).
-(f - 22)**2/5
Let l(k) = k**3 + k**2 - k - 2. Let v(d) = 9*d**3 - 30*d**2 + 99*d - 84. Let n(z) = 6*l(z) - v(z). Factor n(b).
-3*(b - 8)*(b - 3)*(b - 1)
Let u(x) be the second derivative of x**6/90 - x**5/60 - 5*x**4/36 - x**3/6 - 19*x. Solve u(h) = 0.
-1, 0, 3
Let d(w) = -2*w**2 - 14*w + 243. Let j be d(8). Find b such that -j - 9/2*b**2 + 21/2*b = 0.
1/3, 2
Let t(w) be the second derivative of -w**4/12 + 16*w**3/3 + 33*w**2/2 + 294*w. Solve t(d) = 0 for d.
-1, 33
Factor -117/4 - 21/8*k + 3/8*k**2.
3*(k - 13)*(k + 6)/8
Let r = 1333 - 33324/25. Let a(q) be the first derivative of -1/5*q**4 + r*q**5 + 0*q + 0*q**2 + 1/5*q**3 + 12. Factor a(c).
c**2*(c - 3)*(c - 1)/5
Let l(y) be the third derivative of -9*y**2 + 0*y**3 + 0 + 1/40*y**5 + 1/16*y**4 + 0*y. Let l(v) = 0. What is v?
-1, 0
Suppose 17*a - 714 = -646. Factor 1/10*j**a + 0 + 0*j + 0*j**3 - 1/10*j**2.
j**2*(j - 1)*(j + 1)/10
Let b(i) be the third derivative of 5*i**5/6 + 35*i**4/24 - 5*i**3/2 + 144*i**2. Factor b(m).
5*(m + 1)*(10*m - 3)
Let g(v) = -2*v**2 - 3*v - 17. Let l be g(12). Let u = 2393/7 + l. Find r such that 0 - 3/7*r**2 + 0*r - 3/7*r**4 - u*r**3 = 0.
-1, 0
Suppose 10*z - 6*z - 4*k - 4 = 0, -5*z = -4*k - 6. Factor -1/5*m**z + 7/5*m + 0.
-m*(m - 7)/5
Let y(w) = -w**2 + 18*w - 19. Let r be y(16). Suppose 4*x - r = -13. Suppose 2/3*h**2 - 1/3*h**3 - 1/3*h**4 + x*h + 0 = 0. Calculate h.
-2, 0, 1
Suppose 4*i - 5*i - 5*i = 0. Let q(k) be the third derivative of 0*k**3 + i*k - 3*k**2 + 0 - 1/240*k**5 - 1/48*k**4. Factor q(u).
-u*(u + 2)/4
Let i(s) = s**2 + 14*s + 42. Let j be i(-4). Determine u, given that -8/3 + 2/3*u**4 - 2/3*u**j - 16/3*u - 2/3*u**5 + 10/3*u**3 = 0.
-1, 2
Let h(c) be the first derivative of -2*c**5/65 - 2*c**4/13 - 10*c**3/39 - 2*c**2/13 + 64. What is f in h(f) = 0?
-2, -1, 0
Factor 74/11*y - 72/11*y**2 - 2/11*y**3 + 0.
-2*y*(y - 1)*(y + 37)/11
Let h(i) = 3*i**2 - 32*i - 6. Let u be h(11). Suppose 1/9*g**u + 1/9*g**3 + 0 - 2/9*g**4 + 0*g**2 + 0*g = 0. What is g?
0, 1
Let k(c) be the third derivative of c**6/120 - c**5/60 - 79*c**2. Factor k(y).
y**2*(y - 1)
Let n(p) be the first derivative of -p**6/15 + 4*p**5/25 + 3*p**4/10 + 278. Factor n(u).
-2*u**3*(u - 3)*(u + 1)/5
Suppose -r + 13 = 13. Let s(k) = -k**3 - 13*k**2 + 3*k + 44. Let j be s(-13). Find x, given that r - 2/3*x**4 + 0*x + 0*x**2 + 0*x**3 + 2/3*x**j = 0.
0, 1
Let t(r) be the first derivative of 29*r**2/2 - 3*r + 7. Let f be t(2). Suppose 26*u**2 + 3*u - u**2 - 6 + 16*u**3 - f*u**3 + 2*u**2 + 15*u**4 = 0. What is u?
-2/5, 1
Let n(i) be the third derivative of i**6/60 - 7*i**5/30 - i**2 + 13*i. Find j such that n(j) = 0.
0, 7
Let t(z) be the third derivative of -1/390*z**5 + 6*z**2 + 0*z - 5/78*z**4 + 0 - 25/39*z**3. What is x in t(x) = 0?
