be the first derivative of k(o). Determine p so that y(p) = 0.
-1, 0, 8
Factor -80*v**2 - 22*v**2 - 5*v**4 - 925*v - 32*v**2 - 750 - 75*v**3 - 271*v**2.
-5*(v + 2)*(v + 3)*(v + 5)**2
Let i(u) be the second derivative of 7/10*u**6 - 11*u - 12*u**2 + 51/4*u**4 + 6*u**5 + 5*u**3 + 0. Solve i(v) = 0 for v.
-4, -1, 2/7
Let x(f) be the second derivative of f**5/105 - 2*f**4/21 + 8*f**3/21 - 5*f**2 + 12*f. Let m(v) be the first derivative of x(v). Factor m(a).
4*(a - 2)**2/7
Let b(w) be the second derivative of w**6/6 + 43*w**5/2 + 1015*w**4 + 54665*w**3/3 - 121945*w**2/2 - 266*w. Factor b(h).
5*(h - 1)*(h + 29)**3
Let d be -8 + 9 + (-250)/(-176) + 18/(-33). Factor -3/8*a**4 + 9/8*a + 3/8*a**3 + d*a**2 + 0.
-3*a*(a - 3)*(a + 1)**2/8
Let f = -8 - 12. Let m be (-2)/(-12)*(-64)/f. Find t, given that 24/5*t + 54/5*t**2 + m = 0.
-2/9
Suppose 0*a - 11 = -5*x - 3*a, 5*x - 3*a + 1 = 0. Suppose -x = 5*n - 16. Find v, given that -4*v**n - v**3 - v**3 - 3*v**4 = 0.
-2, 0
Let h(o) be the second derivative of -1/35*o**5 + 0*o**2 - 17*o + 0 + 2/21*o**3 + 0*o**4. Factor h(j).
-4*j*(j - 1)*(j + 1)/7
Let w(a) be the first derivative of -5*a**3/3 + 35*a**2 + 223. Suppose w(u) = 0. Calculate u.
0, 14
Let j(n) be the third derivative of n**7/1155 - 13*n**6/330 - n**5/6 - 7*n**4/33 - 4*n**2. Let j(l) = 0. Calculate l.
-1, 0, 28
Let l(d) = -7*d**3 - 5*d**2 + 13*d - 5. Let m(s) = -4*s**3 - 3*s**2 + 7*s - 3. Let u(o) = -6*l(o) + 10*m(o). Determine f, given that u(f) = 0.
-2, 0, 2
Let j be (-2)/5*4/(-28)*75. Factor -12/7*n**3 + 0*n - j*n**4 + 0*n**2 + 0.
-6*n**3*(5*n + 2)/7
Let n(g) be the first derivative of -3*g**4/4 - 5*g**3 + 12*g**2 + 36*g + 250. Determine q so that n(q) = 0.
-6, -1, 2
Let z = 19126 - 19123. Suppose 2 + 1/2*v**z + 5/2*v**2 + 4*v = 0. Calculate v.
-2, -1
Suppose 2*b - 6 = 0, -40*l + 41*l + 5*b = 20. Let j(u) be the first derivative of 0*u**4 + 0*u + 0*u**3 - 4/5*u**l + 0*u**2 - 2/3*u**6 - 2. Solve j(q) = 0.
-1, 0
Let d(q) be the second derivative of 0 + 0*q**5 + 1/3*q**2 + 1/9*q**4 - 1/135*q**6 - 8/27*q**3 - 10*q. Suppose d(c) = 0. Calculate c.
-3, 1
Let m = 45503 - 45500. Let 3*z**2 - 3/2*z**m - 3 + 3/2*z = 0. What is z?
-1, 1, 2
Let s(i) be the second derivative of i**6/15 + i**5/10 - i**4/6 - i**3/3 + 5*i - 14. What is k in s(k) = 0?
-1, 0, 1
Let p(s) = 36*s**2 + 17*s + 20. Let k(x) = -17*x**2 - 9*x - 10. Let w(d) = -13*k(d) - 6*p(d). What is l in w(l) = 0?
-2, -1
Let b(d) = 2*d**2 + 69*d + 37. Let p be b(-34). Let 0 + 10/17*j**4 - 24/17*j**2 - 8/17*j - 6/17*j**p = 0. Calculate j.
-1, -2/5, 0, 2
Factor 72 + 427*o**2 - o**3 - 395*o**2 - 84*o - 3*o**3.
-4*(o - 3)**2*(o - 2)
Let r(q) = -q**2 - 7*q + 3. Let a be r(-7). Factor 7*h**2 + 84*h + 15*h**2 - 12*h**a - 5*h**4 + 14*h**4 - 8*h**4 + 49.
