
Suppose 0 = 103*g - 104*g - 42. Let y be g + 41 + (0 - -3). Factor 1/3*j - 1/3*j**3 + 1/3*j**4 + 2/3 - j**y.
(j - 2)*(j - 1)*(j + 1)**2/3
Let y(b) be the first derivative of -b**4/84 - b**3/7 - 9*b**2/14 - b - 3. Let l(k) be the first derivative of y(k). Find h such that l(h) = 0.
-3
Let h(g) = 2*g + 1. Let m(z) = -z**2 - 31*z - 9. Let p(q) = 18*h(q) + 2*m(q). Factor p(b).
-2*b*(b + 13)
Suppose -5 = 3*s - 5*y, 26 - 21 = 4*s + 5*y. What is z in 0*z**2 + 0*z**3 - 1/4*z**4 + s + 0*z = 0?
0
Let y(c) = 2*c - 66. Let o be y(34). Let i be (1 + -5 + 5)*3/o. Suppose -5/2*f**2 - i + 7/2*f + 1/2*f**3 = 0. Calculate f.
1, 3
Let n = 310 + -304. Let h(j) be the first derivative of 0*j - 5*j**3 + 3/2*j**2 - 9/5*j**5 - n + 21/4*j**4. Factor h(g).
-3*g*(g - 1)**2*(3*g - 1)
Let w be (-3 + 2)/1*-2. Suppose 0 = -4*d - 3*l + 27, 5*l - w = d - 3. Factor 3*p**2 - d - 9*p**3 + 0*p**3 + 0*p**3 - 2*p**4 + 9*p + 5*p**4.
3*(p - 2)*(p - 1)**2*(p + 1)
Suppose -n - 2*n - 4*j = -51, 0 = -5*j. Let w = -15 + n. Factor 21*h**5 - 5*h**w + 6*h**3 + 0*h**2 + 27*h**4 + 5*h**2.
3*h**3*(h + 1)*(7*h + 2)
Factor 519 + 15*x**2 - 34*x**4 - 513 - 17*x + 33*x**4 - 3*x**3.
-(x - 1)**3*(x + 6)
Let o(t) be the second derivative of -t**5/120 - 7*t**4/72 - t**3/9 + t**2 - t + 14. Let o(v) = 0. Calculate v.
-6, -2, 1
Let t = 18 - 3. Suppose 11 = 2*q - t. Factor -q*a + 3*a + 10*a**3 + 5*a**2 + a**3 + 4*a**3.
5*a*(a + 1)*(3*a - 2)
Let m be (-55)/33 + (-1480)/(-600). Factor 2/5*h + 2/5 - 4/5*h**3 - m*h**2 + 2/5*h**5 + 2/5*h**4.
2*(h - 1)**2*(h + 1)**3/5
Suppose 0 = 10*s + 3 - 23. Let c(l) be the third derivative of 1/24*l**4 - 1/60*l**5 + 0*l + 5*l**s + 0 + 0*l**3. Let c(k) = 0. What is k?
0, 1
Let w(a) be the second derivative of 0 - 72*a**2 - 1/5*a**5 + 11/3*a**4 - 16*a**3 - 14*a. Solve w(v) = 0 for v.
-1, 6
Let a = -625/144 + 73/16. Factor a*z + 1/9 - 2/9*z**3 - 1/9*z**4 + 0*z**2.
-(z - 1)*(z + 1)**3/9
Let p(l) = 15*l**4 + 50*l**3 + 5*l**2 + 5*l. Let i(z) = -8*z**4 - 25*z**3 - 3*z**2 - 3*z. Let a(t) = 5*i(t) + 3*p(t). Let a(r) = 0. What is r?
-5, 0
Let y(o) = -o**2 - 5*o - 4. Let n be y(-3). Let 5*l**3 + 9*l + 4*l**2 - 4*l**3 + 2*l**n = 0. Calculate l.
-3, 0
Let c(u) be the first derivative of -166*u**3/15 + 17*u**2 - 4*u/5 + 452. Solve c(x) = 0 for x.
2/83, 1
Suppose r + 5*p = 2*p - 4, p + 2 = 0. Suppose -5*v + 28 - 8*v**r + 4 - 4*v**3 + 21*v = 0. Calculate v.
-2, 2
Suppose 18*a + 22*a - 120 = 0. Factor -2/5*m**5 + 0*m**a + 0*m**2 + 0*m + 0 + 2/5*m**4.
-2*m**4*(m - 1)/5
Suppose 0 = -4*r + 2 + 142. Solve r*x**3 - 3*x**5 - 5*x**2 - 46*x**2 + 15*x + 0*x**5 - 6*x**4 + 9*x**2 = 0 for x.
-5, 0, 1
Suppose 650 + 958 = 401*q + 405. Determine s so that 9/2*s + q - 15/2*s**2 = 0.
