uppose 4*l - 31 = 5*g, 100 = -4*l - g + 113. Let n(t) be the first derivative of 4/33*t**3 + 1/22*t**4 + 0*t + 0*t**2 + l. Factor n(k).
2*k**2*(k + 2)/11
Factor 8*j**4 - 24*j**3 - 144*j + 12*j**4 + 5*j**4 - 132*j**2 - 22*j**4.
3*j*(j - 12)*(j + 2)**2
Solve -6/11*k - 20/11 - 2/11*k**3 + 12/11*k**2 = 0.
-1, 2, 5
Suppose 92*v + 28 = 94*v + 5*f, -f - 4 = -2*v. Suppose 9/5*g**v + 0*g - 9/5*g**2 + 0 + 3/5*g**3 - 3/5*g**5 = 0. What is g?
-1, 0, 1, 3
Suppose q**3 + 384*q + 276*q**2 - 663*q + 2*q**3 = 0. Calculate q.
-93, 0, 1
Factor -1/3*r**2 + 4/3*r + 0.
-r*(r - 4)/3
Factor 8*i**4 + 7*i**4 - 6*i**4 - i**5 + 12*i**2 - 20*i**3.
-i**2*(i - 6)*(i - 2)*(i - 1)
Solve -88/23 - 80/23*a - 14/23*a**2 + 2/23*a**3 = 0 for a.
-2, 11
Suppose -4*t + 16 = -2*y, 0 = t - 0*y - y - 4. Let w = -2 + t. Find r, given that 1/6*r**w + 0*r - 2/3 = 0.
-2, 2
Suppose 10 = 2*d, 5*t + 0*d - 5 = 2*d. Suppose 264 = -205*v + 271*v. Factor 0 + 0*l - 2/5*l**v + 0*l**2 - 2/5*l**t.
-2*l**3*(l + 1)/5
Let k be (-15)/(-6)*(-30)/(-25). Suppose -2*i - 85 = -5*d, -d + 40 = i - 6*i. Factor f**4 + d*f**2 + 12*f**k + f**4 + f**4 + 6*f.
3*f*(f + 1)**2*(f + 2)
What is x in -24*x**3 + x**5 - 3*x**5 + 44*x**2 - 24*x**2 - 6*x + 12*x**4 = 0?
0, 1, 3
Suppose 256 = 2*u + 2*u. Factor -12*i + 442*i**4 - 7*i**2 - 327*i**3 + 115*i**2 - 147*i**5 - u*i**4.
-3*i*(i - 1)**2*(7*i - 2)**2
Let o be (-46)/(-14) + 40/(-140). Let d(h) be the first derivative of -3/5*h**5 + 0*h - o + 0*h**2 + h**3 + 0*h**4. Find u such that d(u) = 0.
-1, 0, 1
Suppose 9*v = 6*v + 10*v. Let m(l) be the third derivative of 0*l**5 - 1/180*l**6 - 7*l**2 - 1/18*l**3 + 1/36*l**4 + v + 0*l + 1/630*l**7. Factor m(d).
(d - 1)**3*(d + 1)/3
Let h(m) = -3*m**3 + 9*m**2 - 54*m + 30. Let b(s) = s**3 - 5*s**2 + 27*s - 15. Let d(p) = -9*b(p) - 4*h(p). What is q in d(q) = 0?
-5, 1
Let m(s) be the third derivative of s**6/24 - 3*s**5/4 + 115*s**4/24 - 25*s**3/2 - 7*s**2 - 7*s. Factor m(v).
5*(v - 5)*(v - 3)*(v - 1)
Let v(k) be the third derivative of -k**7/2100 - k**6/900 + k**5/300 + k**4/60 + 17*k**3/6 + 8*k**2. Let m(c) be the first derivative of v(c). Factor m(w).
-2*(w - 1)*(w + 1)**2/5
Suppose 11*j + w = 5*j + 22, -3*j - 2*w = -17. Determine l so that 1/2*l**j - 1/2*l + 1 - l**2 = 0.
-1, 1, 2
Let a be 0*(-2)/(6/1). Let p(h) be the second derivative of 0*h**4 + 1/40*h**5 + a*h**2 + 0 + 3*h - 1/12*h**3. Factor p(l).
l*(l - 1)*(l + 1)/2
Let k(b) = -b**5 - b**4 - b**2 + b + 4. Let t(c) = c**5 + 22*c**4 - 24*c**3 - 14*c**2 + 23*c - 16. Let j(r) = -4*k(r) - t(r). Factor j(s).
3*s*(s - 3)**2*(s - 1)*(s + 1)
Factor -1316*c**2 + 1 + 140*c**3 - 1 + 0 + 2296*c**2 + 5*c**4.
