4 - 3*b**2 - 23.
(b - 1)**2*(b + 2)**2
Factor -2/7*q**2 - 56 - 8*q.
-2*(q + 14)**2/7
Suppose 4*r = 5*p + 30 - 2, 2*r - 4*p = 14. Suppose -4*b + 2*d + 28 = 0, -3*d - r = -b + 10. Factor 2*m + 2*m**b - 8*m**2 - 13*m**4 + 5*m**4 + 0*m**4 + 12*m**3.
2*m*(m - 1)**4
Let t be (-2)/(3/(-15)*2). Find h, given that -9*h**4 - 7*h**4 - 2*h**3 - 5*h**t - 60*h**2 - 63*h**3 - 20*h - 14*h**4 = 0.
-2, -1, 0
Suppose -24 = -12*y + 175*d - 180*d, 4 = 2*y + 2*d. Factor 7/4*h**3 + 5*h + 9/2*h**2 + y + 1/4*h**4.
(h + 1)*(h + 2)**3/4
Suppose -10*w - 145 - 155 = 0. Let i be 3 + (-132)/152*w/(-9). Factor 0*n + 0 + 0*n**2 + i*n**4 + 4/19*n**3.
2*n**3*(n + 2)/19
Solve s**2 - 84 + 4*s**2 - 7*s**2 - s**2 + 48*s = 0.
2, 14
Let k(s) be the third derivative of -s**5/45 + 11*s**4/27 + 32*s**3/27 + 3*s**2 - 2*s. Factor k(l).
-4*(l - 8)*(3*l + 2)/9
Find d such that 19/8*d - 9/8 + 25/8*d**2 - 3/8*d**3 = 0.
-1, 1/3, 9
Let l(k) = -k**3 + 9*k**2 - 9*k + 11. Let m be l(8). Factor 8*z**4 + 4*z**4 - 3*z - m*z**5 + 134*z**3 + 12*z**2 - 152*z**3.
-3*z*(z - 1)**4
Suppose 5*y + 0*y - 10 = 0. Let w be 8/5 + 12/30. Let -y*k + 5*k**2 + k**w + 4*k**2 + 0*k - 8*k**3 = 0. Calculate k.
0, 1/4, 1
Solve 2/5*a**5 - 82/5*a**2 - 42/5*a**3 + 0 - 8*a + 2/5*a**4 = 0.
-4, -1, 0, 5
Factor -6*o + o**3 + o**3 - 5464*o**2 - 4 + 5464*o**2.
2*(o - 2)*(o + 1)**2
Let h be 0 + 6/((-3)/(-1)). Let t(d) = -d**h + 4*d - 5 - d + 0 - 5. Let l(k) = -k**2 + 2*k - 9. Let o(u) = -7*l(u) + 6*t(u). Solve o(q) = 0 for q.
-3, -1
Factor -3*c**5 - 748*c**4 + 21*c**3 - 742*c**4 + 1496*c**4 + 12*c**2.
-3*c**2*(c - 4)*(c + 1)**2
Let y(x) = x**3 + x**2. Let t(b) = -4*b**3 - 2*b**2 + b - 1. Let z be (11 - 8)/(3/3). Let k(q) = z*y(q) + t(q). Suppose k(m) = 0. Calculate m.
-1, 1
Let h(w) be the third derivative of -w**5/30 + 23*w**4/6 - 529*w**3/3 + 16*w**2 - 2. Solve h(o) = 0 for o.
23
Let a(y) be the third derivative of -y**7/6300 + y**6/450 - y**5/75 - 7*y**4/24 - 21*y**2. Let b(r) be the second derivative of a(r). Let b(t) = 0. Calculate t.
2
Let p(u) be the third derivative of 1/8*u**3 + 0 - 3/32*u**4 + 0*u + 4*u**2 - 1/160*u**6 + 3/80*u**5. Solve p(k) = 0 for k.
1
Let x(m) = 5*m**3 - 8*m**2 + 6*m + 3. Let p(q) = -8*q**3 + 15*q**2 - 10*q - 5. Let w(a) = 3*p(a) + 5*x(a). Find v such that w(v) = 0.
-5, 0
Let c(h) be the second derivative of h**5/15 + 2*h**4/3 - 10*h**3/3 - 11*h**2/2 + h. Let r(p) be the first derivative of c(p). Factor r(v).
4*(v - 1)*(v + 5)
Let d(a) = -4*a**2 - 112*a + 192. Let l = -32 - -16. Let f(p) = -p**2 - 37*p + 64. Let h(b) = l*f(b) + 5*d(b). What is t in h(t) = 0?
4
Factor 0 - 3/4*v + 5/8*v**2 + 1/8*v**3.
v*(v - 1)*(v + 6)/8
Let n(t) = -t**3 - 52*t**2 + 188*t + 12. Let g(r) = 3*r**3 + 105*r**2 - 375*r - 27. Let y(s) = -4*g(s) - 9*n(s). Factor y(u).
