- 17. Let s(v) be the first derivative of f(v). Suppose s(x) = 0. Calculate x.
-1, 0
Find x such that 1/4*x**3 - 5/2*x**2 + 1/4*x**4 + 0 + 2*x = 0.
-4, 0, 1, 2
Let v = 25 - 20. Factor -20*d + 8 + v*d**3 - 7*d**3 - 4*d**4 + 12*d**2 + 6*d**3.
-4*(d - 1)**3*(d + 2)
Let w be (-18)/15 + 0 + 2. Let k(g) = g - 2. Let c be k(2). Determine b, given that -w*b - 2/5*b**4 + b**5 + 16/5*b**2 - 3*b**3 + c = 0.
-2, 0, 2/5, 1
Let s(k) be the first derivative of 3*k**4/8 + 13*k**3/2 + 165*k**2/4 + 225*k/2 + 81. Factor s(f).
3*(f + 3)*(f + 5)**2/2
Let 3/2*t**3 - 1269/2*t**2 + 178929/2*t - 8409663/2 = 0. Calculate t.
141
Let k(q) = -q**2 + 25*q - 61. Suppose -2*i + 3*b - 2*b - 7 = 0, -4*b - 2 = -2*i. Let y(r) = -2*r**2 + 62*r - 152. Let d(w) = i*y(w) + 12*k(w). Factor d(f).
-2*(f - 2)*(f + 7)
Let j(x) be the first derivative of -1/24*x**4 + 0*x + 4 - 5/6*x**2 + 7/18*x**3. Factor j(g).
-g*(g - 5)*(g - 2)/6
Let x(u) be the third derivative of 1/54*u**4 + 0*u**3 + 0 - 21*u**2 + 0*u + 1/270*u**5 - 1/540*u**6. Factor x(g).
-2*g*(g - 2)*(g + 1)/9
Let t be (42/(-35))/(4/(-10)). Let r(l) be the first derivative of l**2 + 16*l**5 - 1 - 16/3*l**t + 25/3*l**6 + 0*l + 3*l**4. Factor r(y).
2*y*(y + 1)**2*(5*y - 1)**2
Let f be (6 - 288/81)*(-22)/(-8). Let w(r) be the second derivative of 4/3*r**2 + f*r**4 + 44/9*r**3 + 2*r + 0. Solve w(q) = 0.
-2/11
Let a(o) be the third derivative of o**8/1344 + o**7/420 + o**6/480 - 260*o**2 + o. Factor a(x).
x**3*(x + 1)**2/4
Let z(v) be the third derivative of v**5/160 + 29*v**4/16 + 841*v**3/4 + 3*v**2 - 4. Find l such that z(l) = 0.
-58
Factor 1/9*p**2 + 2/9 + 1/3*p.
(p + 1)*(p + 2)/9
Let o(y) = y**3 - 3*y**2 + y + 3. Let b = 6 + -3. Let g be o(b). Factor 6*c - 4*c**3 - 2*c**5 + 0*c**2 + g*c**4 - 2 + c**2 - 5*c**2.
-2*(c - 1)**4*(c + 1)
Let m = -38 + 40. Factor 10*t**4 - 15*t - 3*t + m*t**2 + 16*t**2 - 24*t**3 + 14*t.
2*t*(t - 1)**2*(5*t - 2)
Let t(p) be the first derivative of -p**5/110 - p**4/33 + p + 9. Let s(b) be the first derivative of t(b). Factor s(l).
-2*l**2*(l + 2)/11
Let p be (-14 + 11)*-1*(-8)/(-324). Let i(y) be the third derivative of 7/108*y**4 - 1/54*y**5 - 8*y**2 + 0*y - p*y**3 + 0. Suppose i(b) = 0. Calculate b.
2/5, 1
Suppose -z - 1 = 0, -46 = -0*k + k + 4*z. Let r = -42 - k. Factor -2/7*f + 2/7*f**2 + r.
2*f*(f - 1)/7
Let m(j) be the first derivative of -4*j**5/5 + 21*j**4 + 188*j**3/3 - 42*j**2 - 184*j - 818. Find h, given that m(h) = 0.
-2, -1, 1, 23
Let -316*f**2 + 21/2*f**4 - 197/2*f**3 - 24 - 166*f = 0. What is f?
-2, -1/3, -2/7, 12
Let s be (22/(-10) - -2)/(324/(-270)). Let h(x) be the first derivative of 0*x**4 - s*x**3 - 5 + 0*x**2 + 1/4*x + 1/20*x**5. What is p in h(p) = 0?
-1, 1
Suppose 23*i + 17*i + 54 - 214 = 0. Find g, given that -28*g**i + 8/3 - 172/3*g**3 - 28*g**2 + 4*g = 0.
