 -1, 2
Let x(w) be the first derivative of -3*w**4/4 + 3*w**3 + 6*w**2 + 2228. Determine d, given that x(d) = 0.
-1, 0, 4
Let u be -7 - (-10 - (-3)/(-1)). Suppose u*i**3 - 18*i**2 + 10*i**2 + 13*i**4 - 11*i**4 = 0. Calculate i.
-4, 0, 1
Let s = -294 + 296. Factor 11 - 4 + 20*m**s + 4*m**3 - 24*m - 7.
4*m*(m - 1)*(m + 6)
Let g(i) = 439*i - 13606. Let h be g(31). Suppose -h + 3/8*u**3 + 3/4*u**2 - 3/2*u = 0. Calculate u.
-2, 2
Let g(a) = -5*a**4 - 10*a**3 - 15*a**2 - 3*a + 9. Let w(r) = -26*r**4 - 50*r**3 - 76*r**2 - 16*r + 48. Let x(v) = 16*g(v) - 3*w(v). Factor x(c).
-2*c**2*(c + 2)*(c + 3)
Let x(i) = i**3 - i - 3. Suppose -2 = -10*d + 9*d. Let k be x(d). Factor 2*v**2 - 2*v**k - 7*v + 14*v - 2 - 5*v.
-2*(v - 1)**2*(v + 1)
Let m = 3737/14940 + -1/7470. Suppose 0 - 1/4*l**2 - 1/2*l + m*l**3 = 0. What is l?
-1, 0, 2
Let p be 8/(-39)*(98 + -91 - 17/2). Let d(k) be the first derivative of 98/65*k**5 + 0*k + 64/39*k**3 - p*k**2 - 77/26*k**4 - 5. Factor d(x).
2*x*(x - 1)*(7*x - 2)**2/13
Let a(z) be the first derivative of -z**5/150 - z**4/15 - z**2 + 4*z - 148. Let p(o) be the second derivative of a(o). Factor p(u).
-2*u*(u + 4)/5
Let u(s) be the third derivative of 1/40*s**6 - 108*s**2 + 1/4*s**5 + 0*s + 7/8*s**4 + 3/2*s**3 + 0. Factor u(c).
3*(c + 1)**2*(c + 3)
Factor 7/4 - 125/4*l + 8*l**3 + 103/2*l**2.
(l + 7)*(2*l - 1)*(16*l - 1)/4
Let u(c) = -3*c. Let p be u(-3). Suppose 0 = -p*y - 0 + 18. Let 4*i - 5*i - 5*i + i**y + 5*i = 0. Calculate i.
0, 1
Suppose 4*m - 4*k = 12, -67*k - 7 = -3*m - 62*k. Solve 32/5*w - 4/5*w**5 - 4/5*w**2 - 16/5 - 28/5*w**3 + 4*w**m = 0 for w.
-1, 1, 2
Let i(l) be the first derivative of l**6/240 - 13*l**5/120 + l**4/4 + 9*l**2 + 126. Let r(p) be the second derivative of i(p). Factor r(y).
y*(y - 12)*(y - 1)/2
Let z(k) be the third derivative of k**7/945 - 2*k**6/135 - 11*k**5/270 + k**4/6 - 66*k**2. Suppose z(a) = 0. What is a?
-2, 0, 1, 9
Suppose 0 = -1519*t + 854*t - 898*t + 3126. Let f(z) = z - 7. Let q be f(7). Factor -2/7*d**4 + 0*d + q*d**3 + 0*d**t + 0.
-2*d**4/7
Let j be 31 + 6*(-2)/3. Let d(v) = 6*v**2 - 798*v - 7554. Let f(p) = -p**2 + 114*p + 1079. Let k(b) = j*f(b) + 4*d(b). Determine q so that k(q) = 0.
-19
Factor -277*i**2 - 23*i**2 - 3*i**5 - 195*i**3 - 737*i**4 + 695*i**4.
-3*i**2*(i + 4)*(i + 5)**2
Let a(d) = -4*d**2 + 34*d - 50. Let b be a(21). Let u = b - -1110. Suppose -5/2*g**3 - 5/2*g**2 + 10 + u*g = 0. Calculate g.
-2, -1, 2
Let g = 3420 - 3413. Let a(z) be the third derivative of -11*z**2 - 1/6*z**4 + 0 + 0*z**6 + 0*z**3 + 0*z + 1/105*z**g - 1/10*z**5. Factor a(h).
2*h*(h - 2)*(h + 1)**2
Factor -15/2*s**2 + 57/2*s + 1/8*s**3 - 28.
