b + 6/25*b**5 + y*b**3. Solve t(o) = 0.
-2, -1, 0
Factor 1/2*t**3 + 199*t**2 + 0 + 0*t.
t**2*(t + 398)/2
Let m = -433/40 + 2173/200. Let x(y) be the second derivative of -4/15*y**4 + 0 - 4/5*y**2 - m*y**5 + 2*y - 2/3*y**3. Let x(j) = 0. Calculate j.
-2, -1
Suppose 8*a = 16 + 16. Factor -2*k**4 + 86*k - 6*k - 6*k**3 - 12*k**2 - 6*k**3 - 50 - a*k**3.
-2*(k - 1)**2*(k + 5)**2
Let f(t) be the first derivative of -132*t**2 + 121/6*t**3 + 288*t + 5. Suppose f(y) = 0. Calculate y.
24/11
Let k(v) be the first derivative of -v**6/3 - 212*v**5/5 + v**4/2 + 212*v**3/3 + 1551. Find n such that k(n) = 0.
-106, -1, 0, 1
Let h(w) be the first derivative of -161 + 1/9*w**3 - 17/6*w**2 + 0*w. What is i in h(i) = 0?
0, 17
Let x(c) = 65*c**3 + 1000*c**2 - 10*c - 130. Let n(t) = -6*t**3 + t**2 + t + 13. Let h(b) = 10*n(b) + x(b). Factor h(w).
5*w**2*(w + 202)
Let f = -40 - -82. Let c = 52 - f. Factor -2*r**3 + 2 - c*r**5 - 2*r**3 + 18*r**2 - 16*r**4 + 11*r + 3*r**5 - 4*r**2.
-(r - 1)*(r + 1)**3*(7*r + 2)
Let k(m) be the first derivative of m**8/560 + m**7/140 - 11*m**6/120 - 3*m**5/10 - 175*m**3/3 + 118. Let q(a) be the third derivative of k(a). Factor q(o).
3*o*(o - 3)*(o + 1)*(o + 4)
Suppose -l + 0*l = 3*k - 1, -l - k + 3 = 0. Suppose 4*d - 5*j - 92 = -j, 5*d + l*j = 124. Factor -58*f**3 + 0*f**2 - 4*f**2 + d*f**3 - 2*f**4 + 28*f**3.
-2*f**2*(f + 1)*(f + 2)
Let q be ((-8)/308)/((-1440)/252). Let j(o) be the third derivative of 1/132*o**4 + 1/1155*o**7 + 0 + q*o**6 + 0*o + 0*o**3 + 1/110*o**5 + 19*o**2. Factor j(s).
2*s*(s + 1)**3/11
Let m(k) be the third derivative of -3*k**5/35 - 547*k**4/84 + 61*k**3/21 + 14*k**2 + 45*k + 2. Find d, given that m(d) = 0.
-61/2, 1/9
Let d(f) = -f**3 - f**2. Let i(s) = 3*s**3 + s**2. Suppose 29*o - 32*o + 141 = 0. Let l = 46 - o. Let z(v) = l*i(v) - 4*d(v). Find u, given that z(u) = 0.
-3, 0
Let t(m) be the second derivative of m**7/2520 - m**6/120 + 43*m**4/12 + 105*m. Let w(p) be the third derivative of t(p). Factor w(z).
z*(z - 6)
Factor -1792*l**2 - 16008*l - 9565852 - 6450152 - 1792*l**2 + 3580*l**2.
-4*(l + 2001)**2
Let v = 552101/4 + -138025. Suppose -v*g**2 - 9/4 + 5/2*g = 0. What is g?
1, 9
Let r(u) be the first derivative of u**5/30 - u**4/2 + 8*u**3/3 + 77*u**2/2 - 4. Let a(n) be the second derivative of r(n). Solve a(d) = 0 for d.
2, 4
Factor 16*g**2 - 44*g + 16*g**2 - 34*g**2 + 208.
-2*(g - 4)*(g + 26)
Let g(v) = -64*v**2 - 642*v - 18. Let f be g(-10). Factor 28/9*j - 2/9*j**f - 98/9.
-2*(j - 7)**2/9
Factor 744/5*j + 1472/5 + 4/5*j**2.
4*(j + 2)*(j + 184)/5
Let h(a) = -3*a**2 + 106*a - 11. Let w be h(35). Factor -6 - w*g**3 - 96*g + 4*g**4 + 42 + 88*g**2 + 21*g**3 - 24*g**3 - 5*g**3.
4*(g - 3)**2*(g - 1)**2
Let 0 + 51/2*d**2 + 0*d - 103/4*d**3 + 1/4*d**4 = 0. What is d?
