 + 3*d**t + 11. Factor p(n).
2*(n + 1)*(2*n + 1)
Let r(o) be the second derivative of 62*o**7/21 - 8*o**6 + 27*o**5/5 + 2*o**4/3 + 73*o + 3. Factor r(p).
4*p**2*(p - 1)**2*(31*p + 2)
Suppose -48/13*l + 98/13*l**3 - 6/13*l**5 + 64/13*l**4 - 20/13*l**2 + 0 = 0. What is l?
-1, 0, 2/3, 12
Let f(d) be the second derivative of 767*d**5/4 + 1835*d**4/6 - 175*d**3/6 - 5*d**2 + 300*d + 2. Solve f(a) = 0 for a.
-1, -2/59, 1/13
Let u(p) be the third derivative of -p**8/840 - p**7/21 - 37*p**6/150 + 23*p**5/3 + 5*p**4/4 - 75*p**3 + 6326*p**2. Determine m so that u(m) = 0.
-15, -1, 1, 5
Let n(h) be the first derivative of 0*h + 1/12*h**4 + 1/15*h**5 - 23 + 0*h**3 + 0*h**2. Let n(m) = 0. Calculate m.
-1, 0
Factor -25179*a**2 + 25176*a**2 + 55*a + 203*a.
-3*a*(a - 86)
Let f be (10 - 8) + (982 - 0). Let o = -984 + f. Factor -2/3*s**2 + 0 + o*s - 1/3*s**3 + 1/3*s**4.
s**2*(s - 2)*(s + 1)/3
Let u = 15054 + -15048. Let q(y) be the second derivative of -1/14*y**4 - 36*y - 3/70*y**5 + 0 + 1/7*y**3 + 1/35*y**u + 0*y**2. Suppose q(t) = 0. Calculate t.
-1, 0, 1
Let p(r) be the second derivative of 3*r + 33 + 1/3*r**4 - 8/3*r**2 + 8/9*r**3. Factor p(b).
4*(b + 2)*(3*b - 2)/3
Suppose i + 252 = 2*w, 3*w + i = 401 - 28. Suppose 27*n = -w + 260. Suppose 2/5*o**2 - 2/5*o**4 - 4/15*o + 2/15*o**n + 2/15*o**3 + 0 = 0. What is o?
-1, 0, 1, 2
Let c(a) be the second derivative of 2*a**6/15 + 12*a**5/5 + 22*a**4/3 - 56*a**3 + 98*a**2 + 3*a + 63. Suppose c(b) = 0. What is b?
-7, 1
Factor -5*q**3 - 380*q - 107*q**2 - 462 + 1773 + 9 - 23*q**2.
-5*(q - 2)*(q + 6)*(q + 22)
Suppose 10*v - 3*w + 7 = 15*v, 0 = -2*v + w + 5. Determine d, given that -115*d**2 + 33*d**2 - v*d**3 + 56*d**2 = 0.
-13, 0
Let q(t) be the second derivative of -t**6/120 + 87*t**5/40 - 841*t**4/4 + 24389*t**3/3 + 2*t + 301. Factor q(g).
-g*(g - 58)**3/4
Suppose -3*n + 3*s - 6 = 0, 13 = n - s + 3*s. Find a such that a**2 + n - 11609*a + 0*a**3 - a**3 + 0 + 11614*a = 0.
-1, 3
Let r(u) = -u + 16. Let c be r(12). Let z(l) be the second derivative of 1/2*l**c - 5/4*l**3 + 3*l + 3/2*l**2 + 0 - 3/40*l**5. Let z(m) = 0. What is m?
1, 2
Let o = 196933 - 787731/4. Factor 0 + o*g**2 + 37/4*g.
g*(g + 37)/4
Let j(f) be the third derivative of -f**6/1380 - 17*f**5/230 + 40*f**4/69 - 36*f**3/23 - 4416*f**2 + 1. What is b in j(b) = 0?
-54, 1, 2
Factor -201*d - 83*d**2 + 73*d**2 + 252 + 3*d**3 - 44*d**2.
3*(d - 21)*(d - 1)*(d + 4)
Let j be (4 + -5 - -6)/(50/30). Let t(r) be the first derivative of -4 + 5/3*r**3 + 1/4*r**4 + 7/2*r**2 + j*r. What is i in t(i) = 0?
-3, -1
Let l(z) be the third derivative of -10*z**6/27 + 68*z**5/9 - 289*z**4/6 + 93*z**2 + 2*z + 1. Factor l(q).
-4*q*(10*q - 51)**2/9
Suppose -86 = -3*y + t, y + 696*t = 691*t + 18. Let h(f) be the second derivative of y*f - 13/24*f**3 - 1/48*f**4 + 0*f**2 + 0. Factor h(w).
