20)
Let m(r) = 30*r - 1260. Let z be m(42). Let k(p) be the third derivative of 16/45*p**3 + z*p + 2/45*p**4 + 13*p**2 + 1/450*p**5 + 0. Factor k(y).
2*(y + 4)**2/15
What is v in -58*v + 15*v**2 - 143 - 170 - 2 + 3*v**3 - 84*v + 55*v = 0?
-7, -3, 5
Let t be ((-5)/3)/(((-315)/6)/(-39 - -48)). Factor 162/7 + t*k**2 - 36/7*k.
2*(k - 9)**2/7
Let b(q) = 6*q**4 - 10*q**3 - 112*q**2 + 670*q + 4366. Let i(d) = d**4 - d**2 + 2*d + 2. Let g(a) = -b(a) + 5*i(a). Factor g(j).
-(j - 11)**2*(j + 6)**2
Let b(v) be the third derivative of 0*v + 0 + 4*v**3 + 3*v**2 + 1/40*v**5 + 1/120*v**6 - 1/4*v**4. Let r(w) be the first derivative of b(w). Factor r(y).
3*(y - 1)*(y + 2)
Factor 137/2 + 23205/8*t**2 + 169/8*t**3 + 891*t.
(t + 137)*(13*t + 2)**2/8
Suppose 3*v - 2*v = -5*s - 23, 3*v + s = 1. Let 25 - 6*j - 34 - 3*j**4 + 0*j**4 + 8*j**2 + 4*j**v + 6*j**3 = 0. What is j?
-1, 1, 3
Let f(s) be the first derivative of -96*s - 33/4*s**4 - 42*s**3 - 96*s**2 - 3/5*s**5 + 126. What is v in f(v) = 0?
-4, -2, -1
Let t = -2888 + 46229/16. Let i(j) be the first derivative of -j - 5 - 2*j**2 - 1/12*j**3 + t*j**4. Factor i(g).
(g - 1)*(3*g + 2)*(7*g + 2)/4
Factor 27*n**5 - 22*n**4 - 55*n**5 + 7*n - 16*n**3 + 120 + 302*n**2 + 76*n**3 + 27*n**5 + 334*n.
-(n - 5)*(n + 1)**3*(n + 24)
Let n(c) be the first derivative of c**7/2520 - 13*c**6/1080 - 18*c**3 - 20. Let q(v) be the third derivative of n(v). Factor q(y).
y**2*(y - 13)/3
Let k be 0/(-2 + (-63)/(-9)). Let g(f) be the second derivative of 1/16*f**4 + k*f**2 + 1/40*f**6 + 0*f**3 + 0 - 3/40*f**5 + 4*f. Factor g(l).
3*l**2*(l - 1)**2/4
Let o(d) = 6*d**3 + 17*d**2 + 4*d - 2. Suppose 52 = -7*r + 122. Let y(h) = 2*h**3 + 8*h**2 + 2*h - 2. Let i(m) = r*y(m) - 4*o(m). What is s in i(s) = 0?
-1, 1, 3
Let n(b) be the first derivative of b**4 + 20*b**3 - 108*b**2 + 615. Find f, given that n(f) = 0.
-18, 0, 3
Let i(j) = -2*j**2 - 104*j - 165. Let p be i(-51). Let l be 69/p + 1 - (-3640)/7350. Determine d so that -l*d + 0 - 2/5*d**3 + 4/5*d**2 = 0.
0, 1
Let 432/5*a**2 - 144 + 27/5*a**5 + 3264/5*a - 147*a**4 - 2268/5*a**3 = 0. What is a?
-2, 2/9, 1, 30
Let y(m) be the second derivative of -3*m**5/20 + 203*m**4/4 - 10403*m**3/2 + 30603*m**2/2 + 2*m - 154. Factor y(l).
-3*(l - 101)**2*(l - 1)
Suppose 0 + 65/6*g**4 - 2/3*g**5 - 171/2*g**2 - 81/2*g - 67/2*g**3 = 0. Calculate g.
-1, -3/4, 0, 9
Suppose k + 4*l = 19, 19*l + 187 = 5*k + 16*l. Let w(z) be the first derivative of 0*z - 1/6*z**3 - k - 1/16*z**4 + 3/8*z**2. Let w(o) = 0. Calculate o.
-3, 0, 1
Let s be (2400/(-1125))/((-20)/25). Factor 10/9 + s*h**2 - 2/9*h**4 - 4/9*h**3 - 28/9*h.
-2*(h - 1)**3*(h + 5)/9
Let w = -502 - -507. Let 24*d**4 - 3*d - 35*d**3 + 8*d**4 + 36*d**w - 11*d**4 + 2*d**3 - 21*d**2 = 0. What is d?
