. What is n?
0, 1, 3
Let i(r) be the first derivative of -r**6/18 + 62*r**5/15 - 895*r**4/12 - 2110*r**3/9 + 448*r**2/3 + 2048*r/3 - 1949. Find l, given that i(l) = 0.
-2, -1, 1, 32
Let l(j) be the third derivative of -j**8/448 + 3*j**7/56 - j**6/2 + 5*j**5/2 - 15*j**4/2 + 14*j**3 - 20*j**2 + 8. What is d in l(d) = 0?
2, 7
Let s(u) = 162*u**2 + 171*u - 333. Let j(f) = f**3 - f**2 - f + 1. Let q(x) = -3*j(x) + s(x). Factor q(o).
-3*(o - 56)*(o - 1)*(o + 2)
Suppose 1265*x**2 + 5*x**3 + 825398 - 825398 + 2510*x = 0. What is x?
-251, -2, 0
Factor -2*l**3 + 65*l + 223*l + 41*l**2 - 77*l**2.
-2*l*(l - 6)*(l + 24)
Let v be (1/(-4))/(573945/(-71745) + 8). Let q = v + 1198. Let -3*k**3 + q*k + 0*k**4 - 3/2 + 3/2*k**2 + 3/4*k**5 = 0. Calculate k.
-2, -1, 1
Suppose -p + 63 = -8*s + 12*s, 3*s - 47 = -p. Let y(h) be the second derivative of 1/9*h**3 + 0 + 0*h**2 - 1/36*h**4 + s*h. Factor y(c).
-c*(c - 2)/3
Let l(t) be the third derivative of t**6/30 - 11*t**5/5 + 85*t**4/2 - 1150*t**3/3 - 295*t**2. Factor l(z).
4*(z - 23)*(z - 5)**2
Determine p so that 335*p**3 + 0*p**2 + 0*p + 0 + 5/3*p**4 = 0.
-201, 0
Let y = -2993 - -5676. Let t = -29351/11 + y. Factor -2/11*l**2 - t - 36/11*l.
-2*(l + 9)**2/11
Let i = 2053 + -868. Let n = -5917/5 + i. Solve -6/5*l - 1/5*l**2 - n = 0.
-4, -2
Suppose 14*u + 119 = 3*w + 10*u, 5*u = -w + 65. Let v(q) be the second derivative of 1/6*q**4 - w*q + 0 + 2*q**2 - 11/9*q**3. Factor v(o).
2*(o - 3)*(3*o - 2)/3
Factor -1/5*w**3 + 0 + 1/10*w**4 - 39/10*w**2 - 36/5*w.
w*(w - 8)*(w + 3)**2/10
Let -60/7 + 24/7*z + 3/7*z**2 = 0. Calculate z.
-10, 2
Suppose -45 = -9*x + 343*n - 346*n, -x + 3*n - 15 = 0. Determine s so that -96/13*s**5 + 106/13*s**x - 10/13*s + 2/13 - 18/13*s**2 + 16/13*s**4 = 0.
-1, -1/3, 1/4, 1
Let c be 7*(-2)/70 - (-44 + 39). Factor -1/5*h**3 - c + 13/5*h**2 - 2*h.
-(h - 12)*(h - 2)*(h + 1)/5
Let w(h) be the third derivative of h**7/2310 - 7*h**6/110 - h**5/220 + 125*h**4/132 + 28*h**3/11 + 579*h**2. Solve w(b) = 0.
-1, 2, 84
Let u(v) = 33184*v + 199120. Let b be u(-6). Factor -2*k**3 - b*k + 35/3*k**2 - 1/3*k**4 + 20/3.
-(k - 2)*(k - 1)**2*(k + 10)/3
Let f = 8845 + -8840. Let g(t) be the second derivative of 1/4*t**f + 0*t**3 + 0*t**2 - 5/12*t**4 - 38*t + 0. Suppose g(d) = 0. Calculate d.
0, 1
Let f(m) = -4*m**2 - 4*m - 6. Let c(y) = -4*y**2 - 4*y - 4. Suppose 0 = z + 44 - 40. Let a be -4 + 0/z + (1 - 0). Let v(g) = a*c(g) + 2*f(g). Factor v(q).
4*q*(q + 1)
Let p(d) = 7*d + 6. Let z be p(7). Suppose -5*t = -125 - z. Find j, given that 33*j**2 + j - 10*j + 12*j**5 + 3*j - t*j**3 - 3*j**4 = 0.
-2, 0, 1/4, 1
Let k(y) be the second derivative of -y**5/70 + 59*y**4/42 - 215*y**3/21 - 275*y**2/7 - 3*y - 2167. What is r in k(r) = 0?