(s - 56)*(s - 2)**2/8
Let y be 7/(-63)*7884/(-1022). Determine t, given that -8/7*t - y*t**2 - 1/7*t**3 + 0 = 0.
-4, -2, 0
Let n = -37 - -67. Suppose 0 = -4*w + 42 - n. Factor 5*l**2 - 5 - 5*l**w - l - 5*l + 11*l.
-5*(l - 1)**2*(l + 1)
Let h(p) be the first derivative of -17*p**5/20 - p**4/4 + 64*p**2 + 28. Let v(r) be the second derivative of h(r). Find k, given that v(k) = 0.
-2/17, 0
Let c be ((1 - 11) + 4415/440)*(-12)/(-27). Let p(x) be the second derivative of -c*x**4 - 7/33*x**3 - 18*x + 0 - 6/11*x**2. Factor p(n).
-2*(n + 1)*(n + 6)/11
Let n = -1510 + 543. Let o = n + 970. Find f, given that 21/8*f**2 + 0 - 27/4*f**o + 9/4*f + 15/8*f**4 = 0.
-2/5, 0, 1, 3
Let -14*h - 1071 + 5*h**2 - 141*h + 741 = 0. Calculate h.
-2, 33
Let y(w) be the second derivative of -w**5/60 - 131*w**4/6 + 175*w**3/2 - 394*w**2/3 - 4948*w. What is z in y(z) = 0?
-788, 1
Let c(n) be the third derivative of -n**6/180 + 29*n**5/60 - 70*n**3/3 + 3*n**2 + 2. Let q(h) be the first derivative of c(h). Suppose q(d) = 0. What is d?
0, 29
Let x(u) be the first derivative of -1/40*u**5 - 1/4*u**3 + 5/2*u**2 - 25/8*u - 58 - 1/4*u**4. Factor x(h).
-(h - 1)**2*(h + 5)**2/8
Let z(y) = -y**2 - 110*y - 424. Let c be z(-4). Let d(o) be the second derivative of c + 1/12*o**4 - 6*o - 2*o**2 - 1/2*o**3. Determine p so that d(p) = 0.
-1, 4
Let f(v) be the third derivative of v**6/60 - v**5/15 - 7*v**4/4 - 6*v**3 + 2095*v**2. Solve f(i) = 0 for i.
-3, -1, 6
Let h(y) be the second derivative of y**8/2240 + y**7/840 - y**6/120 - 5*y**4/12 + 9*y - 4. Let j(b) be the third derivative of h(b). Factor j(o).
3*o*(o - 1)*(o + 2)
Let x(l) be the second derivative of -2*l**6/15 + 6*l**5/5 + 21*l**4 + 72*l**3 - 78*l. Suppose x(u) = 0. What is u?
-3, 0, 12
Let u = -967/6 + 29011/180. Let t(x) be the third derivative of -30*x**2 + 1/8*x**4 + 0 - u*x**5 + 0*x + 5/9*x**3. Factor t(y).
-(y - 10)*(y + 1)/3
Let n be (-38253)/(-82) - 5/2. Suppose -10*b + n = 64. Determine y so that b*y - 30*y**2 - 5/4*y**4 + 10*y**3 - 20 = 0.
2
Let x(w) be the first derivative of w**6/15 + 56*w**5/25 + 102*w**4/5 - 572*w**3/15 - 4477*w**2/5 + 15972*w/5 + 5121. Suppose x(p) = 0. Calculate p.
-11, 2, 3
Factor 44/3*s**2 - 177/2*s + 3.
(s - 6)*(88*s - 3)/6
Factor -7 + 3311*g**3 - 8*g**2 - 3309*g**3 + 7.
2*g**2*(g - 4)
Suppose -27 = -17*z + 58. Factor -3*i**2 - 12*i**2 + 7*i**2 + 15*i**4 - 5*i**3 + 5*i**z - 7*i**2.
5*i**2*(i - 1)*(i + 1)*(i + 3)
Suppose 58/5*f**2 + 1/5*f**5 + 42/5*f**3 + 9/5 + 13/5*f**4 + 37/5*f = 0. Calculate f.
-9, -1
Let z(u) be the first derivative of u**3/12 + 213*u**2/8 - 215*u/2 + 6781. Solve z(h) = 0 for h.
-215, 2
Let o(r) be the first derivative of r**4/22 - 512*r**3/33 - 515*r**2/11 - 516*r/11 - 3701. Factor o(g).
2*(g - 258)*(g + 1)**2/11
Factor 0*h + 0 + 3/2*h**3 - 3/2*h**5 + 0*h**4 + 0*h**2.
-3*h**3*(h - 1)*(h + 1)/2
Determine w so that 5*w**4 - 319*w**3 - 325*w**2 + 1224*w**3 + 2120*w**2 + 976*w - 81*w = 0.
