/1. Let h be -4 - (-6 + 7) - -9 - x. Factor -3/5*i**h - 1/5 + 1/5*i**3 + 3/5*i.
(i - 1)**3/5
Solve -990/19*a - 216/19 - 516/19*a**2 + 8/19*a**4 - 46/19*a**3 = 0 for a.
-3, -1/4, 12
Let q(g) = 57 - 202 + 73 - 9*g**2 + 51 - 171*g. Let c(o) = -o**2 - 17*o - 2. Let x(r) = -21*c(r) + 2*q(r). Factor x(j).
3*j*(j + 5)
Let s(u) = -u**2 - 408*u - 6272. Let a be s(-16). Factor 1/3*t**4 + a - 2/3*t + 3/2*t**3 + 1/2*t**2.
t*(t + 1)*(t + 4)*(2*t - 1)/6
Suppose -1876 = -4*d + 4*w - 1848, 5*d = 4*w + 32. Let r(y) be the third derivative of 16/63*y**3 - 12*y**2 + 0*y + 1/630*y**5 + 0 - 2/63*y**d. Factor r(s).
2*(s - 4)**2/21
Determine l so that -2992/7 - 1492/7*l + 2/7*l**2 = 0.
-2, 748
Let j = -46 + 118. Let z be j/24*(-10)/(-6). Solve -4/11*i + 2/11*i**4 + 6/11*i**3 - 2/11*i**2 - 2/11*i**z + 0 = 0.
-1, 0, 1, 2
Let p be 21 - 6/1 - (-931)/(-63). Let 4/3*k + 16/9*k**2 - 4/3*k**3 - 2 + p*k**4 = 0. What is k?
-1, 1, 3
Let i = -217931/2 + 108976. Find h, given that -45/4*h - 3/4*h**2 - i = 0.
-14, -1
Let d be -6 - 20*3/(-6). Determine f, given that -12*f**3 + 15*f**2 - 4*f**4 + 5*f**d - 3*f**4 - f**4 = 0.
-5, 0, 1
Let w(d) be the third derivative of 5*d**8/504 - 214*d**7/945 + 247*d**6/540 + 2*d**5/135 - 13*d**4/27 - 1806*d**2. Determine u, given that w(u) = 0.
-2/5, 0, 2/3, 1, 13
Let h(y) be the second derivative of 1/12*y**6 + 101*y + 0*y**4 + 0 + 0*y**3 + 0*y**2 + 3/16*y**5 - 5/168*y**7. Factor h(q).
-5*q**3*(q - 3)*(q + 1)/4
Find s, given that -1121/5*s + 224 + 1/5*s**2 = 0.
1, 1120
Let m(x) be the first derivative of 0*x - 42 + 0*x**2 + 1/14*x**4 - 2/35*x**5 + 2/21*x**3 - 1/21*x**6. Let m(k) = 0. Calculate k.
-1, 0, 1
Let z(j) be the second derivative of -148*j - 14*j**2 - 5*j**3 + 0 - 1/6*j**4. What is l in z(l) = 0?
-14, -1
Let q = 1601 + -1597. Let k(p) be the second derivative of -1/15*p**5 + 1/3*p**q - 4/9*p**3 + 0*p**2 - 6*p + 0. Find o such that k(o) = 0.
0, 1, 2
Let s = -2575 + 48930/19. Let v(n) be the first derivative of s*n**2 - 4/57*n**3 - 9 + 6/19*n. Factor v(c).
-2*(c - 3)*(2*c + 1)/19
Let y(k) = 23*k**2 - 389*k + 19211. Let x(r) = 260*r**2 - 4278*r + 211322. Let z(m) = -6*x(m) + 68*y(m). Let z(f) = 0. What is f?
98
Let x = -146 + 163. Factor -28*c**2 + 0*c**3 - 21*c**2 + x*c**2 - 28*c - 4*c**3.
-4*c*(c + 1)*(c + 7)
Factor 544*m**2 - 24*m**3 + 281*m**2 + 14625*m - 65*m**3 - 5*m**4 + 4*m**3.
-5*m*(m - 13)*(m + 15)**2
Let j be (-12)/(-21) - (77/294 - (-48)/(-56)). Determine w, given that 3 - j*w - 1/6*w**2 = 0.
-9, 2
Let a(m) be the second derivative of -m**9/3780 + m**8/1680 + m**7/315 - 85*m**4/6 + 99*m. Let s(p) be the third derivative of a(p). Solve s(n) = 0.
-1, 0, 2
Let z = -36 - -39. Let l(f) = 36*f**5 - 44*f**3 - 40*f**2 + 16*f + 16. Let x(s) = -7*s**5 + 9*s**3 + 8*s**2 - 3*s - 3. Let q(o) = z*l(o) + 16*x(o). Factor q(m).