-1, 5, 55
Let q be ((-68967)/(-3871))/(18/210*5). Factor 432/7*h - 3/7*h**4 - 192/7 - q*h**2 + 54/7*h**3.
-3*(h - 8)**2*(h - 1)**2/7
Factor 3*u**3 - u**2 - 5*u**2 - 1127*u - 2 + 1082*u + 110.
3*(u - 3)**2*(u + 4)
Suppose 117/2 - 11/4*t**2 + 125/4*t = 0. What is t?
-18/11, 13
Let y(z) be the third derivative of z**6/24 + 7*z**5/4 + 165*z**4/8 - 605*z**3/6 + 976*z**2. Factor y(d).
5*(d - 1)*(d + 11)**2
Suppose -3*j + r = -0*j - 5, -3*r - 15 = 4*j. Let h(s) be the second derivative of j*s**2 + 32*s + 1/20*s**5 + 1/3*s**4 + 0 + 1/2*s**3. Factor h(f).
f*(f + 1)*(f + 3)
Let h be (1 + -161)*41/41. Let r be (1/(-6))/(24/h). Suppose 14/9*p + 2/3 + r*p**2 + 2/9*p**3 = 0. Calculate p.
-3, -1
Factor 1/3*x**4 + 4406*x**2 - 14848/3*x - 26912 + 77*x**3.
(x - 3)*(x + 2)*(x + 116)**2/3
Let 1057*n + 142*n**2 + 103*n**3 - 2089*n + 142*n**2 + 1068*n - 15*n**4 = 0. Calculate n.
-2, -2/15, 0, 9
Let k(s) be the second derivative of -s**5/60 - 5*s**4/8 - 157*s**3/36 + 15*s**2/2 + 2805*s. Factor k(y).
-(y + 5)*(y + 18)*(2*y - 1)/6
Let d(p) = 4*p**2 - 72*p - 11. Let g be d(7). Let y be 2/(-29) - 370/g. Solve 2/11*b**4 + 10/11*b**3 + 0*b + y*b**2 + 0 = 0.
-3, -2, 0
Suppose 14*u = 9*u + 15. Factor -2*z**3 + 32*z - 3*z**3 - 32 + 8*z**2 - 4*z**2 - 2*z**2 + u*z**3.
-2*(z - 4)*(z - 1)*(z + 4)
Let y(b) = -10*b**2 - 70*b - 80. Let p(w) = -w**2 + 21 - 4*w**2 - 36*w - 60. Let o(z) = -5*p(z) + 3*y(z). Factor o(t).
-5*(t + 3)**2
Let f be ((-305)/(-915))/(-1 - 8/(-9)). Let p be (24/f*1)/(-10). Find o, given that -2/5*o**5 - 4/5 + p*o**3 - 16/5*o**2 + 4/5*o**4 + 14/5*o = 0.
-2, 1
Let t(a) = 4*a**2 + 104*a + 576. Suppose 10*w - 132 = 22*w. Let g(q) = -12*q**2 - 310*q - 1728. Let x(d) = w*t(d) - 4*g(d). Factor x(s).
4*(s + 12)**2
Let j(i) be the first derivative of 0*i - 10/3*i**6 + 8*i**2 - 16*i**3 - 29 + i**4 + 48/5*i**5. Solve j(o) = 0.
-1, 0, 2/5, 1, 2
Determine y so that 14551468 - 50*y - 14551418 + 2*y**3 - 3*y**2 + y**2 = 0.
-5, 1, 5
Let r be 8/28 + 52/14. Suppose 0 = -r*u + 17 - 1. Determine d, given that -6*d + 3*d**3 - 4*d**u + d**4 - 3*d**3 + 9*d**2 = 0.
-2, 0, 1
Find k such that 2/3*k**2 + 0*k**4 + 1/9*k**5 - 8/9*k**3 + 7/9*k - 2/3 = 0.
-3, -1, 1, 2
Let y(r) be the second derivative of -r**6/60 + 7*r**5/10 - 25*r**4/24 - 9*r**3/2 - 7011*r. Factor y(v).
-v*(v - 27)*(v - 2)*(v + 1)/2
Factor 5*f**3 + 2600*f**2 - 6162*f + 6939*f - 835*f**2 + 9678*f + 15615.
5*(f + 3)**2*(f + 347)
Let o(s) = s**4 + s**3 + s. Let a(h) = -7*h**4 - 8*h**3 + 4*h**2 - 4*h - 3. Let d(r) = -a(r) - 6*o(r). Factor d(b).
(b - 1)**2*(b + 1)*(b + 3)
Let c(w) be the third derivative of -3*w**8/896 + w**7/80 + 539*w**6/960 + 477*w**5/160 + 389*w**4/96 + 5*w**3/2 - 150*w**2 - 4. Solve c(k) = 0.