-w*(w + 13)/4
Let q(n) = -136*n**2 - 4192*n + 4166. Let b(v) = 106*v**2 + 3144*v - 3124. Let z(t) = -9*b(t) - 7*q(t). Solve z(i) = 0.
1, 523
Let w = 3781 + -3781. Let f(t) be the first derivative of 1/20*t**5 - 4 + w*t**2 + 0*t + 3/16*t**4 + 1/6*t**3. Factor f(s).
s**2*(s + 1)*(s + 2)/4
Let b be (16/((-1120)/1090) + 17)/(12/35). Let -5/6*s**2 + 0 - b*s = 0. Calculate s.
-5, 0
Let z(u) = -u**3 + 6*u**2 - 4*u - 3. Let q be z(5). Suppose 3*v - 4*r - 14 = -q*r, 4*r + 10 = -3*v. Factor v*j**2 + j**2 - j + 13*j.
3*j*(j + 4)
Let x(k) be the second derivative of -k**6/195 + 49*k**5/130 - 523*k**4/78 + 685*k**3/13 - 2700*k**2/13 + 6988*k. What is l in x(l) = 0?
3, 5, 36
Let p(j) be the third derivative of -j**7/70 - 11*j**6/40 + j**5/20 + 11*j**4/8 - 2*j**2 + 1783. Factor p(a).
-3*a*(a - 1)*(a + 1)*(a + 11)
Let p be 35/11 - 8/44. Suppose -2*s**2 - 2304 - p*s**2 + 4*s**2 + 0*s**2 + 96*s + 0*s**2 = 0. Calculate s.
48
Factor 78/5 - 8/5*a**2 - 2/5*a.
-2*(a - 3)*(4*a + 13)/5
Let u(i) = 2*i**2 - 8*i + 6. Let v be ((-792)/(-108))/(-4*(-2)/12). Let y(l) = -3*l**2 + 16*l - 13. Let r(w) = v*u(w) + 6*y(w). Suppose r(b) = 0. Calculate b.
-3, 1
Let k(x) = 14*x**3 - 40*x**2 + 119*x - 115. Let h(q) = 22*q**3 - 60*q**2 + 178*q - 172. Let c(f) = -5*h(f) + 8*k(f). Solve c(v) = 0.
2, 3, 5
Let h be -4*(-8)/(-320)*(80/(-12) - (10 - 15)). Solve 0 - 19/6*n - h*n**3 + 10/3*n**2 = 0 for n.
0, 1, 19
Let h(v) = -v**2 + v - 2. Let l(d) = d**3 - 21*d**2 - 111*d - 201. Let b(i) = -6*h(i) + l(i). Factor b(o).
(o - 21)*(o + 3)**2
Let h = -35231/6 - -17620/3. Factor -h*w**3 - 8/3*w**2 + 1/3 - 5/6*w.
-(w + 1)**2*(9*w - 2)/6
Let o(w) be the first derivative of 50 - 1/3*w**3 + 0*w - 3/16*w**2. Find z, given that o(z) = 0.
-3/8, 0
Let q(p) = -89*p + 2136. Let h be q(24). Let s(g) be the third derivative of -7/36*g**4 - 1/90*g**5 + 6*g**2 - 2/3*g**3 + h*g + 0. Factor s(t).
-2*(t + 1)*(t + 6)/3
Let x(s) be the third derivative of s**6/540 + s**5/135 - s**4/108 - 2*s**3/27 - 1301*s**2 - 2. Factor x(j).
2*(j - 1)*(j + 1)*(j + 2)/9
Suppose 23*f - 39 = 30. Suppose 0 = -f*b - 136 + 142. Let -1/8*x**3 + 0*x**b + 1/8*x + 0 = 0. What is x?
-1, 0, 1
Let h(b) be the first derivative of 2*b**3/3 + 257*b**2 - 3696*b - 2333. Factor h(x).
2*(x - 7)*(x + 264)
Factor -1/8*b**4 - 58509/4*b**2 + 1911195/2*b + 970299 + 593/8*b**3.
-(b - 198)**3*(b + 1)/8
Let f(q) = -5*q**4 + 65*q**3 + 255*q**2 - 5*q. Let w(x) = x**3 + x. Let g(z) = f(z) + 5*w(z). Factor g(o).
-5*o**2*(o - 17)*(o + 3)
Solve 1/2*n**5 + 4*n + 13/2*n**2 - 1/2*n**4 - 6 - 9/2*n**3 = 0.
-3, -1, 1, 2
Let q(i) be the first derivative of i**5/4 - 35*i**4/8 + 30*i**3 - 100*i**2 + 160*i - 1495. Factor q(s).