-4*m**2*(m - 2)*(m + 1)**2
Let x(r) be the second derivative of -r**6/900 + r**5/300 + r**4/30 + 53*r**3/6 - 8*r. Let q(b) be the second derivative of x(b). Factor q(w).
-2*(w - 2)*(w + 1)/5
Determine c so that -338*c + 1/4*c**2 - 1353/4 = 0.
-1, 1353
Let j = 8407/11775 - 110/157. Let p(x) be the third derivative of -1/300*x**6 + j*x**5 + 15*x**2 + 0*x + 4/15*x**3 + 7/60*x**4 + 0. Factor p(c).
-2*(c - 4)*(c + 1)**2/5
Let n(q) be the second derivative of 5/12*q**4 + q**3 + 0 - 56*q + 0*q**2 - 1/20*q**5. Factor n(w).
-w*(w - 6)*(w + 1)
Let c(w) = w**2 + 2866*w - 345908. Let y be c(116). Factor -32*g - 285/4*g**2 - 225/8*g**3 - y.
-(g + 2)*(15*g + 4)**2/8
Let t(n) be the first derivative of -n**6/1080 - n**5/30 + n**4/216 + n**3/3 - 105*n**2/2 + 31. Let l(j) be the second derivative of t(j). Factor l(w).
-(w - 1)*(w + 1)*(w + 18)/9
Let j(a) be the third derivative of a**8/84 - 6*a**7/35 + a**6 - 46*a**5/15 + 11*a**4/2 - 6*a**3 + 3*a**2 + 82. Solve j(d) = 0 for d.
1, 3
Let z = -337189/5 + 67438. Find c, given that 0*c + 0 + 3/5*c**2 + z*c**3 = 0.
-3, 0
Let j(s) = 6*s**2 - 329*s - 348. Let b(c) = -c**2 + 55*c + 58. Let w(m) = 13*b(m) + 2*j(m). Find n, given that w(n) = 0.
-1, 58
Let y = -285 - -324. Determine r, given that -5*r + 2*r - 2*r + 6*r**2 - r**3 + 27 - y = 0.
-1, 3, 4
Suppose 0 = -j + 2*p - 2, -3*j + 3*p - 2 = -p. Factor -544 + 121*u + 640 + 4*u**j - 21*u.
4*(u + 1)*(u + 24)
Let d(n) = -22*n**3 - 13*n**3 + n**2 + 19*n**2 + 135*n. Let k(c) = -9*c**3 + 5*c**2 + 34*c. Suppose -8 = 4*u - 2*u. Let s(w) = u*d(w) + 15*k(w). Solve s(m) = 0.
-2, 0, 3
Determine n so that 4/3*n**4 - 4/3*n + 16/3 - 1/3*n**5 - 20/3*n**2 + 5/3*n**3 = 0.
-2, -1, 1, 2, 4
Let n(z) = 135*z + 255. Let k(b) = -b**2 - 2*b - 5. Let t(h) = -3*k(h) + n(h). Factor t(w).
3*(w + 2)*(w + 45)
Let s be 30/21 + (11 - 0) + 10512/(-1008). Suppose 0 + p - 4/3*p**5 - 13/3*p**4 + 1/3*p**3 + 13/3*p**s = 0. What is p?
-3, -1, -1/4, 0, 1
What is r in -528/5*r + 82/5*r**2 + 0 - 2/5*r**3 = 0?
0, 8, 33
Let c(h) be the first derivative of h**4/3 + 16*h**3/9 - 14*h**2/3 - 40*h/3 + 640. Find r such that c(r) = 0.
-5, -1, 2
Suppose -180*p**4 - 179/4*p**2 - 553/4*p**3 - 23/4*p - 81*p**5 - 1/4 = 0. What is p?
-1, -1/2, -1/9
Let p(t) = 6*t - 16. Let q be p(-7). Let b = q + 60. Let 0 - 4*s - 3 + 1 - 2*s**b = 0. What is s?
-1
Let p(f) be the second derivative of 243*f**4/8 - 83*f**3/4 + f**2/2 + 27*f - 6. Factor p(x).
(3*x - 1)*(243*x - 2)/2
Let p be ((-372)/9)/4 - -11. Let i(l) be the first derivative of -1/15*l**5 + 12 - 1/9*l**3 + 1/4*l**4 + p*l - 1/2*l**2. Determine h so that i(h) = 0.
-1, 1, 2
Let i(l) be the second derivative of -5*l**7/7 + 205*l**6/6 - 881*l**5/2 + 35*l**4 + 4420*l**3/3 - 1445*l**2/2 + 4525*l. Determine a so that i(a) = 0.