-1, -1/3, -1/4, 0, 1
Suppose -p - 251 = -5*p + 5*z, 0 = 3*p + 3*z - 222. Let h = p - 33. Factor -h*i + 3*i**3 + 2*i**3 - i**3 - 12*i**2 + 7 - 27.
4*(i - 5)*(i + 1)**2
Let f be (26/(-13))/(((-2)/3)/(8/6)). Factor f*n + 0 - 2/5*n**3 + 6/5*n**2.
-2*n*(n - 5)*(n + 2)/5
Factor -142*h + 24 - 117*h**2 - 43 - h**4 - 36*h - 61 - 20*h**3.
-(h + 1)**2*(h + 8)*(h + 10)
Factor -141*k - 8*k**3 + 9*k**3 + 60*k**2 - 2*k**3 + 2254 - 552*k + 0*k**3.
-(k - 46)*(k - 7)**2
Suppose 0 = -610*y + 1521*y. Factor y*v - 6/7*v**2 + 0 - 12/7*v**3 - 6/7*v**4.
-6*v**2*(v + 1)**2/7
Let h(l) = -45*l**2 - l + 1. Let k(x) = 2*x**3 - 827*x**2 + 39*x + 137. Let c(o) = -34*h(o) + 2*k(o). Factor c(i).
4*(i - 30)*(i - 2)*(i + 1)
Let -130*r + r**2 + 39 + 274*r + 245 = 0. What is r?
-142, -2
Let j(c) be the third derivative of -c**6/300 + 17*c**5/150 - 19*c**4/15 + 4*c**3 - c**2 + 52. Suppose j(l) = 0. Calculate l.
1, 6, 10
Let q be 290/2465 + (-92)/(-85). Suppose q*s**2 + 0 - 2*s**3 + 18/5*s + 2/5*s**4 = 0. What is s?
-1, 0, 3
Let z be (-2 + (-645)/(-300))/((-6)/(-630)*106 - 1). Solve 0 + 3/8*q**2 - z*q = 0.
0, 42
Let b(n) be the second derivative of -n**7/504 + 11*n**6/144 - 31*n**4/12 - 29*n. Let l(w) be the third derivative of b(w). What is g in l(g) = 0?
0, 11
Let v = -1018225 - -5091128/5. Let -6/5*t - v*t**3 - 24/5 + 3*t**2 = 0. Calculate t.
-1, 2, 4
Let c(d) be the second derivative of 2*d**7/21 - 4*d**6/15 - 9*d**5/5 + 6*d**4 + 166*d + 2. Solve c(u) = 0.
-3, 0, 2, 3
Determine p, given that -196*p - 194*p - 510 + 479*p - 180*p + p**2 - 2*p**2 = 0.
-85, -6
Suppose j + 373 = 382. Suppose 0 = -4*b - 9 - 11, 3*k + j = -3*b. Suppose -44/5*n - 52/5*n**k + 8/5 = 0. Calculate n.
-1, 2/13
Suppose 0 = 2*n - 4*u - 11 + 1, 0 = -5*n + 2*u + 17. Factor 99*y**n - y**2 - 200*y**3 + 4 + 95*y**3 + 24*y.
-(y - 2)*(y + 2)*(6*y + 1)
Suppose -27*m**3 + 780559070 - 14*m**3 + 19992*m**2 + 10590482*m - 2263814*m + 375460004 + 57*m**3 = 0. What is m?
-833/2
Suppose 0*g - 20 = -2*g + 2*n, 5*g + 4*n - 14 = 0. Let f(u) = -3*u**2 + 60*u + 6. Let d(b) = 2*b**2 - 60*b - 5. Let m(k) = g*d(k) + 5*f(k). Factor m(w).
-3*w*(w + 20)
Let n be 8/(-10) - 41608/(-1760). Let p = n + -232/11. Determine o so that p*o**3 + 0*o - 1/2*o**2 + 0 = 0.
0, 2/7
Factor 126*k**2 - 124*k**2 - 19*k - 196*k - 165*k + 78*k.
2*k*(k - 151)
Let w be (5700/(-84) - -1)*(-70)/4. Let x = -7019/6 + w. Factor x*o**4 - 1/6*o**2 + 1/6*o**3 - 1/6*o + 0.
o*(o - 1)*(o + 1)**2/6
Let m(y) = -7*y**2 - 649*y - 1284. Let i(q) = 37*q**2 + 3244*q + 6417. Let c(p) = -2*i(p) - 11*m(p). Solve c(k) = 0.
-215, -2
Let r be 1/1 + 4 + -2. Suppose 41792*j = 42013*j - 884. Find b, given that 3/8*b**2 - 3/8*b**j + 1/2*b + 0 - 5/8*b**r + 1/8*b**5 = 0.