0, 1, 102
Let u = -6706 + 6708. Let h(k) be the first derivative of 1/2*k**u + 0*k**5 - 19 + 1/6*k**6 + 0*k**3 - 1/2*k**4 + 0*k. Solve h(f) = 0 for f.
-1, 0, 1
Let c = 69/5 - 13. Let a = -55231 - -55233. Determine k, given that -4/5*k**3 - c - 12/5*k**a - 12/5*k = 0.
-1
Suppose -6 = -4*k - 2*f, 5*k - 8 = 2*f + 13. Let q be (-21 + 16)/(k + -6). Factor q*c**3 + c**2 - 2/3*c + 0.
c*(c + 1)*(5*c - 2)/3
Let a(r) be the first derivative of -20*r**2 + 0*r - 130/3*r**3 - 57 - 10/3*r**6 + 135/4*r**4 + 11*r**5. Solve a(d) = 0.
-2, -1/4, 0, 1, 4
Let y be (0/(-1))/((24 + 22)/(-23)). Let b(i) be the first derivative of -2/7*i**3 - 3/14*i**2 + 0*i + 1/14*i**6 + 6/35*i**5 + y*i**4 + 11. Factor b(m).
3*m*(m - 1)*(m + 1)**3/7
Suppose -2*a = -3*b + 12, 5*b + 3*a + 2 - 3 = 0. Determine p so that p + 301*p**b - 7*p - 298*p**2 = 0.
0, 2
Let h be 78/(2 - -1) + 1*-2. Let x = 27 - h. Factor -4*o**x + 5*o + 4*o - 5*o + 2 - 10 + 8*o**2.
-4*(o - 2)*(o - 1)*(o + 1)
Let o be (-6)/270*-10 - 48/(-27). Suppose 228 - o*l**4 + 960*l + 2897*l**2 + 4*l**4 - 60*l**3 + 284 - 2511*l**2 = 0. What is l?
-1, 16
Let f(k) be the first derivative of -k**6/120 + k**5/15 - 5*k**4/24 + k**3/3 - k**2/2 + 23. Let m(x) be the second derivative of f(x). Solve m(c) = 0 for c.
1, 2
Let l(u) be the first derivative of 3*u**5/35 - 3*u**4/14 - 29*u**3/7 - 9*u**2 + 170. Determine y, given that l(y) = 0.
-3, -2, 0, 7
Suppose -4*p = -235 + 219. Let b(m) = -3*m. Let u be b(-5). Factor -p*l**3 - u*l + 45 - 10*l**2 - 14*l**2 - l**2 - l**3.
-5*(l - 1)*(l + 3)**2
Suppose -7*n - 52 = -33*n. Factor -n*l**4 - 853 - 127*l**2 - 83*l**3 - 49*l**2 + 1344*l + 35*l**3 - 715.
-2*(l - 2)**2*(l + 14)**2
Let 89996/5*l + 4/5*l**3 - 91204/5 + 1204/5*l**2 = 0. Calculate l.
-151, 1
Let t be 4/8 - (1 + -5 + 4). Let a be (6/9*-2)/(14/(-21)). Factor t + 1/4*u**a + 3/4*u.
(u + 1)*(u + 2)/4
Let r be 44/56 + (-172)/602. Let j(o) be the first derivative of r*o**3 + 1/2*o**2 + 1/20*o**5 + 1/4*o**4 - 30 + 1/4*o. Factor j(h).
(h + 1)**4/4
Let p = 589 - 629. Let k be (-26)/p + (-49)/196. Find s, given that 1/5*s - 1/5*s**2 + k = 0.
-1, 2
Factor 135 + 4693*z**2 - 132*z - 2342*z**2 - 2354*z**2.
-3*(z - 1)*(z + 45)
Let t(v) be the first derivative of -2*v**3/3 - 11*v**2 + 160*v - 58. Suppose t(p) = 0. What is p?
-16, 5
Let i be (-18 - -2) + 5300/318. Let v(p) be the second derivative of 0*p**2 - 1/6*p**4 + i*p**3 - 18*p + 0. Factor v(d).
-2*d*(d - 2)
Let w be (-178)/(-350) - 201/469 - (-121)/50. Factor 1/2 + w*m**3 - 9/2*m**2 + 3/2*m.
(m - 1)**2*(5*m + 1)/2
Let y(r) = r**2 + 2*r - 7. Let u be y(-7). Let m = u + -25. Factor 0*f**2 - 3/7*f + 3/7*f**m + 0.
