7
Determine m, given that -261 - 33*m - 81*m**4 - 91*m**2 - 138*m + 112*m**2 + 321 + 171*m**3 = 0.
-1, 4/9, 1, 5/3
Let j(u) be the first derivative of -5*u**3/3 + 185*u**2/2 - 1500*u - 3179. Solve j(s) = 0.
12, 25
Suppose 1119*h - 1112*h = 112. Let m(n) = -18*n + 288. Let w be m(h). What is i in 3/2*i**4 + w*i**3 + 0*i - 3/2*i**2 + 0 = 0?
-1, 0, 1
Let r(a) = -11*a**3 - 316*a**2 - 1703*a - 2070. Let i(l) = -7*l**3 - 317*l**2 - 1701*l - 2070. Let t(x) = 4*i(x) - 3*r(x). Find b such that t(b) = 0.
-3, -2, 69
Let m(l) = 10*l**2 - l + 3. Let x(d) = -d**2 + 147*d - 8. Let f(s) = -4*m(s) + 2*x(s). Determine o, given that f(o) = 0.
2/21, 7
Let u(b) be the second derivative of -b**4/66 - 73*b**3/33 - 210*b**2/11 + 434*b. What is x in u(x) = 0?
-70, -3
Let b(w) = 8*w**3 - 270*w**2 - 305*w - 18. Let j(s) = 28*s**3 - 944*s**2 - 1068*s - 64. Let d(i) = 32*b(i) - 9*j(i). Let d(g) = 0. Calculate g.
-1, 0, 37
Let d = -1/407 + 27/37. Let c = -1547/22 + 141/2. Factor 0*g - c*g**3 - 6/11*g**2 + d.
-2*(g - 1)*(g + 2)**2/11
Let c(f) be the third derivative of 0*f + 10*f**2 - 1 - 1/5*f**5 - 5/8*f**4 - 1/40*f**6 - f**3. Determine p, given that c(p) = 0.
-2, -1
Let v(l) = -3*l**3 - 53*l**2 - 369*l + 425. Let b(k) = 4*k**3 + 79*k**2 + 554*k - 637. Let s(a) = 5*b(a) + 7*v(a). Suppose s(q) = 0. Calculate q.
-7, 1, 30
Let g = -3457 + 3459. Suppose -5*a + 20 = 0, -2*a - 1 = -d - 7. Factor -3*j**g + d*j + 4*j**2 + 2 - 1.
(j + 1)**2
Let m(p) be the third derivative of p**6/60 + 2*p**5/5 + 11*p**4/3 + 16*p**3 - p**2 - 454. Solve m(o) = 0.
-6, -4, -2
Let l(p) = -p**2 + 2*p. Let t(y) = -8*y**2 + 14*y - 56. Suppose 2*c - 25*c - 23 = 0. Let r(s) = c*t(s) + 10*l(s). Factor r(o).
-2*(o - 7)*(o + 4)
Let h be 806/1001 + 20/70. Let j = -15337/11 + 1397. Let -6/11*n**3 - j*n**2 + 0 + h*n**4 - 12/11*n = 0. Calculate n.
-1, -1/2, 0, 2
Determine j so that -4*j**5 - 60*j + 12818*j**3 + 22*j**4 - 12754*j**3 + 72 - 6*j**4 - 88*j**2 = 0.
-3, -1, 1, 6
Let d(x) be the first derivative of -x**6/120 + x**5/40 + 5*x**4/48 - x**3/4 - 109*x - 33. Let a(m) be the first derivative of d(m). Factor a(b).
-b*(b - 3)*(b - 1)*(b + 2)/4
Let c = 339473/133386 - -5/12126. Solve -16/11*z + c*z**2 + 0 + 2/11*z**4 - 14/11*z**3 = 0.
0, 1, 2, 4
Let u(q) be the third derivative of -q**6/720 - 13*q**5/360 - q**4/4 + 4946*q**2. Find p, given that u(p) = 0.
-9, -4, 0
Suppose -5*y + 14 = x, 3*y - 2*x - 5 - 6 = 0. Suppose y - z - 28 + 16 - 5*z + 3*z**2 = 0. Calculate z.
-1, 3
Suppose 0 = -2*m - 3*p + 23, 3*p - 9 = -3*m + 7*p. Suppose c = 11 - m. Find f, given that 95*f**c + f**3 - 193*f**4 + 99*f**4 = 0.
-1, 0
Let g be (-2)/(-20)*4*5. Let z be 4/(-8) + (-38)/(-4). Determine c so that -10*c**2 - c + 34*c**2 - 13*c**2 - z*c**g = 0.
