p. Let u(x) be the first derivative of f(x). Suppose u(y) = 0. What is y?
-2, 1
Let m(p) be the third derivative of -p**8/672 + p**7/84 - 7*p**6/240 + p**5/40 + 56*p**2. Factor m(k).
-k**2*(k - 3)*(k - 1)**2/2
Suppose -123 - 1080 = 3*h. Let y = h + 2816/7. Factor 6/7 + 3/7*x**2 - y*x.
3*(x - 2)*(x - 1)/7
Let i = -1634/5 + 328. Let m(l) be the first derivative of 0*l + 0*l**3 + i*l**5 - 1/2*l**6 + 0*l**4 + 0*l**2 + 6. Solve m(z) = 0 for z.
0, 2
Let g(m) = -3*m + 33. Let f be g(13). Let a(l) = l**3 - l. Let j(x) = -15*x**3 - 48*x**2 - 39*x - 6. Let y(v) = f*a(v) + j(v). Let y(r) = 0. What is r?
-1, -2/7
Let b = 909 + -906. Factor 0 + 2/19*y**2 + 0*y + 2/19*y**b.
2*y**2*(y + 1)/19
Let p = -2/141 + 49/141. Factor -1/6*k - p*k**2 + 1/6*k**3 + 1/3*k**4 + 0.
k*(k - 1)*(k + 1)*(2*k + 1)/6
Factor -58/5*w - 28/5 - 4/5*w**2.
-2*(w + 14)*(2*w + 1)/5
Solve -2/9*o**3 + 122/3*o - 184/9 - 20*o**2 = 0 for o.
-92, 1
Let x be (24/(-9))/(-4) - (-26)/6. Suppose -35 = -x*t + 4*i, 5*t - 39 = 3*i - 9. Find h, given that 0 + 5/6*h**2 + 2/3*h**t + 1/3*h + 1/6*h**4 = 0.
-2, -1, 0
Suppose -2/9*c**2 + 0 + 100/9*c = 0. What is c?
0, 50
Let r(i) be the third derivative of -1/24*i**4 + 0*i + 0*i**3 - 32*i**2 - 1/10*i**5 - 3/40*i**6 + 0. Solve r(g) = 0.
-1/3, 0
Suppose -5*z + 11 = u - 17, -4*u + 17 = z. Suppose 13*t**2 + 24*t - u*t**5 - 18*t**3 - 15*t**4 - 12*t**2 + 11*t**2 = 0. What is t?
-2, 0, 1
Let i(y) = -y**3 + 15*y**2 - 15*y + 16. Let o be i(14). Suppose -3*k = o*k - 3*k. Let 0*w**2 + 2/5*w**3 + w**5 + 0*w + 7/5*w**4 + k = 0. What is w?
-1, -2/5, 0
Find h such that 94/3*h**2 - 1/9*h**3 - 8836/3*h + 830584/9 = 0.
94
Let f = -26/35 - -8/7. Let m be -1*0*4/12. Factor -8/5*i**4 + 12/5*i**3 - 8/5*i**2 + m + 2/5*i + f*i**5.
2*i*(i - 1)**4/5
Let n(g) be the third derivative of g**7/945 + g**6/270 - g**5/270 - g**4/54 + 4*g**2 - 3. Factor n(c).
2*c*(c - 1)*(c + 1)*(c + 2)/9
Let q(u) be the third derivative of u**7/945 - u**6/54 + 5*u**5/54 + 18*u**2 - 1. Factor q(m).
2*m**2*(m - 5)**2/9
Factor 1/4*f**4 + 9/4*f - 2 + 7/4*f**2 - 9/4*f**3.
(f - 8)*(f - 1)**2*(f + 1)/4
Let i(y) = -y**2 - 32*y - 58. Let x be i(-2). Factor -2*u + 2/17*u**3 - 14/17*u**x - 18/17.
2*(u - 9)*(u + 1)**2/17
Suppose -5*o + 5 = 0, -p + 7*o - 2*o = -157. Suppose -9*r + 198 = p. Let 3*i**2 + 0*i + 0 - 6*i**5 + 39/2*i**r - 33/2*i**3 = 0. Calculate i.
0, 1/4, 1, 2
Determine y so that -108*y + 57 + 156*y - 5*y**2 + 4*y**2 - 12 + 4*y**2 = 0.
-15, -1
Let j = -253 - -361. Let s = 326/3 - j. Determine d, given that 2/3*d**2 + 2*d**4 + 0*d + s*d**5 + 2*d**3 + 0 = 0.
-1, 0
Let x = 7 + -5. Let -x*v + 4*v**3 - 5*v - v**2 + v + 2*v + 1 = 0. Calculate v.
-1, 1/4, 1
Let i(w) be the second derivative of w**10/5400 + w**9/1575 - w**8/2100 + 7*w**4/6 + 5*w. Let x(g) be the third derivative of i(g). Factor x(j).