(h - 7)**2*(h + 1)**2
Suppose -l + 2*p = 8, -13 = 2*l - l - 3*p. Determine h so that -36*h**4 + 106*h + 28*h**5 + 16*h**l - 48*h**3 - 106*h = 0.
-1, 0, 2/7, 2
Let z(x) = 11*x**3 + 56*x**2 + 235*x + 274. Let t(o) = -10*o**3 - 56*o**2 - 234*o - 276. Let m(u) = 7*t(u) + 6*z(u). Find l such that m(l) = 0.
-8, -3
Let o(u) be the second derivative of -u**7/441 - 2*u**6/105 - u**5/210 + 4*u**4/21 - 16*u**3/63 + u - 1. Find y such that o(y) = 0.
-4, 0, 1
Let u(i) be the second derivative of i**9/1008 - i**7/280 - 10*i**3/3 + 10*i. Let s(p) be the second derivative of u(p). Factor s(b).
3*b**3*(b - 1)*(b + 1)
Let u(b) = 6*b**4 - 5*b**3 - 2*b**2 - 6*b - 7. Let z(j) = -j**4 + j**3 + j**2 + 1. Let p(l) = 3*u(l) + 21*z(l). Determine c so that p(c) = 0.
-2, 0, 1, 3
Let p(i) be the first derivative of 4/27*i**3 - 4/9*i + 1/18*i**4 - 1/9*i**2 - 16. Find u such that p(u) = 0.
-2, -1, 1
Let o(q) be the third derivative of q**6/60 - q**5 + 16*q**4 - 352*q**3/3 + 2*q**2 + 45. Factor o(v).
2*(v - 22)*(v - 4)**2
Let m(s) = -7*s**2 + 12*s - 13. Let p = -11 - -14. Suppose c + 2 = -p. Let f(d) = -22*d**2 + 36*d - 38. Let g(r) = c*f(r) + 16*m(r). Factor g(a).
-2*(a - 3)**2
Let u be (-22)/121 - ((-933)/231 + 3). Determine r so that u - 3/7*r**3 + 3/7*r - 6/7*r**2 = 0.
-2, -1, 1
Let v(a) be the first derivative of 1/20*a**4 + 0*a**3 - 5/2*a**2 + 0*a + 1/200*a**6 + 4 + 3/100*a**5. Let n(x) be the second derivative of v(x). Factor n(y).
3*y*(y + 1)*(y + 2)/5
Let o(g) be the first derivative of -3/10*g**5 + 0*g - 13 + 0*g**2 - g**3 - 9/8*g**4. Factor o(c).
-3*c**2*(c + 1)*(c + 2)/2
Let x(v) be the second derivative of 3*v**8/11200 - v**7/2100 - v**6/180 - v**5/75 - 2*v**4/3 - 2*v. Let i(a) be the third derivative of x(a). Factor i(t).
(t - 2)*(3*t + 2)**2/5
Let o(d) be the first derivative of 1/15*d**6 + 22 + 0*d**2 + 1/5*d**4 - 6/25*d**5 + 0*d**3 + 0*d. What is y in o(y) = 0?
0, 1, 2
Let u = -1796 - -1798. Let h(s) be the first derivative of -3/2*s**3 + 0*s**u + 3/8*s**4 - 3 + 0*s. Factor h(t).
3*t**2*(t - 3)/2
Let k = 5815 + -5812. Find g, given that -1/4*g**4 - 1/2*g + 3/4*g**2 + 0*g**k + 0 = 0.
-2, 0, 1
Let d(y) be the third derivative of 0*y + 1/76*y**4 + 19*y**2 + 0 - 2/57*y**3 + 2/95*y**5 + 7/1140*y**6. Factor d(x).
2*(x + 1)**2*(7*x - 2)/19
Let j(h) be the second derivative of -2/9*h**2 + 1/54*h**4 - 1/27*h**3 + 0 - h. Factor j(z).
2*(z - 2)*(z + 1)/9
Let a(q) be the third derivative of -q**7/525 + q**6/150 + 9*q**5/50 + 13*q**4/15 + 28*q**3/15 - 42*q**2 + q. Let a(h) = 0. What is h?
-2, -1, 7
Suppose 65*g - 68 = 48*g. Let b(c) be the first derivative of 76/5*c**5 + 32*c**3 + g*c + 3*c**6 + 31*c**4 + 17*c**2 + 10. Factor b(z).
2*(z + 1)**4*(9*z + 2)
Let z(b) be the third derivative of -b**8/34272 - b**7/21420 - 7*b**5/30 - b**2. Let f(c) be the third derivative of z(c). Find h, given that f(h) = 0.