-1, -1/3, 2/7
Let o(i) = -i**2 + 8*i + 5. Let k be o(8). Factor 5*g - 20*g**2 - k*g**3 + 36*g**2 - 16*g**2.
-5*g*(g - 1)*(g + 1)
Suppose -322 = -4*n - v, 3*n - 159 = v + 79. Let c be 16/(-20) + 84/n. Factor -a + 3/4 + c*a**2.
(a - 3)*(a - 1)/4
Let o(c) be the third derivative of -c**6/660 + c**5/15 + 4*c**4/11 - 325*c**2. Factor o(i).
-2*i*(i - 24)*(i + 2)/11
Let g(b) be the first derivative of -2*b**6/3 + 28*b**5/5 + 3*b**4 - 92*b**3/3 + 28*b**2 + 82. Solve g(w) = 0.
-2, 0, 1, 7
Let p(i) = -5*i**2 + 110*i - 15. Let z(b) = -2*b - 3. Let n(m) = p(m) - 5*z(m). Factor n(l).
-5*l*(l - 24)
Factor 10 + 8*z**2 + 0 - 10 + 7*z + 3*z**3 + 2.
(z + 1)**2*(3*z + 2)
Suppose 5*x + x + 90 = 0. Let k(d) = -d**4 - 10*d**3 + 15*d**2 + 4. Let q(j) = 5*j**4 + 40*j**3 - 60*j**2 - 15. Let o(z) = x*k(z) - 4*q(z). Factor o(u).
-5*u**2*(u - 1)*(u + 3)
Let n(h) = -22*h**3 + 64*h**2 + 106*h - 5. Let z(l) = 31*l**3 - 95*l**2 - 160*l + 7. Let f(s) = 7*n(s) + 5*z(s). Determine d so that f(d) = 0.
-2, 0, 29
Let n(o) be the first derivative of -o**3/18 - 13*o**2/2 - 507*o/2 + 48. Factor n(v).
-(v + 39)**2/6
Let v = 13 - 17. Let h be v/6 + (-10)/(-15). Solve d**2 - 4*d**2 - 3*d**3 + 0*d**2 + h*d**2 + 3 + 3*d = 0 for d.
-1, 1
Let f be (-8)/(-20)*(-92)/(-8). Let o = -243/55 + f. Factor o*u**2 + 0 + 0*u + 2/11*u**4 + 4/11*u**3.
2*u**2*(u + 1)**2/11
Let o = 19 - 15. Suppose o*m - 32 = -4*u, 5*u - 25 = 2*m + 8. Suppose u + 3*v - 40*v**2 - 11 - 29*v = 0. Calculate v.
-2/5, -1/4
Let s(l) = l**2 - 73*l + 1150. Let w be s(23). Suppose 0*x**2 + 1/2*x - 1/8*x**3 + w = 0. Calculate x.
-2, 0, 2
Suppose 0 = 2*u - 7*u + 10. Suppose k - 3 = -1. What is r in -10*r**k - 3*r**3 - 2*r**3 + 10*r**u = 0?
0
Let g(q) be the third derivative of q**6/40 - 3*q**5/20 - 2*q**4 - 6*q**3 - 24*q**2. Factor g(a).
3*(a - 6)*(a + 1)*(a + 2)
Suppose -3*j + 17 = 2*p, p = -2*j + 3 + 4. Factor 25*w**4 + 35*w - 5*w**5 - p*w**3 + 7*w**3 - 24*w**3 - 15 - 10*w**2.
-5*(w - 3)*(w - 1)**3*(w + 1)
Factor 51*b**5 - 14*b**5 - 9*b**4 - 19*b**2 - 18*b**5 - 6*b - 20*b**5 - 21*b**3.
-b*(b + 1)**3*(b + 6)
Let i(v) be the first derivative of 0*v**2 + 39/5*v**5 + 6*v**6 + 7 + 4*v**3 + 0*v - 15*v**4. Suppose i(g) = 0. Calculate g.
-2, 0, 1/4, 2/3
Let f be -4*2/(-44)*1. Let n = -909/22 - -83/2. Factor -f*y + 4/11 - n*y**2.
-2*(y - 1)*(y + 2)/11
Let x(n) be the third derivative of n**5/390 - 50*n**4/39 + 10000*n**3/39 + 40*n**2 - 6*n. Let x(q) = 0. What is q?
100
Suppose -4*d + 32 = 3*t, 65 = 5*t - d - 4*d. Let l = 3 + t. Factor 2*k + l*k**2 + k**4 + k**3 - 4*k**3 - 3*k - 12*k**2.
k*(k - 1)**3
Let p(y) = -5*y**3 - 23*y**2 - 85*y - 58. Let q(f) = -6*f**3 - 22*f**2 - 84*f - 56. Let c(j) = 4*p(j) - 3*q(j). Solve c(h) = 0.