-2/5, 1
Let n(p) be the third derivative of p**7/1575 - 11*p**6/900 + 13*p**5/150 - 49*p**4/180 + 4*p**3/9 + 320*p**2. Find d, given that n(d) = 0.
1, 4, 5
Let w(h) be the third derivative of -h**5/660 + 9*h**4/44 + 5*h**3/6 - 528*h**2. Let w(j) = 0. Calculate j.
-1, 55
Let c(l) be the third derivative of 0*l**3 + 1/165*l**5 + 1/1155*l**7 + 0 + 1/220*l**6 + 0*l**4 + 0*l + 7*l**2. Factor c(u).
2*u**2*(u + 1)*(u + 2)/11
Let s(g) be the first derivative of 0*g**3 + 1 + 0*g + 0*g**2 - 2/3*g**6 - g**4 - 8/5*g**5. Suppose s(q) = 0. What is q?
-1, 0
Let q be -12 + (506/66 - -5). Factor -q*d + 1/6*d**3 + 0 + 0*d**2.
d*(d - 2)*(d + 2)/6
Let r(m) be the second derivative of m**6/50 - 12*m**5/25 + m**4/2 + 36*m**3/5 + 27*m**2/2 + 2*m + 564. Let r(u) = 0. What is u?
-1, 3, 15
Let x be 0*(3*-1)/(7 + 14/(-14)). Factor 10/9*g**2 + 1/9*g**3 + x + 25/9*g.
g*(g + 5)**2/9
Factor 0*i + 1/6*i**2 - 1/6*i**3 + 0.
-i**2*(i - 1)/6
Let u be (12/(-135))/((-693)/(-55) - 13). Factor -u*t**3 + 4/9*t + 0 + 2/9*t**2.
-2*t*(t - 2)*(t + 1)/9
Let l(a) = -2*a**2 + 195*a + 299. Let n be l(99). Factor 8*v - 32 - 1/2*v**n.
-(v - 8)**2/2
Let b(z) be the first derivative of -13 + 20*z**2 + 100*z + 4/3*z**3. Factor b(o).
4*(o + 5)**2
Let d = 97/477 - -1/53. Let n(s) be the first derivative of d*s**2 - 2 + 0*s - 2/27*s**3. Find a, given that n(a) = 0.
0, 2
Suppose -12 = 2*w - 2, -w = -5*l + 20. Factor -2*n**2 - 2*n**3 - 3*n**l + 375*n**5 - 376*n**5 - 4*n**4.
-n**2*(n + 1)**2*(n + 2)
Suppose -20*c - 2*o = -23*c - 12, -o = 7*c - 6. Solve 12/5*k + 44/5*k**3 + c + 46/5*k**2 + 2*k**4 = 0 for k.
-3, -1, -2/5, 0
Let n(y) be the third derivative of 0 - 1/15*y**4 + 2*y**2 - 1/90*y**5 + 0*y - 4/45*y**3. Factor n(g).
-2*(g + 2)*(5*g + 2)/15
Suppose 3*d = 5*d. Let r(k) be the third derivative of d*k**5 + 0 + 1/3*k**3 + 3*k**2 + 1/6*k**4 - 1/105*k**7 + 0*k - 1/30*k**6. Find f, given that r(f) = 0.
-1, 1
Let f(k) be the first derivative of k**6/18 + 3*k**5/5 + 5*k**4/2 + 44*k**3/9 + 4*k**2 + 11. Factor f(o).
o*(o + 2)**3*(o + 3)/3
Solve -4/3*k - 16 + 2/3*k**2 = 0 for k.
-4, 6
Let w(k) be the third derivative of 1/1785*k**7 - 1/68*k**4 + 1/340*k**6 + 0 + 0*k + 5*k**2 - 2/51*k**3 + 1/510*k**5. Determine p so that w(p) = 0.
-2, -1, 1
Let k(g) be the second derivative of -g**6/6 - 5*g**5/2 + 65*g**4/12 + 55*g**3/3 - g + 14. Determine b so that k(b) = 0.
-11, -1, 0, 2
Let s(v) = -43*v**2 + 256*v + 14. Let z be s(6). Solve 2/13*g**z - 2/13*g - 4/13 = 0 for g.
-1, 2
Let c = -1005 + 1010. Factor 0*i**2 + 0*i**3 + 0 + 1/6*i**4 + 0*i - 1/6*i**c.
-i**4*(i - 1)/6
Let p = -10188/5 + 1983. Let m = p + 55. Determine f, given that 4/5*f**3 + m + 2/5*f**5 - 6/5*f + 4/5*f**2 - 6/5*f**4 = 0.
-1, 1
Suppose 3*c - 5 - 10 = -5*t, -5*t - 4*c = -15. Factor 12*q**2 + 2*q - q**3 - 3*q**t - 10*q.