0, 1/2
Let v(o) be the second derivative of -o**7/231 + 23*o**6/165 - 39*o**5/110 - 21*o**4/22 + o - 2620. Determine k so that v(k) = 0.
-1, 0, 3, 21
Factor -5/2*i**2 + 105/2*i - 105/2*i**3 + 0 + 5/2*i**4.
5*i*(i - 21)*(i - 1)*(i + 1)/2
Let d(u) be the third derivative of u + 0 + 1/66*u**5 - 1/660*u**6 + 1/66*u**4 - 67*u**2 - 8/11*u**3. Determine x, given that d(x) = 0.
-2, 3, 4
Let l(s) be the third derivative of -s**6/90 + s**5/6 - s**4 + 23*s**3 + 142*s**2. Let b(y) be the first derivative of l(y). Suppose b(n) = 0. Calculate n.
2, 3
Suppose -56 + 26 = -10*b. Factor o + 2*o**2 - o**5 + b*o**4 + 9*o**4 - 14*o**4.
-o*(o - 1)*(o + 1)**3
Let g(k) be the second derivative of -k**7/147 + 13*k**6/105 + 3*k**5/70 - 37*k**4/42 - 26*k**3/21 - 2216*k. Let g(m) = 0. Calculate m.
-1, 0, 2, 13
Find k, given that -176*k**3 + 148464*k**5 - 148462*k**5 + 231*k**2 + 29*k**2 - 28*k - 86*k + 28*k**4 = 0.
-19, 0, 1, 3
Let b = -249 - -249. Factor 133 - 12*c**2 - 149 - 4*c**3 - 36*c + 12*c + b*c**3 + 2*c**3.
-2*(c + 2)**3
Let l(y) be the third derivative of -1/450*y**5 + 0*y**3 + 0*y + 18*y**2 + 1/60*y**4 - 3. Factor l(t).
-2*t*(t - 3)/15
Let p(z) = -z**2 - 1. Let w = -116 + 111. Let y(g) = 2. Let t(c) = w*p(c) - 5*y(c). Let t(f) = 0. What is f?
-1, 1
Suppose 139*s - 113979 + 113979 = 0. Factor 0*t + t**4 + s*t**2 + 1/3*t**5 + 0 + 2/3*t**3.
t**3*(t + 1)*(t + 2)/3
Let t(d) be the first derivative of -d**6/6 + 73*d**4/4 - 24*d**3 - 1319. Suppose t(v) = 0. What is v?
-9, 0, 1, 8
Let b(q) be the third derivative of -q**6/780 - 9*q**5/130 - 27*q**4/26 + 41*q**2 - q + 2. Suppose b(p) = 0. What is p?
-18, -9, 0
Let r(p) be the first derivative of 3*p**4/8 + 6*p**3 - 207*p**2/4 - 120*p + 1921. Let r(m) = 0. Calculate m.
-16, -1, 5
Let r(y) be the second derivative of -y**4/15 + 16*y**3/3 - 152*y**2/5 - 194*y. Factor r(x).
-4*(x - 38)*(x - 2)/5
Suppose -2*y + 4 = r, -3 = -48*r + 47*r - y. Factor 0 + 8/7*a**3 + 12/7*a**4 + 4/7*a**5 + 0*a**r + 0*a.
4*a**3*(a + 1)*(a + 2)/7
Let j(y) = -2324*y - 18590. Let r be j(-8). Determine z, given that 272/7*z**4 - 122/7*z + 20/7 + 32/7*z**r + 478/7*z**3 - 32/7*z**5 = 0.
-1, 1/4, 10
Factor -888*u + 65*u**2 + 30*u**3 + 1806*u - 883*u.
5*u*(u + 1)*(6*u + 7)
Let q(y) = 2*y**2 - 2. Let x(f) = 2*f**4 + 34*f**3 + 66*f**2 - 202*f + 100. Let t(r) = -20*q(r) + 2*x(r). Solve t(d) = 0.
-15, -4, 1
Let r(o) = o**3 + 3*o**2 - 4*o - 5. Let v be r(-3). Let q = -3 + v. Factor -85*s**2 + 21*s**q - 8*s**5 - 4*s**5 - 6*s**3 + 0*s**4 + 82*s**2.
-3*s**2*(s - 1)**2*(4*s + 1)
Let v = -13832 - -41131/3. Let i = v - -122. Factor 0 + i*b**2 + 1/3*b**5 - b**3 - 1/3*b**4 + 2/3*b.
b*(b - 2)*(b - 1)*(b + 1)**2/3
Suppose l + 4 - 2 = g, 4*g + 3*l + 27 = 0. Let p be (g - (-2 + -2))*15. Factor -p*u**2 + 19*u**2 - 18 + 2 + 12*u.