-3*u*(u - 8)**2
Let l(i) be the third derivative of i**7/70 + 13*i**6/20 + 189*i**5/20 + 27*i**4 - 216*i**3 - 6*i**2 + 5. Factor l(p).
3*(p - 1)*(p + 3)*(p + 12)**2
Let r(z) be the first derivative of 3/10*z**4 + 2/15*z**3 - 4/5*z - 2 + 2/25*z**5 - 3/5*z**2. Find c, given that r(c) = 0.
-2, -1, 1
Let m(t) be the first derivative of 3 + 3/5*t - 1/10*t**2 + 1/20*t**4 - 1/5*t**3. Solve m(s) = 0.
-1, 1, 3
Let n be -1 - (6/(-16) + (-21)/8). Let t(x) be the first derivative of 1/3*x - 1/12*x**4 - 1/2*x**n + 1/3*x**3 - 1. Solve t(j) = 0 for j.
1
Suppose -24*k - 6*k**3 - 1/3*k**4 - 61/3*k**2 - 28/3 = 0. Calculate k.
-14, -2, -1
Let t(b) be the third derivative of -b**5/24 + b**4/12 + b**3/12 - 3*b**2 + 18. Factor t(j).
-(j - 1)*(5*j + 1)/2
Let 1/5*a**2 - 9/5 + 0*a = 0. Calculate a.
-3, 3
Solve 0 + 2*m**3 + 3/2*m - 13/4*m**2 - 1/4*m**4 = 0 for m.
0, 1, 6
Let b(c) = 14*c**4 - 30*c**3 + 62*c**2 - 50*c + 4. Let u(r) = 5*r**4 - 10*r**3 + 21*r**2 - 17*r + 1. Let h(p) = -3*b(p) + 8*u(p). Factor h(m).
-2*(m - 2)*(m - 1)**3
Let h(v) be the second derivative of -3*v**5/10 - 31*v**4/8 + 2*v**3 - 514*v. Suppose h(n) = 0. Calculate n.
-8, 0, 1/4
Let f(k) be the second derivative of -k**4/3 - 58*k**3/3 - 10*k - 3. Factor f(u).
-4*u*(u + 29)
Let p(z) = 3*z**4 - 17*z**3 + z**2 + 65*z + 39. Let u(x) = 5*x**4 - 25*x**3 + x**2 + 97*x + 58. Let f(n) = 8*p(n) - 5*u(n). Determine a, given that f(a) = 0.
-11, -1, 2
Let r = -5279/168 + 220/7. Let q(w) be the second derivative of 0 + 1/80*w**5 - w - 1/40*w**6 + r*w**7 + 1/16*w**4 + 0*w**2 - 1/12*w**3. Factor q(o).
o*(o - 2)*(o - 1)**2*(o + 1)/4
Let a(p) be the third derivative of p**7/8820 - p**6/252 + 5*p**5/84 - 2*p**4/3 + 13*p**2. Let r(u) be the second derivative of a(u). What is d in r(d) = 0?
5
Let z(k) be the third derivative of -k**5/360 - k**4/36 - k**3/12 + 28*k**2. Suppose z(o) = 0. Calculate o.
-3, -1
What is h in 123/5*h**2 + 68921/5 - 5043/5*h - 1/5*h**3 = 0?
41
Let s(x) be the first derivative of -2*x**5/35 - x**4/14 + 2*x**3/21 + x**2/7 + 9. Determine h so that s(h) = 0.
-1, 0, 1
Factor 12*a**3 + 3*a**3 + 5*a**2 - 11*a**3 + 43*a**2 - 4*a - 48.
4*(a - 1)*(a + 1)*(a + 12)
Let h = -10 - -20. Let l be 7/14*1*h. Factor 0*f + 0*f**4 + 0 - 2/5*f**l + 4/5*f**2 + 6/5*f**3.
-2*f**2*(f - 2)*(f + 1)**2/5
Solve 176/3*j**2 + 56*j**4 - 116*j**3 + 0 + 4/3*j**5 + 0*j = 0 for j.
-44, 0, 1
Let j(b) be the third derivative of -b**5/36 + 5*b**4/36 + 166*b**2. Suppose j(f) = 0. Calculate f.
0, 2
Factor 14*i**4 - 154*i + 25*i**3 + 117*i**2 - 246*i - 1277*i**2 - 17*i**4 + 94*i**3.
-i*(i - 20)**2*(3*i + 1)
Suppose -38*l + 37*l = 6. Let c be (6 + -2 + -4)/(-2 - l). Solve -6/13*r - 4/13 + 2/13*r**3 + c*r**2 = 0.