-2/5, 0
Let d(z) = z**3 - 13*z**2 + z - 17. Let r be d(13). Let v be (0 + r + 1)*(-3)/4. What is g in 1/4 + v*g**2 - 3/2*g = 0?
1/3
Let c(i) be the first derivative of -i**6/36 - i**5/5 - 11*i**4/24 - i**3/3 - 82. What is k in c(k) = 0?
-3, -2, -1, 0
Suppose -179 - 125 = 4*b. Let r = -76 - b. Factor -1/2*f**2 + r + f - 1/2*f**3.
-f*(f - 1)*(f + 2)/2
Let p(x) be the second derivative of -x**7/1260 - x**6/180 - x**5/60 - 13*x**4/12 - 4*x. Let y(j) be the third derivative of p(j). Factor y(h).
-2*(h + 1)**2
Let b(o) = 60*o**3 - 404*o**2 + 564*o - 284. Let h(g) = -17*g**3 + 115*g**2 - 161*g + 81. Let w(y) = -9*b(y) - 32*h(y). Find t such that w(t) = 0.
1, 9
Suppose 0 = 29*b - 23*b. Let h(v) be the third derivative of 1/40*v**6 + 3/20*v**5 + 1/12*v**4 + b - 2/105*v**7 + 0*v + 0*v**3 + 5*v**2. Factor h(g).
-g*(g - 2)*(g + 1)*(4*g + 1)
Let g = 91 + -88. Factor i**2 + 11*i**3 - 1 + i - 11*i**g - i**3.
-(i - 1)**2*(i + 1)
Let g be (14 - (-9 - -11)) + -12. Solve -2/23*a**3 + 0*a + 4/23*a**2 + g = 0 for a.
0, 2
Let q(u) be the first derivative of 2/33*u**3 + 9 - 4/11*u + 1/11*u**2. Determine w so that q(w) = 0.
-2, 1
Let 2/11*s**5 + 2/11*s + 12/11*s**3 - 8/11*s**4 + 0 - 8/11*s**2 = 0. What is s?
0, 1
Let g(h) be the first derivative of 15*h**6/2 - 69*h**5 + 155*h**4/4 + 615*h**3 + 900*h**2 + 500*h - 171. Let g(l) = 0. What is l?
-1, -2/3, 5
Solve -4/21*h**2 - 2/7*h**3 + 16/21*h**4 - 2/7*h**5 + 0*h + 0 = 0.
-1/3, 0, 1, 2
Let c = -5114/3 + 1705. Factor -1/3*w + 1/3*w**3 + w**2 - c*w**4 - 2/3.
-(w - 2)*(w - 1)*(w + 1)**2/3
Let t(r) = r + 12. Let o be t(-6). Factor -a**3 + o*a**2 - 120*a + 124*a + 3*a**3.
2*a*(a + 1)*(a + 2)
Let c = 1081/8755 + -3/515. Let a(f) be the first derivative of -2/51*f**3 + 0*f + 13 - 1/34*f**4 + c*f**2. Factor a(v).
-2*v*(v - 1)*(v + 2)/17
Let c be 19 - 1 - (42 + -36). Let t(m) be the first derivative of -32/15*m**3 - 4/5*m**2 + 4/5*m + c. Factor t(y).
-4*(2*y + 1)*(4*y - 1)/5
Let s = 113 + -106. Solve -21*r**2 - 13*r**2 - s*r - 2*r**3 + r**3 + 3 + 39*r**2 = 0.
1, 3
Let s be 0 - (-12)/(-90)*-20. Determine y so that -4 + s*y**2 + 4/3*y = 0.
-3/2, 1
Let p(t) be the first derivative of t**3/3 - 9*t**2/2 + 14*t - 8. Solve p(u) = 0 for u.
2, 7
Let o = 22 - 26. Let j(d) = d**5 - 8*d**4 + 7*d**3 + 7*d**2 - 17*d + 1. Let g(t) = -4*t**4 + 4*t**3 + 4*t**2 - 8*t. Let a(b) = o*j(b) + 9*g(b). Factor a(x).
-4*(x - 1)**2*(x + 1)**3
Suppose 0 - 6/7*c**2 - 2/7*c**4 - 18/7*c + 10/7*c**3 = 0. What is c?
-1, 0, 3
Let n(f) be the third derivative of f**8/1344 - f**7/280 + f**6/240 + f**5/120 - f**4/32 + f**3/24 - 255*f**2. Factor n(u).
(u - 1)**4*(u + 1)/4
Suppose x + 15 = 6*x. Suppose 5*u = -2*j -