4*j**3*(j + 2)*(7*j - 2)/5
Let b(x) be the second derivative of 5*x**4/12 - 595*x**3/6 - 68*x + 2. What is o in b(o) = 0?
0, 119
Let 83/8*x + 43/2*x**2 + 5/4 = 0. Calculate x.
-1/4, -10/43
Let n be (-13)/((-260)/70) + 5/10. Let 1/2*p**3 - p**2 - 2*p + n = 0. What is p?
-2, 2
Let p(v) = -4*v**2 + 40*v - 3. Let x(c) = 3. Let l(s) = -1. Let q(w) = 4*l(w) + x(w). Let g(h) = p(h) - 3*q(h). Factor g(k).
-4*k*(k - 10)
Let a(x) = -2*x**2 - x. Let z(o) = 23*o**2 + 26*o + 14. Let t(g) = -22*a(g) - 2*z(g). Determine h so that t(h) = 0.
-14, -1
Suppose 3*u = 9*u - 12. Let w be (-222)/(-44) + 13/(143/(-6)). Determine p so that 0 + 3/2*p**u - w*p = 0.
0, 3
Let v = -190 - -193. Suppose -4*k + t = -v*t - 12, -k - t = -1. Let -3*u**k + 3/2*u + 3/2*u**3 + 0 = 0. What is u?
0, 1
Find p such that 60*p - 36 - 29 - 5*p**2 - 53 + 42 - 24 = 0.
2, 10
Let 13 + 48*f - 44 + 3*f**2 - 11 - 9 = 0. What is f?
-17, 1
Let n(c) be the third derivative of -c**7/42 - 7*c**6/24 - 5*c**5/12 + 35*c**4/24 + 5*c**3 + 203*c**2. Factor n(x).
-5*(x - 1)*(x + 1)**2*(x + 6)
Let n(c) = -c + 7. Let i be n(5). Suppose -12 = -3*w - 3*h, -5*w + h + 6 = -i. Factor 10*b**3 + 2 - 4*b**4 + 2*b**w - 3*b - 8*b**2 + b.
-2*(b - 1)**3*(2*b + 1)
Suppose -3/2*x**4 - 3/2*x**3 + 6*x + 6*x**2 + 0 = 0. What is x?
-2, -1, 0, 2
Let g(q) be the second derivative of q**7/84 - q**6/90 - 21*q**5/40 + 17*q**4/12 - 10*q**3/9 - 433*q. Suppose g(r) = 0. Calculate r.
-5, 0, 2/3, 1, 4
Let w(c) be the first derivative of c**5/15 - 3*c**4/2 + 19*c**3/3 + 130*c**2/3 - 100*c - 529. Factor w(m).
(m - 10)**2*(m - 1)*(m + 3)/3
Let k(m) be the first derivative of m**3/6 + m**2 - 6*m + 258. Factor k(v).
(v - 2)*(v + 6)/2
Let y(p) be the second derivative of 8/9*p**3 + 2/15*p**5 + 0 + 0*p**2 - 2/45*p**6 - 40*p + 7/9*p**4. Factor y(z).
-4*z*(z - 4)*(z + 1)**2/3
Let t be (-13)/(-114) - 22/(-4598)*11. Solve t*f**4 + 2/3*f**3 + 1/3*f + 0 + 5/6*f**2 = 0.
-2, -1, 0
Let g = -12 - -26. Suppose -6 = 4*a - g. Find r such that -25*r**2 - 18*r**3 - 6*r**2 + 0*r**4 - 36*r - 3*r**4 - 8*r**a - 12 = 0.
-2, -1
Let i(b) = 3*b + 7. Let l be i(-3). Let n be ((-5)/((-45)/6))/(l/(-1)). Let -2/3*m**3 + n*m**5 + 1/3*m**4 + 1/3 - 2/3*m**2 + 1/3*m = 0. Calculate m.
-1, 1
Let d be (-1079)/(-35) + 5*10/(-35). Factor -42/5*r - d - 3/5*r**2.
-3*(r + 7)**2/5
Suppose -v - 28 = -30. Let c be 66/30 + -1 - v/(-5). Find o, given that 2/5*o - 1/5*o**2 + 0 - c*o**3 - o**4 = 0.
-1, 0, 2/5
Let t be 2 + (0 - (3/(-2))/((-33)/(-44))). Determine s so that 0 + 1/2*s**t - 3/2*s**3 + 3/2*s - 1/2*s**2 = 0.
-1, 0, 1, 3
Solve -6*b + 8/3*b**3 - b**4 + 7*b**2 - 8/3 = 0 for b.