-1, 2
Let q(t) = 39*t**2 - 3*t**2 + 42 - 22*t**3 - 14*t + 58*t**3 - 34*t. Let y(i) = 5*i**3 + 5*i**2 - 7*i + 6. Let n(d) = -6*q(d) + 44*y(d). Factor n(b).
4*(b - 1)**2*(b + 3)
Let g(f) be the first derivative of -147*f**4/20 - 224*f**3/5 - 174*f**2/5 - 48*f/5 + 15. Determine a so that g(a) = 0.
-4, -2/7
Suppose -27 = -3*r + 3*m, -2*r + 0*m = m - 6. Let c(y) be the second derivative of 0 + 9/20*y**r + 1/10*y**6 - 3*y**2 - 3/2*y**3 + 1/4*y**4 + 4*y. Factor c(s).
3*(s - 1)*(s + 1)**2*(s + 2)
Determine q, given that -8450/3*q**2 + 260/3*q - 2/3 = 0.
1/65
Factor 2*p**5 + 2*p**5 - 13*p**3 - 9*p**3 - 18*p**3 + 24*p**3.
4*p**3*(p - 2)*(p + 2)
Let g(m) be the second derivative of m**6/2160 - m**5/90 + m**4/12 - 25*m**3/6 - 2*m - 18. Let q(b) be the second derivative of g(b). Factor q(p).
(p - 6)*(p - 2)/6
Let k be ((-1)/(-4))/((-9)/(-54)) + 1. Factor 5/2*c**4 - k*c**3 + 0 + 5/6*c**2 - 5/6*c**5 + 0*c.
-5*c**2*(c - 1)**3/6
Let o(f) = 4*f**5 + 8*f**4 + 34*f**3 - 6*f**2 - 90*f - 48. Let g(h) = -h**5 - h**4 - h**3 - h**2 - 1. Let s(b) = -6*g(b) - o(b). Suppose s(j) = 0. Calculate j.
-3, -1, 3
Let a = -6315 + 6324. Factor -3/4*u**4 - a*u + 3*u**3 - 27/4 + 3/2*u**2.
-3*(u - 3)**2*(u + 1)**2/4
Let q(w) be the first derivative of w**7/840 - w**6/120 + w**5/60 - 26*w**3/3 - 33. Let b(o) be the third derivative of q(o). Find v such that b(v) = 0.
0, 1, 2
Suppose 0 = 4*l, -5*l - 3 - 25 = -4*k. Let w be (1*-2)/((-10)/35). Solve -8*f**2 + 5*f**3 + w + 4*f - k - f**3 = 0.
0, 1
Suppose 0*s = -3*s. Let s*g**3 + 2*g**5 + 3*g**5 + 3*g**3 + 10*g**4 + 2*g**3 = 0. Calculate g.
-1, 0
Let d(n) = n**2 + 4*n. Let y(u) = -2*u**4 + 16*u**3 + 42*u**2 + 72*u - 18. Let t(m) = -44*d(m) + 2*y(m). Factor t(k).
-4*(k - 9)*(k - 1)*(k + 1)**2
Let h(z) be the second derivative of -z**9/1512 + z**7/140 - z**6/90 + 7*z**3/3 + 18*z. Let j(x) be the second derivative of h(x). Factor j(f).
-2*f**2*(f - 1)**2*(f + 2)
Let h be 4/6 - (-294)/126. Factor -1/3*r + 1/3 - 1/3*r**2 + 1/3*r**h.
(r - 1)**2*(r + 1)/3
Let u be 7/7*4*4. Let y be 7/2*(-32)/(-56). Find k such that 2*k**4 + 10*k**2 - u*k**y + 1 - 1 + 4*k = 0.
-2, 0, 1
Let j(p) = 34*p - 2. Let b be j(1). Factor -24*d**2 + 3*d**3 + b*d**2 - 4*d**4 + d**3.
-4*d**2*(d - 2)*(d + 1)
Let n(t) be the second derivative of -11*t**6/40 + 3*t**5/10 + 3*t**4/16 + 274*t. Factor n(q).
-3*q**2*(q - 1)*(11*q + 3)/4
Let m(s) be the first derivative of -s**3/9 + 7*s**2/6 - 4*s + 13. What is k in m(k) = 0?
3, 4
Let -179*j + 965*j + 560*j**2 - 142*j**5 + 532*j + 138*j**5 - 118*j + 88*j**4 - 548*j**3 = 0. What is j?
-1, 0, 3, 10
Suppose 0*i = -4*f - 5*i + 24, -f + 4*i - 15 = 0. Factor -3*a**2 + 4*a - 1 - 1 - f + 2*a.
-3*(a - 1)**2
Let l(t) be the third derivative of -t**8/112 + t**7/35 + 3*t**6/40 - t**5/5 - t**4/2 - 19*t**2. Factor l(x).
-3*x*(x - 2)**2*(x + 1)**2
