 0 - 2/11*t**x = 0.
-2, -1, 0, 1
Let r(i) = i**2 - i - 5. Let h(o) = -2*o**2 + 2*o + 6. Let w(f) = -3*h(f) - 2*r(f). Solve w(q) = 0 for q.
-1, 2
Let d(o) be the third derivative of o**9/68040 - o**7/3780 + o**6/1620 - o**4/12 - 2*o**2. Let y(p) be the second derivative of d(p). Let y(f) = 0. What is f?
-2, 0, 1
Let c(t) be the third derivative of 1/10*t**6 + 2/15*t**5 - 4/3*t**3 + 6*t**2 + 0 + 0*t - 1/2*t**4. Suppose c(m) = 0. Calculate m.
-1, -2/3, 1
Let i(n) = 2*n**3 - 14*n**2 + 20*n - 8. Let q(y) = 4*y**2 + 7*y - 3 + 15*y**3 - 9*y**2 - 14*y**3. Let h(d) = 3*i(d) - 8*q(d). Factor h(z).
-2*z*(z - 1)*(z + 2)
Let r be (-1)/(2/(12/(-3))). Suppose 2 + 2*z - 4*z**3 - 3*z**2 + r*z**3 + z**2 = 0. Calculate z.
-1, 1
Let n be (42/(-15))/((-2)/10). Suppose 18 = 3*q - 3*p, 3*q = -0*q + 2*p + n. Factor k**3 - 3*k**4 - q*k**2 + 0*k**3 - 5*k**3 + k**4.
-2*k**2*(k + 1)**2
Let f(u) = 14 + 33*u + u + 42*u**2 - 11*u**2 + 3*u**2. Let x(r) = 7*r**2 + 7*r + 3. Let w(q) = -3*f(q) + 14*x(q). Determine d so that w(d) = 0.
-1, 0
Let p(d) = 4*d**3 - d**2 + 11*d - 7. Let i(t) = -2*t**3 + t**2 - 5*t + 3. Let k(m) = -7*i(m) - 3*p(m). Factor k(g).
2*g*(g - 1)**2
Let k(y) be the second derivative of -y**6/20 + y**5/40 + y**4/12 - 9*y. Factor k(f).
-f**2*(f - 1)*(3*f + 2)/2
Suppose 0 = -s - s - 76. Let b = -112/3 - s. Factor 0*z**2 + 2/3 - 4/3*z**3 + 4/3*z - b*z**4.
-2*(z - 1)*(z + 1)**3/3
Suppose 5*o + 97 + 38 = 0. Let s be 18/o + 68/66. Factor -2/11*t**2 - 2/11*t + s.
-2*(t - 1)*(t + 2)/11
Suppose 2*r - 15*r + 52 = 0. Let o(i) be the second derivative of -1/60*i**r + 0 + 0*i**3 + 0*i**2 + 0*i**5 + 4*i + 1/150*i**6. Factor o(c).
c**2*(c - 1)*(c + 1)/5
Let c(i) be the first derivative of 2*i**6/3 - 8*i**5/5 + 8*i**3/3 - 2*i**2 - 10. Find q such that c(q) = 0.
-1, 0, 1
Factor 2/3*w**2 + 0 + 0*w + 7/3*w**3.
w**2*(7*w + 2)/3
Let p be (-4)/((-28)/403) - -4. Let m = p - 61. Factor 30/7*t**2 + 22/7*t**3 + 18/7*t + 6/7*t**4 + m.
2*(t + 1)**3*(3*t + 2)/7
Let m(w) = 22*w**2 + 20*w. Let g(a) = -7*a**2 - 7*a. Let c(j) = -8*g(j) - 3*m(j). Find o such that c(o) = 0.
-2/5, 0
Let j(s) be the first derivative of 4/9*s**3 + 1/3*s**2 + 1/6*s**4 - 2 + 0*s. Suppose j(n) = 0. What is n?
-1, 0
Let d(b) = b**2 + b + 1. Let s be d(-2). Suppose -2*q + 4*q - 16 = -4*j, -6 = s*q - 4*j. Factor 3/2*r**q + 2 + 4*r.
(r + 2)*(3*r + 2)/2
Let l(p) be the first derivative of 0*p**2 + 12*p - 8 - 3*p**3 - 3/4*p**4. Find f such that l(f) = 0.
-2, 1
Let q = -13438/11 + 1222. What is i in 14/11*i**2 + 0 - q*i = 0?
0, 2/7
Let r be (-8)/(-3)*(-21)/14. Let b(g) = g**2 + 4*g + 2. Let a be b(r). Factor 1/4*l + 1/4 - 1/4*l**a - 1/4*l**3.
-(l - 1)*(l + 1)**2/4
Find w such that 16/7*w**2 - 54/7*w**3 + 0 - 8/7*w**5 + 8/7*w + 38/7*w**4 = 0.
-1/4, 0, 1, 2
Let n be 3/(-5)*(-4)/3. Let t be (-528)/(-160) + 1/(-2). Factor n + t*g + 2*g**2.
2*(g + 1)*(5*g + 2)/5
Solve 2/9*p**2 - 2/9*p**3 + 4/9*p + 0 = 0.
-1, 0, 2
Solve 0 - 4/3*w**2 - 2/3*w**4 - 2*w**3 + 0*w = 0 for w.