-5
Suppose 13 = 6*o - o - 4*d, 5*o - 5*d - 10 = 0. Suppose 2*q = -2*a + o*a - 102, 2*q + 68 = 2*a. Factor r - 4*r**3 + 3*r + 3*r**4 - 1 + a*r**2 - 36*r**2.
(r - 1)**2*(r + 1)*(3*r - 1)
Let b = 471/10 - 47. Let f(d) be the third derivative of -7/8*d**4 - 3/2*d**3 + 0 - 5*d**2 + 0*d - b*d**5. Factor f(c).
-3*(c + 3)*(2*c + 1)
Let w be (-2)/10 - 19/5320*-161. Solve -w*z**3 + 3/8*z + 3/8*z**2 - 3/8 = 0.
-1, 1
Let f = -265 + 310. Let i be 18/f - (8/(-5) + 2). Factor 0 + i*d + 1/4*d**4 - 1/4*d**2 + 1/4*d**5 - 1/4*d**3.
d**2*(d - 1)*(d + 1)**2/4
Let h = -3827 + 3841. Let 5/2*a - 1 + 12*a**2 - h*a**3 - 40*a**4 = 0. Calculate a.
-1/2, 1/4, 2/5
Let -2 - 28/15*k + 2/15*k**2 = 0. What is k?
-1, 15
Suppose -297 - 34*h**2 - 15*h**5 - 300 - 115*h**3 + 597 + 4*h**2 - 80*h**4 = 0. What is h?
-3, -2, -1/3, 0
Let y(i) = 24 + 87*i - 67 - 12*i**2 - 149. Let b(t) = 3*t**2 - 22*t + 48. Let n(v) = -9*b(v) - 2*y(v). Determine r so that n(r) = 0.
4
Suppose 5*z = -25, 5*z + 7 = 4*s - s. Let j be (-32)/(-56)*(5/s + 2). Factor j*t**4 + 0 + 0*t - 2/3*t**5 + 2/3*t**3 - 2/3*t**2.
-2*t**2*(t - 1)**2*(t + 1)/3
Solve 3/4*o - 3/4*o**3 + 15/4*o**2 - 15/4 = 0 for o.
-1, 1, 5
Suppose 3*b + 431*o - 6 = 432*o, b + 4*o - 2 = 0. Let -3 - 1/2*t**b - 5/2*t = 0. Calculate t.
-3, -2
Factor -1584/5*i**2 - 1/5*i**4 - 68/5*i**3 - 13552/5*i - 21296/5.
-(i + 2)*(i + 22)**3/5
Let b(t) be the second derivative of -5*t**4/12 - 15*t**3 + 95*t**2/2 + 81*t. Factor b(l).
-5*(l - 1)*(l + 19)
Let f = -79 + 91. Suppose -4*p + 0 = -f. Factor -8/3*s**p - 8/3*s**4 + 4/3*s - 2/3 + 2*s**2.
-2*(s + 1)**2*(2*s - 1)**2/3
Suppose 3*p + 99 = 12*p. Let s(g) = 26*g**2 + 28*g + 14. Let r(n) = -51*n**2 - 56*n - 27. Let d(f) = p*s(f) + 6*r(f). Factor d(l).
-4*(l + 1)*(5*l + 2)
Let g = 48 + -43. Let h = 16/3 - g. Suppose 0 - 2/3*k**4 - h*k + 0*k**3 + 2/3*k**2 + 1/3*k**5 = 0. What is k?
-1, 0, 1
Let w(l) be the third derivative of -l**6/18 - 13*l**5/24 - 5*l**4/8 + l**3 - 7*l**2. Let x(j) be the first derivative of w(j). Factor x(d).
-5*(d + 3)*(4*d + 1)
Let t be (-2*(0 - (-4)/16))/(2/(-12)). Determine c, given that -8/7*c**t + 8/7 - 2/7*c**4 + 8/7*c - 6/7*c**2 = 0.
-2, -1, 1
Let n be ((-2)/3)/((-3)/(-27)). Let o be -1*n/18 + 10/42. Suppose 48/7*b + 24/7*b**2 + o*b**3 + 32/7 = 0. Calculate b.
-2
Suppose 5*h + 4*g - 2 = 0, 0*g = g + 2. Let j be 16/9 - 2/(-9). Factor -4 + 1 - 4 + h*z**j + 5.
2*(z - 1)*(z + 1)
Let n(s) = 2*s**3 + s**2 - 2. Let d(u) = -4*u**3 - 27*u**2 + 22*u + 6. Let v(w) = -d(w) - 3*n(w). Determine m so that v(m) = 0.
0, 1, 11
Factor 0*r + 28/3*r**3 + 4*r**2 + 4/3*r**5 + 20/3*r**4 + 0.