-4*q*(q - 2)*(q - 1)
Let a = -12 + 26. Let w be ((-204)/a)/(-6) + (-6)/14. Determine k so that -1/2*k**3 + 0 + 3/2*k**w + 0*k = 0.
0, 3
Let t(o) = -3*o**5 - 5*o**4 + 19*o**3 - o**2 + 5*o - 5. Let y(b) = 4*b**5 + 4*b**4 - 20*b**3 - 6*b + 6. Let g(a) = -6*t(a) - 5*y(a). Factor g(m).
-2*m**2*(m - 3)*(m - 1)**2
Suppose 4*t = 3*t + 3. Suppose -3*r + 4 = -k, 0 = -k + 2*r + 1 - t. Factor 0*u + 0 + 1/3*u**k - 1/3*u**3.
-u**2*(u - 1)/3
Let q(a) be the second derivative of -a**5/12 - 20*a**4/9 - a + 199. Suppose q(y) = 0. Calculate y.
-16, 0
Let w(r) be the second derivative of -3/4*r**5 + 1/6*r**6 + 0*r**2 + 22*r + 0 + 5/2*r**3 - 5/12*r**4. Find v, given that w(v) = 0.
-1, 0, 1, 3
Suppose 0 = f + 3 - 5. Let o be 24/4 + (-4)/2. Suppose f*w**4 + 0*w**4 + 0*w**o = 0. Calculate w.
0
Let c = -79 - -5. Let h = -293/4 - c. Suppose -1/4*o**4 + 0 + h*o**5 + 1/2*o + 1/4*o**2 - 5/4*o**3 = 0. What is o?
-1, -2/3, 0, 1
Suppose -31 = -2*r - 27. Let q(w) be the first derivative of -6*w**r - 4 + 18*w + 2/3*w**3. Factor q(k).
2*(k - 3)**2
Let t(j) be the second derivative of j**6/105 - 4*j**5/7 + 179*j**4/21 + 40*j**3 + 63*j**2 + 265*j. Suppose t(r) = 0. What is r?
-1, 21
Let l(z) be the third derivative of -7*z**6/60 - 359*z**5/30 - 113*z**4/3 - 100*z**3/3 + 2*z**2 - 16. Factor l(f).
-2*(f + 1)*(f + 50)*(7*f + 2)
Factor 0*f**2 + 0*f + 1/7*f**5 - 4/7*f**4 + 3/7*f**3 + 0.
f**3*(f - 3)*(f - 1)/7
Let h(g) = -8*g**2 - 1000*g - 12512. Let f(l) = 3*l**2 + 400*l + 5005. Let d(p) = -12*f(p) - 5*h(p). Factor d(j).
4*(j + 25)**2
Solve 113965*n - 4*n**2 - 4 + 0*n**2 - 113957*n = 0.
1
Let u(a) be the second derivative of -a**6/18 + a**5/4 - 10*a**3/9 - 59*a. Factor u(d).
-5*d*(d - 2)**2*(d + 1)/3
What is v in -1/4*v**4 + 0 - 5/4*v**3 + 2*v - 1/2*v**2 = 0?
-4, -2, 0, 1
Let p be 5/((-20)/(-4)) + 13. Let u(z) be the first derivative of 3/5*z**5 + 5 - p*z**3 - 9*z + 33/2*z**2 + 9/2*z**4 - 1/2*z**6. Solve u(d) = 0 for d.
-3, 1
Let g(m) be the first derivative of 29/2*m**2 + 7/4*m**4 + 127/15*m**3 + 3/25*m**5 + 10*m + 14. Factor g(z).
(z + 1)*(z + 5)**2*(3*z + 2)/5
Let j(v) = 29*v. Let s be j(-1). Let a = s - -41. Find r, given that r**2 + 7*r - a*r + 2*r**3 - 2*r**2 - 2 + 0*r**2 = 0.
-1, -1/2, 2
Let z(g) = g**2 - 10*g - 1. Let d be z(11). Let j = 14 - d. Factor -j*k**3 - 176 + 4*k + 176.
-4*k*(k - 1)*(k + 1)
Let g(k) be the third derivative of k**5/60 - 17*k**4/24 + 5*k**3 - 113*k**2. Suppose g(y) = 0. What is y?
2, 15
Let u**2 + 13/4*u**4 - 4*u**3 + 0 - 3/4*u**5 + 0*u = 0. Calculate u.
0, 1/3, 2
Let v be 15/((-30)/4)*5/2. Let n be v/((-110)/4)*1. Determine m so that 0*m + 4/11*m**5 + n*m**4 + 0 - 4/11*m**3 - 2/11*m**2 = 0.
-1, -1/2, 0, 1
Let b(x) be the third derivative of x**6/540 + x**5/90 + 11*x**3/3 + 17*x**2. Let z(v) be the first derivative of b(v). 