5*c**2*(c + 14)**2
Let z be -2 - ((-3)/(-18))/(15/(-300)). Factor -10/3*h**3 + 8*h**2 - 6*h + z.
-2*(h - 1)**2*(5*h - 2)/3
Let t(j) = 2*j**2 - 24*j + 28. Let k(b) = b**3 - b**2 + 2. Let m(s) = -2*k(s) - t(s). Suppose m(g) = 0. What is g?
-4, 2
Let f = -72 + 74. Determine a so that -123*a**2 - 50*a - 192 + 67 + 118*a**f = 0.
-5
Let r(q) be the second derivative of -4*q**4/63 - 11*q**3/63 - q**2/7 - 499*q. Factor r(o).
-2*(o + 1)*(8*o + 3)/21
Factor 88*r**2 + r - 28*r**2 - 3*r - 28*r**2 - 8 - 31*r**2.
(r - 4)*(r + 2)
Let v = 158 - 99. Let -2*t**2 + 63*t**3 - 114*t**3 + v*t**3 = 0. What is t?
0, 1/4
Let p(x) be the first derivative of x**7/105 - x**6/30 + x**5/30 - 2*x**2 + 27. Let s(z) be the second derivative of p(z). Factor s(u).
2*u**2*(u - 1)**2
Suppose -8 + 0 = -r. Let o(h) = -h + 11. Let w be o(r). Suppose i**2 + i**2 + i**2 + 3*i**w + 0*i**3 = 0. What is i?
-1, 0
Let v(a) = 114*a - 111. Let h be v(1). What is m in 0 + 8/3*m - 4/3*m**h - 4/3*m**2 = 0?
-2, 0, 1
Let s(c) be the first derivative of 2*c**3/39 + 160*c**2/13 + 12800*c/13 + 479. Factor s(l).
2*(l + 80)**2/13
Suppose 4*t - 9 - 11 = 0. Factor -40*v**2 - 126 + 126 + 35*v + t*v**3.
5*v*(v - 7)*(v - 1)
Let p = 6679 + -40073/6. Factor 0 + 1/3*i - p*i**2.
-i*(i - 2)/6
Let f(r) be the third derivative of 7*r**7/180 - 14*r**6/45 + 16*r**5/15 - 5*r**4/24 - 10*r**2. Let z(d) be the second derivative of f(d). Factor z(h).
2*(7*h - 8)**2
Let h(m) be the second derivative of 5*m**4/18 - 13*m**3/18 + m**2/2 - 41*m. Suppose h(w) = 0. Calculate w.
3/10, 1
Factor 3*i**4 + 4*i - 4*i**4 + 231*i**3 - 234*i**3.
-i*(i - 1)*(i + 2)**2
Let n(i) be the first derivative of -i**9/12096 + i**8/420 - 2*i**7/105 - 11*i**3 + 3. Let p(o) be the third derivative of n(o). Factor p(c).
-c**3*(c - 8)**2/4
Factor p**4 + 5*p + 2*p**3 - 107*p**2 - p + 100*p**2.
p*(p - 1)**2*(p + 4)
Determine l, given that -28/17 - 2/17*l**3 - 10/17*l + 16/17*l**2 = 0.
-1, 2, 7
Let k(m) be the first derivative of -5*m**4 + 485*m**3/3 + 190*m**2 - 125*m - 273. Determine u, given that k(u) = 0.
-1, 1/4, 25
Suppose -17 = 40*w - 137. Factor 14/19*c - 10/19*c**2 - 6/19 + 2/19*c**w.
2*(c - 3)*(c - 1)**2/19
Suppose 0 = t + 2*r + 13, -5*r + 2 = -3*t + 18. Let b be 2*(t/(-9))/1. Solve 4/3*j + 2 - b*j**2 = 0 for j.
-1, 3
Let o be (-4)/10 + 531/15. Let a = o - 31. Factor 6*d**a + 11*d**3 - 2*d**3 - 3*d + 0*d**4.
3*d*(d + 1)**2*(2*d - 1)
Let o = 11324/7 + -1614. Suppose -21 = -2*w + 2*a - 15, -28 = -4*w - 4*a. Factor -4/7*n + 0 - 46/7*n**4 - 54/7*n**3 - 2*n**w - o*n**2.
-2*n*(n + 1)**3*(7*n + 2)/7
Solve 6/5*g + 2/5*g**3 + 0 + 8/5*g**2 = 0 for g.
-3, -1, 0
Let b(k) = -k**2 - 3*k + 2. Let j be b(-3). Determine s so that 20*s**2 + j*s - 37*s**2 - s + 18*s**2 = 0.