4*r**2*(r + 1)**2*(r + 3)/3
Suppose -90 = -20*o - 25*o. Let v(f) be the first derivative of -1/2*f**4 - 3 + 0*f - f**o + 4/3*f**3. What is w in v(w) = 0?
0, 1
Let v(z) be the second derivative of z**6/210 + 3*z**5/140 - 2*z**3/21 + 142*z. Factor v(m).
m*(m - 1)*(m + 2)**2/7
Determine t, given that 18/11*t + 20/11 - 2/11*t**2 = 0.
-1, 10
Let m(k) be the third derivative of 0 + 5/6*k**3 + 0*k + 7/100*k**5 + 1/2*k**4 - 23*k**2 + 1/300*k**6. Factor m(u).
(u + 5)**2*(2*u + 1)/5
Let l(w) be the second derivative of 4/3*w**3 + 1/60*w**6 - 7/40*w**5 - 19*w + 0*w**2 + 1/3*w**4 + 0. Solve l(g) = 0.
-1, 0, 4
Let a(r) = -r**2 + r. Let j = -3 + 4. Let p(n) be the second derivative of -n**4/2 + 6*n. Let b(t) = j*p(t) - 4*a(t). Solve b(h) = 0 for h.
-2, 0
Let b(o) = -3*o**4 + o**3 + 3*o**2 - o - 2. Let v(d) = 39*d**4 - 12*d**3 - 39*d**2 + 12*d + 27. Let q = 3 - 5. Let j(u) = q*v(u) - 27*b(u). Factor j(m).
3*m*(m - 1)**2*(m + 1)
Let w(l) = -l**2 + 16*l + 1. Let d be w(15). Suppose 0*u = -4*u + d. Suppose -5*g**5 + g - 2*g**2 - 2*g**4 + 3*g**5 + g**5 + 4*g**u = 0. What is g?
-1, 0, 1
Let d be (10 - 532/42)*3/(-2). Let a(i) be the first derivative of -2/27*i**3 - 6 + 0*i + 2/9*i**2 - 1/18*i**d. Let a(y) = 0. Calculate y.
-2, 0, 1
Solve -6251*w**4 + 4 + 280*w + 4573*w**5 + 19986*w**4 + 14275*w**3 + 5305*w**2 - 84*w**5 = 0 for w.
-1, -2/67
Let k(b) be the first derivative of 1/12*b**4 + b + 2 + 1/8*b**2 - 1/6*b**3. Let p(w) be the first derivative of k(w). Determine c, given that p(c) = 0.
1/2
Let o(m) be the first derivative of -147/8*m**4 - 7*m**3 + 0*m - m**2 + 2 - 343/20*m**5. What is u in o(u) = 0?
-2/7, 0
Let h be ((119/28)/17)/(1/9). Find k, given that 9/4*k**3 + h*k**4 + 0*k + 3/4*k**5 + 0 + 3/4*k**2 = 0.
-1, 0
Let t(w) = 5*w**2 - 25*w + 14. Let x = 41 - 46. Let l(z) = 5*z**2 - 25*z + 15. Let k(c) = x*t(c) + 6*l(c). Determine a so that k(a) = 0.
1, 4
Let a(g) = g**2 - 5*g - 1. Let k be a(6). Suppose -k*z - 3*f + 48 = -6*f, 3*z + 3*f - 24 = 0. Factor 6*d - 4*d**2 - z*d + 3*d.
-4*d**2
Let s be (-20)/(-25)*-5 - 51/(-12). Let n(w) be the second derivative of s*w**3 - 8*w + 1/24*w**4 + 0*w**2 + 0. Factor n(j).
j*(j + 3)/2
Let f(d) be the third derivative of -2*d**7/35 - 19*d**6/30 - 2*d**5/3 + 32*d**4/3 - 64*d**3/3 + 4*d**2 + 56*d. Let f(p) = 0. What is p?
-4, 2/3, 1
Let t(a) be the third derivative of a**6/24 + 5*a**5/12 + 5*a**4/12 - 20*a**3/3 - 71*a**2. Factor t(u).
5*(u - 1)*(u + 2)*(u + 4)
Let u(l) be the second derivative of 1/3*l**3 + 0 - 2*l**2 + 8*l + 1/6*l**4. What is q in u(q) = 0?
-2, 1
Let s(h) be the second derivative of -25/12*h**4 - 55/3*h**3 + 8*h - 20*h**2 + 0. Factor s(g).
-5*(g + 4)*(5*g + 2)
Let t(m) be the first derivative of -m**4/36 + 2*m**3/9 - 2*m**2/3 + 6*m - 4. Let r(j) be the first derivative of t(j). Factor r(o).
-(o - 2)**2/3
Let a(s) = -4*s**5 + 3*s**4 + 43*s**3 - 155*s**2 + 123*s + 5. Let j(w) = -w**4 - w**3 + w**2 - w + 1. 