4*(u - 1)*(u + 4)
Let f(z) be the first derivative of -z**4/2 - 200*z**3 - 597*z**2 - 596*z + 402. Determine p so that f(p) = 0.
-298, -1
Suppose -u = 2, 2*u = -3*k - 2*u - 1259. Let v = k + 421. Let 0 + 4/9*s**2 + 0*s - 8/9*s**3 + 4/9*s**v = 0. What is s?
0, 1
Let y(i) be the second derivative of i**6/120 - 37*i**5/80 + 403*i**4/48 - 393*i**3/8 - 405*i**2/2 - 14*i + 25. Factor y(j).
(j - 20)*(j - 9)**2*(j + 1)/4
Let w = 354 - 394. Let p(h) = -h**3 + h**2 - h + 2. Let j(k) = -7*k**3 + 25*k**2 - 45*k + 35. Let o(x) = w*p(x) + 5*j(x). Let o(i) = 0. Calculate i.
-19, 1
Let p be (232/(-32) + 8)/9*4. Let c(m) be the first derivative of -27 - m**2 + m + p*m**3. Factor c(q).
(q - 1)**2
Let b(g) be the first derivative of g**6/90 + 3*g**5/10 + 7*g**4/3 + 113*g**3/3 - g**2 + 88. Let d(t) be the third derivative of b(t). Let d(s) = 0. What is s?
-7, -2
Let b = 188592 + -188589. Factor 32/3*i**b + 24*i - 4/3*i**4 + 0 - 28*i**2.
-4*i*(i - 3)**2*(i - 2)/3
Let b be (-58)/(-29) + (-759)/(-5)*-1. Let y = -149 - b. Solve 6/5*v**2 - y + 6/5*v - 4/5*v**3 = 0 for v.
-1, 1/2, 2
Suppose 2*g = 4*n + 30, 6 = -g - g. Let s be (-5 - n)/2*(-6)/(-72). Factor -5/6*q**2 - s*q + 0.
-q*(5*q + 1)/6
Suppose -59*n + 37*n = -33*n. Let w(o) be the third derivative of n*o - 1/50*o**5 - 5*o**2 - 1/15*o**3 + 1/20*o**4 + 1/300*o**6 + 0. Factor w(f).
2*(f - 1)**3/5
Let p(s) = s - 7. Let r be p(9). Factor 4 - 20*h**3 + 11 + 30*h**2 - 44*h - 1 + 18*h**2 + r*h**4.
2*(h - 7)*(h - 1)**3
Let z be (-151152)/(-2680) - -22*1. Factor 10*r**4 + 1898/5*r**2 + z - 132*r**3 + 1848/5*r.
2*(r - 7)**2*(5*r + 2)**2/5
Let r(g) = 65*g**2 + 1035*g - 12095. Let f(u) = -3*u**2 - 47*u + 550. Let q(a) = 45*f(a) + 2*r(a). Factor q(d).
-5*(d - 7)*(d + 16)
Suppose w + 7*m - 73 = 2*m, 3*w = -5*m + 269. Suppose -5*g = 78 - w. Factor 0*k + 17/2*k**2 - 2 + 5/2*k**g + 9*k**3.
(k + 1)**2*(k + 2)*(5*k - 2)/2
Let v(q) = -9*q**3 + 41*q**2 + 116*q - 104. Let a(d) = -10*d**3 + 40*d**2 + 130*d - 105. Let s(n) = 4*a(n) - 5*v(n). Factor s(z).
5*(z - 10)*(z - 1)*(z + 2)
Let t(b) be the first derivative of b**6/3 + 48*b**5/5 + 113*b**4/2 - 2020*b**3/3 - 8100*b**2 - 14000*b + 3139. Solve t(y) = 0 for y.
-10, -1, 7
Let q = 2787/2330 - -9/2330. Let o be (-2)/((-1)/((-1)/(-1))). What is n in 3/5*n**4 + 0 - q*n**o + 3/5*n**3 + 0*n = 0?
-2, 0, 1
Let t(v) = -6*v**2 + 48*v + 3. Let g be t(8). Suppose -3 + 8 = -5*o. Let q(s) = s**3 + s**2. Let j(f) = f**3 - f**2. Let n(b) = g*q(b) + o*j(b). Factor n(z).
2*z**2*(z + 2)
Let s = 148 + -144. Determine k, given that k**2 - s*k**3 - 9 + 9*k - 4 + 11 - 4*k**2 = 0.
-2, 1/4, 1
Let y(k) be the second derivative of -38809*k**5/100 + 23246*k**4/3 + 4726*k**3/15 + 24*k**2/5 + 1876*k - 3. Suppose y(d) = 0. What is d?
-2/197, 12
Let x(j) = 178*j**2 -