-1, 0
Let q be (-34)/(-170) + 1/(-5). Let i(w) be the third derivative of 0*w + 0*w**4 - 1/900*w**6 - 13*w**2 + 0 - 1/150*w**5 + q*w**3. Factor i(h).
-2*h**2*(h + 3)/15
Let d(y) = -y**3 - 6*y**2 + 3. Let o be d(-6). Let s be 2/2 - o - -4. Factor -6*p**3 - 7*p**4 + s*p**5 - 2*p**2 + p**4 - 4*p**5.
-2*p**2*(p + 1)**3
Solve -32*t**2 + 25 - 85 + 65*t + 27*t**2 = 0 for t.
1, 12
Let n(t) be the third derivative of 16*t**7/1995 - 2*t**6/95 - 29*t**5/190 + 47*t**4/228 - 2*t**3/19 + 48*t**2. Suppose n(a) = 0. Calculate a.
-2, 1/4, 3
Solve -2/5*c**2 + 24 - 56/5*c = 0.
-30, 2
Suppose 14 = 3*u - 4. Suppose -u*n = -4*n - 6. Suppose 0*f + 3*f - n + 4 + 1 - 2*f**2 = 0. Calculate f.
-1/2, 2
Let q(z) be the third derivative of -z**6/900 + 11*z**5/75 - 121*z**4/15 + 10648*z**3/45 + 7*z**2 + 2. Determine m, given that q(m) = 0.
22
Let u(m) be the third derivative of -m**7/1260 + m**6/144 + 13*m**5/360 + 7*m**4/144 - 101*m**2. Solve u(y) = 0.
-1, 0, 7
Let t(b) be the second derivative of 5*b**4/12 - 35*b**3/6 - 45*b**2 - 2*b - 13. What is r in t(r) = 0?
-2, 9
Let d be (0/(-13 + 4))/(-1). Let b(r) be the third derivative of -1/4*r**4 - 1/30*r**5 + 0*r - 2/3*r**3 + d - 8*r**2. Let b(q) = 0. What is q?
-2, -1
Suppose 95*q - 98*q = 4*t - 2, 5*t + 13 = 4*q. Factor -2/9*j**q - 2/9*j + 0.
-2*j*(j + 1)/9
Let p(l) be the second derivative of l**6/10 + 3*l**5/10 + l**4/4 + 19*l + 4. What is i in p(i) = 0?
-1, 0
Let g = 1 - 1. Suppose -y - 2*y = g. Factor -2*z - z + y*z + 3*z**2 - 3*z.
3*z*(z - 2)
Let i be ((1 - 1)/((-30)/15))/1. Let j(g) be the second derivative of -1/12*g**3 - 2*g + i*g**2 + 0 + 1/24*g**4. Determine y so that j(y) = 0.
0, 1
Let f(o) be the second derivative of -o**4/66 + 2*o**3/33 + 3*o**2/11 + 14*o - 3. Determine l so that f(l) = 0.
-1, 3
Suppose -7*l**3 + 15*l**4 - 7*l**3 + 260*l + 60 + 124*l**3 + 275*l**2 = 0. Calculate l.
-3, -2, -1/3
Let w(j) be the third derivative of -5*j**8/1512 + 31*j**7/315 - 527*j**6/540 + 193*j**5/90 + 448*j**4/27 + 196*j**3/9 + 9*j**2 - 29. Let w(m) = 0. Calculate m.
-1, -2/5, 6, 7
Suppose 215*h = 12 - 12. Solve 2/13*x**4 + h*x + 0 + 0*x**3 + 0*x**2 + 2/13*x**5 = 0 for x.
-1, 0
Suppose -52 + 48 = -x. Let v(y) be the first derivative of 2/15*y**6 - 1/5*y + 2/15*y**3 - 1/25*y**5 - 2/5*y**x + 2/5*y**2 + 5. What is h in v(h) = 0?
-1, 1/4, 1
Let a(t) be the third derivative of -t**6/120 - 3*t**5/160 + t**4/32 + 17*t**3/3 + 24*t**2. Let v(m) be the first derivative of a(m). Factor v(o).
-3*(o + 1)*(4*o - 1)/4
Let d(h) be the first derivative of -247*h + 30*h**2 + 21*h - 12 - 173*h - h**3 + 99*h. Suppose d(r) = 0. What is r?
10
Let y(p) be the second derivative of -5*p**7/14 + 11*p**6/5 - 27*p**5/10 - 4*p**4 + 23*p**3/2 - 9*p**2 + 194*p - 1. Solve y(l) = 0.
-1, 2/5, 1, 3
Let d(h) = -h**2 - 3*h - 1. Let x be d(-3). Let g be (-16)/20 + 1 + (0 - x). Determine y, given that -3/5*y**4 - g*y**3 + 0*y - 3/5*y**2 + 0 = 0.
-1, 0
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