-1, 1/6, 1, 17
Let f be (-11)/((-308)/8)*14. Factor 16384 - 19456*x + f*x**4 + 57*x**3 - 191*x**3 + 3264*x**2 - 62*x**3.
4*(x - 16)**3*(x - 1)
Let u(l) be the second derivative of l**5/210 + l**4/6 + 139*l**2 - 84*l. Let g(y) be the first derivative of u(y). Factor g(a).
2*a*(a + 14)/7
Let b(m) be the first derivative of -2/9*m**3 - 8/3*m**2 + 47 - 14/3*m. Let b(l) = 0. What is l?
-7, -1
Let w be 397 + (-6 - 6)/4 - -5. Let x = 401 - w. What is d in -6*d + 0 - 24*d**x + 27/2*d**3 = 0?
-2/9, 0, 2
Let r(n) be the second derivative of 13 - 55/6*n**3 + 3*n - 4*n**2 + 7/12*n**4. Factor r(q).
(q - 8)*(7*q + 1)
Let x = 5173/4005 - 111/89. Let w(d) be the first derivative of -3 + 0*d**2 + x*d**3 - 2/15*d. Find y, given that w(y) = 0.
-1, 1
Find m such that -177/7*m - 36/7*m**2 - 90/7 + 15/7*m**3 = 0.
-2, -3/5, 5
Let n(h) be the third derivative of h**8/560 + h**7/25 + 23*h**6/200 - 127*h**5/50 - 36*h**4/5 + 576*h**3/5 + h**2 + 344*h. What is b in n(b) = 0?
-8, -3, 2, 3
Let i = 5 - -20. Factor i*n**4 - 4*n**4 - 225*n**2 - 6*n**3 + 0*n**2 - 9*n**3 + 3*n**5.
3*n**2*(n - 3)*(n + 5)**2
Let i(p) be the first derivative of -2*p**3/33 - 36*p**2/11 - 136*p/11 - 618. Determine m so that i(m) = 0.
-34, -2
Let c(j) = -69*j**2 - 4713*j - 9696. Let l(m) = -7*m**2 - 471*m - 970. Let s(i) = 4*c(i) - 39*l(i). Factor s(a).
-3*(a + 2)*(a + 159)
Let o(a) = -20*a**3 - 27*a**2 + 135*a + 675. Let b(g) = -17*g**3 - 27*g**2 + 135*g + 675. Let f(x) = -7*b(x) + 6*o(x). Suppose f(j) = 0. What is j?
-3, 15
Suppose -3*i - 2*j = 28, 2*i - 6*j - 14 = -5*j. What is d in 8/3*d**3 + 2*d**2 + i*d + 2/3*d**4 + 0 = 0?
-3, -1, 0
What is n in 4*n**2 - 36*n + 113*n - 53*n - 96 - 44*n = 0?
-3, 8
Let i = 2/6987 + 20953/27948. Factor -3/4*f**5 + 0 + 3/4*f**4 + 3/4*f**3 - i*f**2 + 0*f.
-3*f**2*(f - 1)**2*(f + 1)/4
Let x be -278*((-43)/(-70) - 33/55). Let o = -25/7 - x. Factor -o*j**3 - 2/5*j**2 + 0 + 0*j.
-2*j**2*(j + 1)/5
Suppose -59*g + 190 = -18 + 31. Suppose -2*x**g + 8*x - 1/2*x**2 + 1/2*x**4 - 6 = 0. What is x?
-2, 1, 2, 3
Let o(p) be the second derivative of -361*p**5/5 - 988*p**4 - 4056*p**3 - 359*p. Let o(b) = 0. What is b?
-78/19, 0
Let d be -8 + 9 - (8 - 9). Let m(f) be the third derivative of 1/10*f**4 + 0 + 1/600*f**6 + 0*f + 4/15*f**3 - 7*f**d + 1/50*f**5. Let m(j) = 0. Calculate j.
-2
Let u(y) be the third derivative of 0*y + 5/84*y**4 - 1/210*y**5 + 2/7*y**3 - 15*y**2 + 6. Factor u(x).
-2*(x - 6)*(x + 1)/7
Let t(l) be the second derivative of 2*l**2 + 0 - 2/21*l**7 - 2/5*l**6 - 2/5*l**5 + 2*l**3 - 202*l + 2/3*l**4. Solve t(x) = 0.
-1, 1
Let k(x) be the third derivative of -x**5/180 + 17*x**4/72 - 8*x**3/9 + 3*x**2 + 233. Factor k(b).
-(b - 16)*(b - 1)/3
Let a be (-6200)/(-