17*o**4 + 0 + 300/17*o - 2/17*o**5 - 370/17*o**2 = 0.
-6, 0, 1, 5
Let w(r) = -110*r**2 - 9915*r - 19465. Let p(d) = 3*d**2 + 268*d + 526. Let l(v) = -75*p(v) - 2*w(v). Suppose l(z) = 0. What is z?
-52, -2
Find j such that 1/3*j**4 + 1/2*j**3 - 1/6 - 1/2*j - 1/6*j**2 = 0.
-1, -1/2, 1
Let c(y) be the third derivative of -34*y**2 + 0 - 1/60*y**6 - 1/315*y**7 + 0*y**3 + 0*y**4 + 0*y + 2/45*y**5. Factor c(v).
-2*v**2*(v - 1)*(v + 4)/3
Let m(l) = -l**2 - 4*l. Let x be m(-4). Suppose -2*j = -5*v + 9, 2*j = 3*v - 2*v + 3. Solve -2/5*p**2 - 2/5*p**4 + x + 0*p + 4/5*p**j = 0.
0, 1
Let p(m) be the third derivative of -m**6/180 + m**5/9 - 25*m**4/36 - m**2 - 52. Factor p(b).
-2*b*(b - 5)**2/3
Let b(u) = 15*u**2 - 156*u + 1899. Let q(v) = 43*v**2 - 467*v + 5693. Let k(a) = 17*b(a) - 6*q(a). Factor k(l).
-3*(l - 25)**2
Let w(p) be the first derivative of 3*p**3 - 1 + 0*p + 3/4*p**4 + 3*p**2. Let w(z) = 0. What is z?
-2, -1, 0
Factor -4/3*f**2 + 28 - 34/3*f.
-2*(f - 2)*(2*f + 21)/3
Let i(c) be the first derivative of 12 - 2/5*c**2 - 1/15*c**3 - 4/5*c. Solve i(n) = 0 for n.
-2
Let 2*o**2 - 584/5*o + 232/5 = 0. Calculate o.
2/5, 58
Let w = 133 - 125. Let y be 1/30*4 - w/(-40). Factor 0 + 1/3*u + y*u**2.
u*(u + 1)/3
Let y = 160 + -44. Let q be (4 + y/(-30))/(9/30). Factor q*a + 0 - 2/9*a**2.
-2*a*(a - 2)/9
Let u be 6 - 1*(6 + -4). Let t = -1241/42 - -208/7. Factor -t*p**u + 0 + 0*p**3 + 1/2*p**2 + 1/3*p.
-p*(p - 2)*(p + 1)**2/6
Let j be (7/28*-3)/(1/(-4)). What is x in -9*x - x**4 + 39*x**3 + x - 37*x**j + 4*x**2 = 0?
-2, 0, 2
Suppose 0 = 9*s - 4*s + 5*c + 15, 1 = -2*s - c. Let f be 30/(-4)*s/(-9). Factor 7/3*n**2 + f*n - 2/3.
(n + 1)*(7*n - 2)/3
Let b(z) = 1. Let a(w) = 1 - 137*w + 66*w + 67*w + 3*w**2. Let d be (-4)/6 + 2/(-6). Let k(h) = d*a(h) + 5*b(h). Solve k(x) = 0.
-2/3, 2
Let x = 32159 + -32153. Find b such that 16 + 28*b**4 - 36*b**2 + 56/3*b - 62/3*b**3 - x*b**5 = 0.
-2/3, 1, 2, 3
Let k(j) be the third derivative of j**6/240 - j**5/20 + j**4/6 + 46*j**2. Let k(z) = 0. What is z?
0, 2, 4
Suppose -17*n = r - 22*n - 3, 5*r - 15 = -4*n. Solve -4/5*b**4 + 2/5*b**2 + 0 + 0*b + 7/5*b**r = 0 for b.
-1/4, 0, 2
Suppose 175/3 - 5/3*j**2 - 170/3*j = 0. What is j?
-35, 1
Let c(p) be the second derivative of -5*p**4/12 + 70*p**3/3 - 490*p**2 + 42*p. Let c(m) = 0. What is m?
14
Let g(r) be the third derivative of 0*r**4 + 1/60*r**6 - 1/30*r**5 + 1/105*r**7 + 0*r**3 + 0 + 10*r**2 - 1/168*r**8 + 0*r. Suppose g(k) = 0. What is k?
-1, 0, 1
Let a be (-868)/(-70) - 10 - (1 + 1/1). Factor 7/5*o - 3/5*o**3 - a - 2/5*o**2.
-(o - 1)*(o + 2)*(3*o - 1)/5
Suppose -36 = 36*b - 144. Suppose -v - 21 = -8*v. Factor -9/2*t**b - 4 + 10*t - v*t**2.