-2, -1, 0
Let p be -1 + (-12)/(-10) - -6 - 5. Solve 0 + p*u**3 + 0*u**4 - 3/5*u**5 - 3/5*u + 0*u**2 = 0.
-1, 0, 1
Let u(s) be the first derivative of -s**5/90 - s**4/36 + 2*s**3/9 - 5*s**2/2 - 4. Let c(a) be the second derivative of u(a). Factor c(o).
-2*(o - 1)*(o + 2)/3
Let o(t) = -t**2 - 6*t + 7. Let i(k) = -3*k + 3. Let w(r) = 5*i(r) - 3*o(r). Factor w(z).
3*(z - 1)*(z + 2)
Suppose -4 = -y + 2. Factor -3 + 2*a + y + a**2 - 3.
a*(a + 2)
Factor 1/5*c**2 + 2/5*c**3 - 2/5*c + 0 - 1/5*c**4.
-c*(c - 2)*(c - 1)*(c + 1)/5
Let q(i) be the third derivative of i**5/240 + 5*i**4/96 + i**3/4 + 19*i**2. Factor q(u).
(u + 2)*(u + 3)/4
Let p(h) be the third derivative of 0*h + 0 + 0*h**4 + 6*h**2 - 1/420*h**6 + 1/735*h**7 + 0*h**3 - 1/210*h**5 + 1/1176*h**8. Suppose p(k) = 0. Calculate k.
-1, 0, 1
Let p be 1/(-2) + (-33)/(-6). Suppose -p*f = 5 - 25. Factor -u**3 - 4*u**5 - 10*u**f + 0*u**5 - 5*u**3 + 2*u**2 + 3*u - u.
-2*u*(u + 1)**3*(2*u - 1)
Suppose 99 - 105 - 7*r - 3*r**2 + 5*r - 7*r = 0. What is r?
-2, -1
Let g(a) be the second derivative of -2*a**6/3 + 15*a**5/4 - 20*a**4/3 + 5*a**3/2 + 5*a**2 + 56*a. Find f, given that g(f) = 0.
-1/4, 1, 2
Let q(g) be the second derivative of g**6/195 - g**4/26 + 2*g**3/39 - 10*g. Let q(w) = 0. What is w?
-2, 0, 1
Let n be -4*1/(-2) + 0. Factor -2*z**n - 3 + 19*z**4 - 20*z + 2*z - 67*z**4 - z**2 + 72*z**3.
-3*(z - 1)**2*(4*z + 1)**2
Let b be (-11)/(1463/14) - 40/(-19). Let 1/4*t**5 - 3/4*t**4 - 1/4*t**b + 0*t + 3/4*t**3 + 0 = 0. What is t?
0, 1
Let h = -442 - -442. Factor -1/6*a**3 + h - 1/6*a**4 + 1/6*a**2 + 1/6*a.
-a*(a - 1)*(a + 1)**2/6
Let h(d) be the third derivative of -1/180*d**5 + 3*d**2 - 1/120*d**6 - 1/210*d**7 + 0*d**4 - 1/1008*d**8 + 0*d**3 + 0 + 0*d. Determine y so that h(y) = 0.
-1, 0
Let k(s) be the third derivative of -s**8/1344 + s**7/280 + s**6/240 - s**5/40 - s**4/96 + s**3/8 - 12*s**2. What is d in k(d) = 0?
-1, 1, 3
Let b be (122/4)/((-6)/(-21)). Let c = b - 106. Suppose 1/4*l + 0 - c*l**3 + 5/4*l**4 - 1/4*l**2 - 1/2*l**5 = 0. What is l?
-1/2, 0, 1
Let x = -6 - -11. Suppose 0*o + x*o = 0. Factor 0*t + o + 2/5*t**2.
2*t**2/5
Let q = 5 - 0. Let y = q + -3. Determine j so that 1/4*j**3 - 1/4*j**4 + 0*j + 0*j**y + 0 = 0.
0, 1
Let q(v) = -v**2 - v + 4. Let u(d) = -2*d**2 - 2*d + 7. Let w(n) = 7*q(n) - 4*u(n). Determine o so that w(o) = 0.
-1, 0
Suppose 0 - 2/13*m + 2/13*m**2 = 0. Calculate m.
0, 1
Let j = -17 - -3. Let d = j + 16. Factor -2/5*k**3 + 4/5 + 2/5*k - 4/5*k**d.
-2*(k - 1)*(k + 1)*(k + 2)/5
Let g(h) be the third derivative of 0*h + 0*h**5 + 1/480*h**6 + 0 - 2*h**2 + 1/12*h**3 - 1/32*h**4. Factor g(r).
(r - 1)**2*(r + 2)/4
Let m(h) be the first derivative of h**6/42 + h**5/35 - h**4/28 - h**3/21 + 2. Factor m(b).
b**2*(b - 1)*(b + 1)**2/7
Let p(u) be the second derivative of u**4/84 + 3*u**3/14 - 5*u**2/7 - 24*u. Factor p(s).
(s - 1)*(s + 10)/7
Let y(s) be the third derivative of -s**5/20 + s**4/2 - 3*s**3/2 + 15*s**2. Factor y(q).
-3*(q - 3)*(q - 1)
Suppose 2/3 + 1/3*l**2 - l 