-179, -1, 0
Factor -42491*r**2 + 10827*r + 21238*r**2 + 21248*r**2 - 26128980 + 12033*r.
-5*(r - 2286)**2
Let v = -197519/3 - -66163. Find q, given that -v*q**2 + 1000/3 + 100*q - 299/3*q**3 - 10*q**4 - 1/3*q**5 = 0.
-10, -1, 1
Let l(w) = 21*w**3 + 658*w**2 - 417*w - 264. Let d(u) = -19*u**3 - 657*u**2 + 418*u + 261. Let g(x) = 2*d(x) + 3*l(x). What is i in g(i) = 0?
-27, -2/5, 1
What is f in 0 + 99/4*f**2 + 3/4*f**4 - 12*f - 27/2*f**3 = 0?
0, 1, 16
Let c(t) = 24*t + 4. Let i be c(0). Determine v so that 80*v**3 - 6 + 0 + 33*v - 168*v**i - 227*v**3 + 12*v**2 - 48*v**5 + 0*v**2 = 0.
-2, -1, 1/4
Suppose 3*u - 2*w = 57, 3*w - 78 + 21 = -3*u. Let o(z) be the third derivative of -5/3*z**4 + 0 - u*z**2 + 5/6*z**3 + 0*z + 4/3*z**5. Factor o(d).
5*(4*d - 1)**2
Let k(x) be the first derivative of -56*x**2 - 1/8*x**4 + 128*x - 161 - 31/6*x**3. Factor k(h).
-(h - 1)*(h + 16)**2/2
Find u such that -8*u**5 + 4*u**5 - 256 - 64*u + 128*u**2 + 32*u**3 + 1560*u**4 - 1576*u**4 = 0.
-4, -2, 2
Let f(s) be the first derivative of -s**6/720 + s**5/240 - 76*s**3/3 + 23. Let m(i) be the third derivative of f(i). Factor m(x).
-x*(x - 1)/2
Let v(u) = -u**3 - 7*u**2 - 3*u + 10. Let r be v(-4). Let a = -22 - r. Factor 8 - w**3 + 5*w**3 + 12*w**2 + 4*w**4 - 27*w + 7*w - 8*w**a.
-4*(w - 1)**3*(w + 2)
Find b, given that 5041/2 + 143/2*b**2 + 1/2*b**3 + 5183/2*b = 0.
-71, -1
Let v(w) be the second derivative of -3*w**5/40 - 15*w**4/8 - 9*w**3 + 105*w**2 - 13*w - 253. Factor v(n).
-3*(n - 2)*(n + 7)*(n + 10)/2
Let k be 720/162 - -12 - (1 - 11/9). Factor k - 20/3*t + 2/3*t**2.
2*(t - 5)**2/3
Suppose 0 = 6*v - 2 - 4. Let l be (v/(-2))/((-6)/96). Let l + 4*h**2 - 1 + 5 - 7*h**2 = 0. What is h?
-2, 2
Let p be ((-24)/9)/(2/(-57)). Suppose -89*z**5 - 95*z**5 - 44*z**3 - p*z**4 - 8*z**2 + 144*z**5 = 0. What is z?
-1, -1/2, -2/5, 0
Let v(m) be the third derivative of 31 + 1/270*m**5 + 7/540*m**6 - m**2 - 1/945*m**7 - 7/108*m**4 + 0*m**3 + 0*m. What is j in v(j) = 0?
-1, 0, 1, 7
Let g be -12 - (-1054)/(-170)*((-22)/4 + 3). Solve -15/4*t + 1/4*t**2 + g = 0.
1, 14
Let w(m) be the first derivative of m**6/360 - m**5/15 - 3*m**4/8 + 3*m**3 - 9*m + 89. Let y(x) be the third derivative of w(x). Factor y(p).
(p - 9)*(p + 1)
Let a(c) be the first derivative of 9*c**4/4 + 662*c**3 + 7179*c**2/2 + 3906*c - 3341. What is d in a(d) = 0?
-217, -3, -2/3
Suppose -4*y + 16 = 0, 2*x - 4*x = -5*y - 172. Let -8*a**2 + 40*a**4 - 48 + 16*a**4 - 51*a + 65*a**5 - 61*a**5 + x*a**3 - 49*a = 0. What is a?
-12, -1, 1
Factor -28373*h + 26*h**3 + 2*h**4 - 4*h**2 + 2*h**2 + 28347*h.
2*h*(h - 1)*(h + 1)*(h + 13)
Let z(x) be the third derivative of 2*x**2 + 0*x + 1/108*x**6 + 0*x**3 + 0