-(t + 2)*(3*t - 2)**2/2
Let t be 4/90 - (-2040)/1350. Factor 4/9*k + 0 - t*k**2.
-2*k*(7*k - 2)/9
Let x(i) be the second derivative of 1/2*i**6 + 0 - 5/4*i**4 - 5/3*i**3 + 30*i + 1/2*i**5 + 0*i**2. Let x(b) = 0. Calculate b.
-1, -2/3, 0, 1
Let g(m) be the third derivative of -m**7/168 + m**6/24 - m**5/12 - 5*m**3/3 - 34*m**2. Let u(x) be the first derivative of g(x). Factor u(k).
-5*k*(k - 2)*(k - 1)
Let n(p) be the second derivative of 0 + 0*p**2 + 1/70*p**5 + 8*p + 1/21*p**4 + 1/21*p**3. Factor n(l).
2*l*(l + 1)**2/7
Suppose -2*p - 4*x = 0, -31*p - x = -30*p - 1. Determine h, given that 4/7*h**p - 16/7*h + 16/7 = 0.
2
Let 27*r**2 + 6*r + 75*r**3 + 33*r**4 - 174*r**5 - 30*r**3 + 183*r**5 = 0. Calculate r.
-1, -2/3, 0
Determine s, given that -4/9*s**4 + 16/9*s + 0 + 4/9*s**2 - 16/9*s**3 = 0.
-4, -1, 0, 1
Suppose -2*c - 9 = 49. Let n = c - -101. Factor -36*v**2 - 8*v**3 - n*v - 2/3*v**4 - 54.
-2*(v + 3)**4/3
Factor 3320 - 3*a**3 + 24*a**2 - 36*a - 3320.
-3*a*(a - 6)*(a - 2)
Let o = 430 + -426. Let k(b) be the second derivative of -1/6*b**3 + 0 - 5*b + 1/12*b**o - 1/2*b**2 + 1/20*b**5. What is i in k(i) = 0?
-1, 1
Let t(y) be the first derivative of -3*y**5/35 - 9*y**4/14 - 4*y**3/7 + 9*y**2/7 + 15*y/7 - 83. Suppose t(x) = 0. What is x?
-5, -1, 1
Let m(c) be the second derivative of -1/20*c**6 + 1/24*c**4 - 12*c + 3/8*c**3 - 1/10*c**5 + 0 - 1/168*c**7 + 1/2*c**2. Factor m(z).
-(z - 1)*(z + 1)**3*(z + 4)/4
Let l be 2/(-1) + 544/60 + -7. Let t(w) be the first derivative of 0*w - 7 - 1/12*w**4 + l*w**5 - 1/9*w**3 + 1/18*w**6 + 0*w**2. Let t(q) = 0. Calculate q.
-1, 0, 1
Factor -26/7*h**2 - 256/7*h + 40/7.
-2*(h + 10)*(13*h - 2)/7
Suppose 9*v = 10*v - 25. Let j = 33 - v. Factor n**5 + 2*n**4 + j*n**4 - 7*n**4 - n**4.
n**4*(n + 2)
Let g(b) = 37*b**2 - 105*b - 107. Let p(k) = -15*k**2 + 53*k + 54. Let f(q) = 4*g(q) + 10*p(q). Find u such that f(u) = 0.
-1, 56
Let q = 31821 - 159103/5. Let 0*m + 0 - q*m**5 + 0*m**3 + 4/5*m**4 + 0*m**2 = 0. Calculate m.
0, 2
Let l(i) be the second derivative of -i**6/30 + 2*i**5/15 - i**4/6 - 3*i**2 - 8*i. Let h(k) be the first derivative of l(k). Factor h(t).
-4*t*(t - 1)**2
Suppose 6*q = 2*q + 20. Suppose 0 = -q*s + 13 + 32. Factor -s*m + 10*m + 2*m - m**3 - 2.
-(m - 1)**2*(m + 2)
Factor 64/9*m + 0 - 32*m**3 + 160/9*m**4 + 128/9*m**2 - 28/9*m**5.
-4*m*(m - 2)**3*(7*m + 2)/9
Suppose -12 = -4*s - d, 0 = -3*d - 3 + 15. What is x in 0*x**s + 0*x + 1 - 2 - x + x**2 + x**3 = 0?
-1, 1
Let k(t) be the second derivative of -11*t - 1/48*t**4 - 3/8*t**2 + 0 + 1/6*t**3. Find p, given that k(p) = 0.
1, 3
Let z(x) be the second derivative of -x**7/560 - x**6/40 - 9*x**5/80 - x**4/4 - 9*x**3/2 + 45*x. Let p(l) be the second derivative of z(l). Factor p(c).