-2, -1/3, 1, 4
Suppose -5*d + 4*a + 24 = 0, -d + 2*a = 11 - 17. Let p(n) be the second derivative of -10*n + 0*n**d + 0*n**2 + 0 + 1/120*n**5 - 1/36*n**3. Factor p(k).
k*(k - 1)*(k + 1)/6
Let i = -108 + 113. Factor -324*p**3 + 7*p + i*p + 320*p**3 - 8*p**2.
-4*p*(p - 1)*(p + 3)
Let k(h) = h**2 + h. Let a(f) = 2*f**3 + 24*f**2 - 114*f + 216. Let t(b) = a(b) - 12*k(b). Suppose t(p) = 0. Calculate p.
-12, 3
Let u = 138001/240 + -575. Let y(d) be the third derivative of 8*d**2 + 0*d + 1/96*d**4 + 0 - u*d**5 + 0*d**3. Determine c, given that y(c) = 0.
0, 1
Let l(a) = a**3 - 42*a**2 - 4*a + 171. Let b be l(42). Determine q, given that 0 - 48/5*q - 24/5*q**2 - 3/5*q**b = 0.
-4, 0
Let h = 443 - 219. Solve 89*k**4 - 41*k**4 + 0*k**4 - h*k**5 + 4*k + 130*k**3 + 42*k**2 = 0.
-2/7, -1/4, 0, 1
Let r = 60627/8 - 7578. Factor -9/4*t - r*t**2 + 21/8.
-3*(t - 1)*(t + 7)/8
Solve -74/13*p - 36/13 - 4/13*p**2 = 0 for p.
-18, -1/2
Let d be (-32)/(-4) + -4 - 1. Factor -3*s**3 + 23 - s**d - 8*s**2 - 23.
-4*s**2*(s + 2)
Let n = -18 + 30. Suppose n = o + 3*o. Factor o*z**2 - 3*z**3 - 3*z**4 + 5*z - z + 3*z - 4*z.
-3*z*(z - 1)*(z + 1)**2
Let d(f) be the third derivative of -f**8/4032 + f**7/630 + f**6/180 + f**5/2 + 13*f**2. Let r(z) be the third derivative of d(z). Factor r(v).
-(v - 2)*(5*v + 2)
Let z(c) = 15*c**2 + 3*c - 23. Let h(x) = 8*x**2 + 8*x - 6. Let a(q) = -q - 1. Let m(v) = -6*a(v) - h(v). Let j(n) = 11*m(n) + 6*z(n). Factor j(u).
2*(u - 3)*(u + 1)
Determine n so that 106 - 2*n**3 - 211 + 105 - 2*n**2 = 0.
-1, 0
Let i(z) = z**2 + 5*z + 2. Let f(u) be the second derivative of u**3/6 + 3*u. Let s(n) = -2*f(n) + i(n). Factor s(y).
(y + 1)*(y + 2)
Factor -3*z**2 - 132/7 - 3/7*z**3 + 120/7*z.
-3*(z - 2)**2*(z + 11)/7
Let g = -553 - -555. Let k(r) be the second derivative of 6*r + 0*r**g - 1/6*r**5 - 1/9*r**3 + 0 - 2/45*r**6 - 2/9*r**4. Factor k(f).
-2*f*(f + 1)**2*(2*f + 1)/3
Let n = -192 + 69. Let d = n + 619/5. Factor 2/5*f + 0 - 2/5*f**5 - d*f**2 + 4/5*f**4 + 0*f**3.
-2*f*(f - 1)**3*(f + 1)/5
Suppose 48 = -8*t + 20*t. Let l(s) be the third derivative of 1/210*s**6 - 1/245*s**7 + 0 + 0*s**3 + 4*s**2 + 0*s + 0*s**t + 0*s**5 - 1/588*s**8. Factor l(p).
-2*p**3*(p + 2)*(2*p - 1)/7
Let a(b) be the third derivative of b**6/240 - b**5/40 - 3*b**4/16 - 5*b**3/12 + 222*b**2 + 2. Let a(z) = 0. What is z?
-1, 5
Factor 2/13*d + 2/13*d**3 + 0 - 4/13*d**2.
2*d*(d - 1)**2/13
Let c(j) = -j. Let d be c(-2). Let u = -363 - -870. Factor 16 - 107*y + u*y**d - 4 - 49*y.
3*(13*y - 2)**2
Let t(a) = -2*a**3 - 8*a**2 + a. Let l be t(0). Solve -7/4*p - 1/4*p**2 + l = 0 for p.
-7, 0
Let v(r) be the first derivative of -55*r + 39 - 5/3*r**3 - 30*r**2. Factor v(s).
-5*(s + 1)*(s + 11)
Let o be (10/20)/((-1)/4). Let b be -5 + 4 + (-8)/o. Factor -2*w**b + w**3 + 5*w**3 - w**3.
3*w**3
Factor 6*a**2 - 14*a**3 + 230 + 4*a**4 + 2*a