-8, -4, -1
Determine p, given that 37/2*p**2 + 0 - 1/2*p**4 + 13*p + 5*p**3 = 0.
-2, -1, 0, 13
Let u(h) = -155*h**3 + 110*h**2 + 100*h. Let p(f) = 17*f**3 - 12*f**2 - 11*f. Let r(x) = -55*p(x) - 6*u(x). Factor r(y).
-5*y*(y - 1)*(y + 1)
Let t be -4 - ((-4)/(12/(-9)) + -7). Let a = 2/9 - t. Suppose -a - 2/9*z**2 - 16/3*z**3 - 32/9*z**4 + 4/3*z = 0. Calculate z.
-1, 1/4
Suppose l = 13 - 11. Suppose 3*d - 4 - l = 0. Factor -5/4*m**d + 3/4*m + 9/4 + 1/4*m**3.
(m - 3)**2*(m + 1)/4
Let c(i) = -5*i**3 + 15*i**2 + 8*i + 15. Let r(p) = -p**3 + p**2 + 2*p + 1. Let k(a) = -2*c(a) + 22*r(a). Factor k(j).
-4*(j - 1)*(j + 2)*(3*j - 1)
Let f(t) be the third derivative of 0*t + 10/3*t**4 + 0 + 0*t**3 - 2/3*t**5 + 1/24*t**6 - 50*t**2. Let f(q) = 0. What is q?
0, 4
Let l be 6/(-20)*2*(-56)/42. Let n(m) be the first derivative of 0*m + 13 - 4*m**3 + 3*m**4 + 2*m**2 - l*m**5. Factor n(t).
-4*t*(t - 1)**3
Suppose 2*l + 24 = 6*l. Determine n so that 13*n**3 - l*n - 8*n**3 + 11*n + 10*n**3 + 20*n**2 = 0.
-1, -1/3, 0
Suppose -1 = -b - 9. Let h = -7 - b. What is n in -3 + 2*n**2 - h + 0*n**2 - 2*n = 0?
-1, 2
Let m(b) = b**4 - 6*b**3 - 9*b**2 + 2*b - 6. Let x(f) = f**4 - 5*f**3 - 8*f**2 + 2*f - 5. Let k(o) = 5*m(o) - 6*x(o). Let k(y) = 0. Calculate y.
-2, 0, 1
Factor -6 - 4*y**4 - 3*y**3 - 5*y**4 - y**4 - 3*y**2 + 11*y**4 + 11*y.
(y - 3)*(y - 1)**2*(y + 2)
Let n(d) be the second derivative of 19*d - 2 - 6/5*d**4 + 11/5*d**3 - 8/5*d**2 + 2/25*d**5. Let n(y) = 0. What is y?
1/2, 8
Let a(b) be the third derivative of -1/54*b**4 + 1/90*b**5 + 0 + 30*b**2 + 0*b**3 + 0*b. Find s, given that a(s) = 0.
0, 2/3
Let z(t) be the second derivative of -t**6/6 - 15*t**5/4 - 145*t**4/12 + 345*t**3/2 - 405*t**2 + 21*t - 2. Determine o so that z(o) = 0.
-9, 1, 2
Let 16/7*g**2 + 2/7*g - 2/7*g**3 - 16/7 = 0. What is g?
-1, 1, 8
Let r(i) be the third derivative of i**7/840 - 7*i**6/480 + 13*i**5/240 + i**4/32 - 3*i**3/4 + 26*i**2. Find w, given that r(w) = 0.
-1, 2, 3
Let j be 0 + (3 - 1351*(-1)/(-451)). Let h = 1361/1804 - j. Solve 1/2*o + 1/4*o**3 + 0 - h*o**2 = 0 for o.
0, 1, 2
Let a(y) be the third derivative of y**8/1176 - 4*y**7/147 + 19*y**6/60 - 169*y**5/105 + 88*y**4/21 - 128*y**3/21 + 56*y**2. Find w, given that a(w) = 0.
1, 2, 8
Let g(w) be the third derivative of -w**6/420 - 4*w**5/105 + 19*w**4/84 - 10*w**3/21 + 4*w**2 - 42. Solve g(r) = 0.
-10, 1
Suppose 5*t = y - 0*y - 63, 4*y = t + 176. Suppose -y*n**3 + 8 - 28*n + 35*n**3 + 42*n**2 - 14*n**2 = 0. Calculate n.
1/2, 1, 2
Let m(y) be the third derivative of y**7/1050 - y**6/150 + y**5/50 - y**4/30 - 5*y**3/2 - 25*y**2. Let j(i) be the first derivative of m(i). Factor j(s).
4*(s - 1)**3/5
Let s(j) be the third derivative of 0*j - 1/120*j**5 + 28*j**2 + 0 - 11/192*j**4 - 1/8*j**3 + 1/9