-1, 0, 1, 4
Let r(f) be the third derivative of 10*f**4 + 0*f + 159*f**2 + 75/2*f**3 + 61/240*f**5 + 0 + 1/480*f**6. Determine x, given that r(x) = 0.
-30, -1
Let i(p) be the first derivative of p**3/12 - 278*p**2 + 309136*p - 3094. Find o, given that i(o) = 0.
1112
Suppose 3*c + 5*q + 22 = 11, 2*c + 6*q + 18 = 0. Determine n so that 1/3*n**4 - n**2 + n**c + 2 - 7/3*n = 0.
-3, -2, 1
Let r be (-510)/(-135) - (-976)/(-549). Suppose r + 1/2*b**4 - 3/2*b - 5/2*b**2 + 3/2*b**3 = 0. What is b?
-4, -1, 1
Let m be (-171)/54 + 4 - 3/(-18)*15. Suppose -m*h**3 + 20 + 40/3*h - 5*h**2 = 0. What is h?
-2, -3/2, 2
Let 28*t**2 - 82/3 - 2/3*t**4 - 80/3*t + 80/3*t**3 = 0. Calculate t.
-1, 1, 41
Let a(o) be the first derivative of o**5/330 + 17*o**4/66 - 35*o**3/33 - 3*o**2/2 + 23*o - 194. Let t(s) be the second derivative of a(s). Factor t(p).
2*(p - 1)*(p + 35)/11
Let q(v) be the first derivative of 3*v**5/20 + 3*v**4/8 - 5*v**3 + 9*v**2 + 1068. Find d, given that q(d) = 0.
-6, 0, 2
Let q(b) be the third derivative of -1/210*b**5 + 1/735*b**7 - 6*b + 1/1176*b**8 - b**2 + 0*b**4 + 0 + 0*b**3 - 1/420*b**6. What is h in q(h) = 0?
-1, 0, 1
Let w be 18/(-48) - 203/(-8). Suppose 5*r = 5*z + w + 5, z + 4 = 0. Determine b, given that 7 - 12*b + 12*b + r*b**2 - 9 = 0.
-1, 1
Let x(a) be the first derivative of -4*a**5/25 - 33*a**4/5 - 384*a**3/5 - 1512*a**2/5 - 612. Factor x(o).
-4*o*(o + 6)**2*(o + 21)/5
Let k(b) be the second derivative of b**5/5 - b**4/3 - 88*b**3/3 - 192*b**2 + 2017*b. Factor k(j).
4*(j - 8)*(j + 3)*(j + 4)
Let o be -2*18/(-15)*(-15)/8. Let m = 49/10 + o. Factor -18/5*u + 0 - m*u**3 + 12/5*u**2.
-2*u*(u - 3)**2/5
Let u = 123 - 110. Suppose 3*w + 3 = -o, 4*o - 1 = -5*w - u. Factor 4/3*h**2 + 1/3*h**4 + w + 0*h + 4/3*h**3.
h**2*(h + 2)**2/3
Let b(i) be the first derivative of 2*i**5/5 - 12*i**4 + 30*i**3 - 22*i**2 - 1432. Solve b(m) = 0.
0, 1, 22
Let f = -61 - -68. Factor 11*c**3 - 4*c - f*c**3 + 8*c - 8*c**2 + 0*c.
4*c*(c - 1)**2
Let f(l) = l**3 - l**2. Let n(i) = 3*i**3 + 114*i**2 - 3100*i - 23064. Let w(j) = -4*f(j) + n(j). Suppose w(s) = 0. Calculate s.
-6, 62
Let p(a) = 50*a**3 + 13*a**3 - 75 - 65*a**2 - 180*a + 15*a**4 - 8*a**3. Let c(j) = j**2 - 1. Let y(i) = 5*c(i) + p(i). Solve y(n) = 0 for n.
-4, -1, -2/3, 2
Let l(h) be the second derivative of h**5/10 - 23*h**4/6 - 26*h**3 - 981*h. Factor l(b).
2*b*(b - 26)*(b + 3)
Let m(i) be the first derivative of -2*i**5/35 - 5*i**4/14 + 4*i**3/21 + 24*i**2/7 - 613. Determine z so that m(z) = 0.
-4, -3, 0, 2
Find h such that -1192*h**2 - 35000 - 20375*h - 2633*h**2 - 12*h**4 - 5*h**4 - 205*h**3 + 22*h**4 = 0.
-5, 56
Factor -200/7 - 304/7*l - 106/7*l**2 - 2/7*l**3.
-2*(l + 1)*(l + 2)*(l + 50)/7
Let i(c) = -c - 1. Let q(u) = -u**3 - 7*u**2 - 15*u - 9. Let d be -1 - (4/22 + 855/(-165)). Let n(v) = d*i(v) - q