-3*(c + 1)**2*(c + 4)/2
Let k(f) be the third derivative of -5*f**8/336 - f**7/42 + 19*f**6/24 + 13*f**5/12 - 65*f**4/4 - 60*f**3 - 3*f**2 + 75. What is h in k(h) = 0?
-4, -2, -1, 3
Let z be (-154 + 11)/11 - -13. Factor z - 5/2*m**2 - 1/2*m**4 - m - 2*m**3.
-m*(m + 1)**2*(m + 2)/2
Determine o, given that 297/4*o - 3/4*o**2 - 147/2 = 0.
1, 98
Factor -2/3*r**4 + 26/3 + 76/3*r + 20/3*r**3 + 24*r**2.
-2*(r - 13)*(r + 1)**3/3
Let t(p) be the second derivative of p**7/231 - 2*p**6/33 + 18*p**5/55 - 9*p**4/11 + 9*p**3/11 - 143*p. What is s in t(s) = 0?
0, 1, 3
Let x(v) be the first derivative of -v**8/13440 + v**6/960 + v**5/480 - 2*v**3/3 + 7. Let c(g) be the third derivative of x(g). Factor c(w).
-w*(w - 2)*(w + 1)**2/8
Let y(c) be the third derivative of c**5/180 - c**4/36 - 2*c**2 - 2*c. Factor y(q).
q*(q - 2)/3
Suppose 2*g + 18 = -3*a, -20 = 4*g + a - 3*a. Let c be 3/g*(-6 - 0). Factor -2*q**2 + q**c - 2*q + 4*q + q**3 - 2*q**2.
2*q*(q - 1)**2
Let -4*k**4 + 24*k + 4*k**5 - 2*k**2 - 28*k**3 + 14*k**2 - 8*k**2 = 0. What is k?
-2, -1, 0, 1, 3
Suppose -6*r = -r + 15. Let w(q) = -4*q - 7. Let v be w(r). Determine d so that 0*d + 0 - 2/7*d**4 + 2/7*d**2 - 8/7*d**v + 8/7*d**3 = 0.
-1, -1/4, 0, 1
Let n(x) be the first derivative of 1/12*x**3 - 3/2*x - 1/8*x**2 - 15. Determine f, given that n(f) = 0.
-2, 3
Let m(i) be the third derivative of i**5/100 - i**4/40 - 2*i**3 - 18*i**2. Factor m(d).
3*(d - 5)*(d + 4)/5
Let z(u) = 2*u**2 + 10*u - 11. Let n be z(-6). Factor n - 722*t + 0*t**4 - t**4 - 2*t**3 + 724*t.
-(t - 1)*(t + 1)**3
Let g(p) be the third derivative of 0*p + 1/30*p**5 - 1/6*p**4 + 1/60*p**6 + 0*p**3 + 10*p**2 + 0. Factor g(y).
2*y*(y - 1)*(y + 2)
Find v, given that -8*v**3 + 20*v + 0 + 142/3*v**2 - 10/3*v**4 = 0.
-5, -2/5, 0, 3
Suppose 3*c - 160 = -2*c. Factor -23 - c - 72*o - 60*o**2 + 50*o**3 + 39.
2*(o - 2)*(5*o + 2)**2
Suppose -2*t + 0*t = y + 5, 5*y + 12 = 3*t. Let p be 2/(-56)*t + 3/12. Factor 6/7*w**4 - p*w**5 + 0 + 0*w + 2/7*w**2 - 6/7*w**3.
-2*w**2*(w - 1)**3/7
Let t(h) be the second derivative of 0*h**2 + 7/5*h**5 + 0 - 4/3*h**4 - 13*h + 0*h**3. Factor t(o).
4*o**2*(7*o - 4)
Let q(z) be the first derivative of -3*z**5/20 + z**4/2 + z**3/2 - 3*z**2 + 40*z + 16. Let m(w) be the first derivative of q(w). Factor m(n).
-3*(n - 2)*(n - 1)*(n + 1)
Let u(o) be the third derivative of 1/15*o**5 + 11*o**2 + 1/2*o**4 + 0 + 0*o - 1/10*o**6 - 2/3*o**3. Determine y so that u(y) = 0.
-1, 1/3, 1
Let r(h) be the third derivative of -h**6/150 - 22*h**5/75 - 7*h**4/10 + 198*h**2 + 2*h. Find p, given that r(p) = 0.
-21, -1, 0
Suppose 4*a + 2*w - 20 = 0, 1312*a - 1317*a - 2*w = -22. Factor 24/5*y + 2/5*y**a + 72/5.
2*(y + 6)**2/5
Let r(l) = l**2 - 8*l + 4. Let t be r(9). Factor -6*g**4 + 8 - 3*g**5 - 64*g**2 - 25*g**5 - 136*g**3 - 9*g + t*g - 98*g**4.
-4*(g + 1)**4*(7*g - 2)
Find n, 