-4, -3, -1/3, 10
Let d(c) be the first derivative of c**4/48 - 5*c**3/12 + 9*c**2/8 + 51*c - 103. Let k(g) be the first derivative of d(g). Solve k(t) = 0 for t.
1, 9
Let t(s) = 52*s**2 - 188*s + 216. Let h(b) = -10*b**2 + 38*b - 43. Let r(k) = k**2 - 12*k + 11. Let x be r(9). Let o(u) = x*h(u) - 3*t(u). Factor o(v).
4*(v - 10)*(v - 1)
Let v be 6805*(-7)/(-105) - 2/(-6). Let z = 1366/3 - v. Factor 4/3*g - z - 1/3*g**2.
-(g - 2)**2/3
Let k(z) be the first derivative of -z**4/36 + z**3/6 + 5*z**2/3 + 105*z - 19. Let r(c) be the first derivative of k(c). Suppose r(p) = 0. Calculate p.
-2, 5
Let o(s) = 7*s**2 - 127*s - 204. Let x(f) = -8*f**2 + 128*f + 156. Let n(z) = -5*o(z) - 4*x(z). Let n(p) = 0. What is p?
-3, 44
Factor -261 + 3/2*y**2 - 165/2*y.
3*(y - 58)*(y + 3)/2
Suppose -2*l + 3*d = 265, 2*l = 3*l + 5*d + 113. Let y = l + 131. Factor -85*i**3 - 2*i - 11*i**4 + i**2 - 8*i**2 + 105*i**y.
-i*(i - 1)**2*(11*i + 2)
Factor 6*k**3 - 8*k**3 + 5044918*k**2 - 5051172*k**2 - 4885936*k + 4892192.
-2*(k - 1)*(k + 1564)**2
Let u(l) be the third derivative of l**7/5670 + l**6/405 + l**5/90 - 13*l**4/2 + l**3/3 - 19*l**2 + 2*l. Let p(a) be the second derivative of u(a). Factor p(k).
4*(k + 1)*(k + 3)/9
Let b(x) be the second derivative of -x**7/840 + x**6/60 - 35*x**3/6 + 36*x - 2. Let q(c) be the second derivative of b(c). Factor q(k).
-k**2*(k - 6)
Let y(q) = 509*q**2 + 215809*q + 23284991. Let f(d) = 127*d**2 + 53952*d + 5821243. Let g(x) = 9*f(x) - 2*y(x). Find l such that g(l) = 0.
-1079/5
Factor -2/3*d**5 - 7776*d - 4976/3*d**3 - 208/3*d**4 + 7488*d**2 + 0.
-2*d*(d - 2)**2*(d + 54)**2/3
Suppose 24 + 12 = 2*w. Suppose -23*l = w*l. Determine t, given that 48/5*t**3 - 18*t**4 + 0 + 10*t**5 - 8/5*t**2 + l*t = 0.
0, 2/5, 1
Let w = -110362 - -441449/4. What is n in -1/8 + 3/8*n**2 + 0*n - w*n**3 = 0?
-1/2, 1
Let g be (6/(-12))/(297/150 + -2). Suppose 0 = -4*j - 17 + g. Suppose 43*x**2 - 18*x**j + 15*x**3 + 10*x - 5*x**4 - 7*x**5 + 2*x**5 = 0. What is x?
-1, 0, 2
Let t = -292478 + 1462391/5. Factor 3 - 2/5*a - t*a**2.
-(a - 3)*(a + 5)/5
Find y such that -80*y**2 + 108*y**3 - 23*y**3 - 39*y**3 - 42*y**3 + 400*y = 0.
0, 10
Factor 0 + 52488/7*n + 36936/7*n**2 + 7146/7*n**3 + 2/7*n**5 + 228/7*n**4.
2*n*(n + 3)**2*(n + 54)**2/7
Let w be 2*((-1)/2 - -1). Suppose w = 2*j - 3. Factor m + 0*m**j + 2*m**2 - m**2.
m*(m + 1)
Factor 729 + 162*m**2 - 8993*m**4 + 17983*m**4 + 648*m - 8993*m**4.
-3*(m - 9)*(m + 3)**3
Let r(w) be the first derivative of 4 + 0*w**3 + 17/2*w**2 + 5/24*w**4 - 1/6*w**5 + 0*w + 1/24*w**6. Let f(v) be the second derivative of r(v). Factor f(x).
5*x*(x - 1)**2
Let g(v) = -v**2 - 8*v - 20. Let i be g(-10). Let c = 42 + i. Determine k, given that 23*k**3 - 15*k**2 - 28*k**3 + 2 - c = 0.
-3, 0
Suppose 332/7*x**2 + 0 + 338/7*x**3 - 96*x + 2/7*x**4 = 0. What is x?
-168, -2,