3*f*(f - 1)*(f + 1)/7
Let -822*j**3 - 15*j**4 - 108504/5*j - 52272/5 - 60267/5*j**2 = 0. What is j?
-132/5, -1
Let o(f) be the third derivative of -f**6/280 + 288*f**5/35 - 55296*f**4/7 + 28311552*f**3/7 - f**2 - 428*f. Factor o(z).
-3*(z - 384)**3/7
Let j(s) be the third derivative of s**6/240 - 263*s**5/120 - 529*s**4/48 - 265*s**3/12 + 216*s**2 - 8*s. Factor j(q).
(q - 265)*(q + 1)**2/2
Let u(b) be the third derivative of -b**8/4480 - b**7/840 - b**6/480 + 101*b**4/24 + 3*b**2 - 1. Let i(y) be the second derivative of u(y). Factor i(t).
-3*t*(t + 1)**2/2
Suppose 26*r + 220 = 6*r. Let f be (-1)/121*r*0. What is s in 0*s - 6/7*s**2 + f + 2/7*s**3 = 0?
0, 3
Let v(y) be the first derivative of 44/13*y - 8/13*y**3 - 241 - 9/13*y**2 - 1/26*y**4. Factor v(c).
-2*(c - 1)*(c + 2)*(c + 11)/13
Let c(a) be the first derivative of a**3/3 + 75*a**2/2 - 486*a + 9802. Solve c(d) = 0 for d.
-81, 6
Let u(k) be the first derivative of -k**7/7140 - 19*k**6/3060 - 4*k**5/51 + 25*k**4/51 - 23*k**3 - 77. Let l(x) be the third derivative of u(x). Factor l(i).
-2*(i - 1)*(i + 10)**2/17
Let x = -8337 + 8340. Factor -82/7*n + 44/7*n**2 - 2/7*n**x + 40/7.
-2*(n - 20)*(n - 1)**2/7
Let o(c) be the second derivative of c**5/30 - 17*c**4/12 + 16*c**3/3 - 5*c**2 + 3*c. Let a(w) be the first derivative of o(w). Suppose a(p) = 0. Calculate p.
1, 16
Let u(g) be the second derivative of -g**5/5 - 27*g**4 - 208*g**3 - 616*g**2 + 3*g - 54. Solve u(j) = 0.
-77, -2
Determine h, given that 4/5*h**4 + 112/5*h**3 + 884/5*h**2 + 1352/5*h + 0 = 0.
-13, -2, 0
Let i(o) be the first derivative of -21*o**2 + 22 + 9/8*o**4 + 3/10*o**5 - 3*o**3 - 36*o. Factor i(t).
3*(t - 3)*(t + 2)**3/2
Let 7*g**2 + 36 - 4*g**4 - 42*g + 17/2*g**3 + 1/2*g**5 = 0. What is g?
-2, 2, 3
Let q be 3 + -2 - (2 - 1). Let y = 509714 + -509714. Suppose q*p + 2/7*p**2 + y = 0. Calculate p.
0
Let x(g) be the second derivative of -3/2*g**3 + 3/20*g**5 + 14*g**2 + 0 - 18*g - 1/24*g**4 + 1/120*g**6. Let j(i) be the first derivative of x(i). Factor j(w).
(w - 1)*(w + 1)*(w + 9)
Let k be 21 - (-437)/171 - 20. Let 2/9*w**2 - 20/9*w + k = 0. What is w?
2, 8
Let s(t) be the third derivative of t**6/210 - 43*t**5/105 - 71*t**4/21 + 368*t**3/21 + 40*t**2 + 5*t. Factor s(v).
4*(v - 46)*(v - 1)*(v + 4)/7
Find a such that -98/11*a**2 + 4/11*a**3 + 336/11 - 244/11*a + 2/11*a**4 = 0.
-6, -4, 1, 7
Let g = 15519 + -15517. Let o(x) be the second derivative of 0*x**g + 1/3*x**4 + 0 + 25*x + 10/3*x**3. Find v, given that o(v) = 0.
-5, 0
Factor -350 - 2856*i - 3244*i + i**3 + 6627*i - 178*i**2.
(i - 175)*(i - 2)*(i - 1)
Let d(a) be the third derivative of -a**5/60 - 1105*a**4/6 - 2442050*a**3/3 - 107*a**2 - 4*a - 2. What is f in d(f) = 0?
-2210
Let m = -530948 + 3716640/7. Determine s, given that -m*s**5 - 128/7*s**4 - 1024/7*s**3 + 0 + 0*s + 0*s**2 = 0.
-16, 0
Let q be 2*((-798)/(-56) -