5*(s - 4)**3*(s - 2)/4
Let s(w) be the second derivative of 5*w**4/12 + 470*w**3 + 198810*w**2 + 331*w. Factor s(y).
5*(y + 282)**2
Let a = 247 + -205. Suppose 25*p**4 - a*p**3 - 147*p**2 - 17*p**4 - 11*p**4 = 0. What is p?
-7, 0
Factor -5/2*y**3 + 40*y + 5*y**2 - 80.
-5*(y - 4)*(y - 2)*(y + 4)/2
Suppose -122*w - 3*w**4 - 12*w**2 - w**4 + 10*w**3 + 221*w + 10*w**3 + 16 - 119*w = 0. What is w?
-1, 1, 4
Let v = -98908/105 - -942. Let z(g) be the third derivative of 0*g + 0 + 2/35*g**5 - v*g**6 - 21*g**2 + 2/21*g**3 - 2/21*g**4 + 2/735*g**7. Factor z(i).
4*(i - 1)**4/7
Let j(y) = 2*y + 10. Let x be j(11). What is r in -x*r**2 + 288 + 80*r**2 - 46*r**2 - 48*r = 0?
12
Let k(p) = -2*p**4 + 11*p**3 - 11*p - 7. Let a(n) = -3*n**4 + 13*n**3 - n**2 - 13*n - 8. Let v(j) = -3*a(j) + 4*k(j). Factor v(u).
(u - 1)*(u + 1)**2*(u + 4)
Let y be 195/(-30) + 12 - (-1)/(-2). Suppose 200 + y*b**2 + 46*b + 67*b + 13*b - 16*b = 0. What is b?
-20, -2
Let i be -3*(-8)/6 - 48/(-8). Find x such that x**2 + 47 - 6*x**2 - 35*x - 17 + i = 0.
-8, 1
Let f(i) be the second derivative of -3*i**4/4 + 19*i**3 + 240*i**2 - 172*i - 5. Solve f(v) = 0.
-10/3, 16
Solve -4/3*q**5 - 16/3*q**4 + 16/3*q - 4/3*q**3 + 40/3*q**2 - 32/3 = 0.
-2, 1
Let i(o) be the second derivative of -o + 2*o**3 + 1/4*o**4 + 58 + 9/2*o**2. Find f, given that i(f) = 0.
-3, -1
Let o(w) be the first derivative of -5*w**4/8 - 20*w**3/3 + 395*w**2/4 - 175*w + 2384. Determine j so that o(j) = 0.
-14, 1, 5
Let y(w) be the second derivative of -3/50*w**5 + 0 + 1/10*w**3 - 68*w + 0*w**2 + 0*w**6 + 1/70*w**7 + 0*w**4. Find z, given that y(z) = 0.
-1, 0, 1
Let p(f) be the second derivative of -f**4/16 + 61*f**3/8 - 45*f**2/2 + 5*f + 57. Factor p(o).
-3*(o - 60)*(o - 1)/4
Let i(u) = 82*u**2 - 11*u - 3733. Let s(v) = 16*v**2 - 2*v - 746. Let x(h) = 6*i(h) - 31*s(h). Factor x(w).
-4*(w - 13)*(w + 14)
Let u(s) be the second derivative of s**5/50 + 3291*s**4/10 + 10830681*s**3/5 + 35643771171*s**2/5 - 34*s + 141. Factor u(h).
2*(h + 3291)**3/5
Let o(h) be the second derivative of 1/30*h**6 + 1/2*h**3 + 0 + 7/12*h**4 - 49*h + 1/4*h**5 + 0*h**2. Factor o(y).
y*(y + 1)**2*(y + 3)
Let b(k) be the first derivative of -k**5 - 640*k - 190*k**3 - 40 + 560*k**2 + 95/4*k**4. Factor b(y).
-5*(y - 8)**2*(y - 2)*(y - 1)
Let p = -21 - -25. Suppose 2*s = 2*y + 2*y - 48, 4*y = -3*s + 68. Let i**2 - p*i - y*i + 10*i = 0. What is i?
0, 8
Let o(u) = 3*u**2 - 3*u + u**2 - 8 + 13*u - 3*u**2. Let b be o(-13). Factor 6*c**4 - 5*c**4 - 4*c**2 - b*c + 35*c - 4*c**3 + 3*c**4.
4*c*(c - 1)**2*(c + 1)
Let x(m) be the third derivative of 4*m**3 + 1/60*m**5 + 0*m + 7/12*m**4 + 0 + 74*m**2. Factor x(w).
(w + 2)*(w + 12)
Let y(m) be the third derivative of 31*m**5/16 - 157*m**4/32 + m**3/4 - 3621*m**2. Factor y(s).
3*(